US 9,015,092 B2Grant

Dynamically reconfigurable stochastic learning apparatus and methods

Issue Date:2015-04-21

•24 Claims

•24 Drawing Sheets

Abstract

Generalized learning rules may be implemented. A framework may be used to enable adaptive signal processing system to flexibly combine different learning rules (supervised, unsupervised, reinforcement learning) with different methods (online or batch learning). The generalized learning framework may employ average performance function as the learning measure thereby enabling modular architecture where learning tasks are separated from control tasks, so that changes in one of the modules do not necessitate changes within the other. Separation of learning tasks from the control tasks implementations may allow dynamic reconfiguration of the learning block in response to a task change or learning method change in real time. The generalized learning apparatus may be capable of implementing several learning rules concurrently based on the desired control application and without requiring users to explicitly identify the required learning rule composition for that application.

Metadata

Assignee

Brain Corporation

Inventors

Oleg Sinyavskiy
Vadim Polonichko

Application Information

Application Number:US 13/487,576

Filing Date:2012-06-04

Priority Date:2012-06-04

Art Unit:2129

Classifications

IPC:

G06N3/08G06N99/00

Patent Drawings (24 sheets)

Description

Cross-Reference to Related Applications

[0001] This application is related to a co-pending and co-owned U.S. patent application Ser. No. 13/385,938 entitled “TAG-BASED APPARATUS AND METHODS FOR NEURAL NETWORKS”, filed Mar. 15, 2012, co-owned U.S. patent application Ser. No. 13/487,533 entitled “STOCHASTIC SPIKING NETWORK LEARNING APPARATUS AND METHODS”, filed contemporaneously herewith, co-owned U.S. patent application Ser. No. 13/487,499 entitled “STOCHASTIC APPARATUS AND METHODS FOR IMPLEMENTING GENERALIZED LEARNING RULES”, filed contemporaneously herewith, co-owned U.S. patent application Ser. No. 13/487,621 entitled “IMPROVED LEARNING STOCHASTIC APPARATUS AND METHODS”, filed contemporaneously herewith, each of the foregoing incorporated herein by reference in its entirety.

Copyright

[0002] A portion of the disclosure of this patent document contains material that is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all copyright rights whatsoever.

Background

[0003] 1. Field of the Disclosure

[0004] The present disclosure relates to implementing generalized learning rules in stochastic systems.

[0005] 2. Description of Related Art

[0006] Adaptive signal processing systems are well known in the arts of computerized control and information processing. One typical configuration of an adaptive system of prior art is shown in FIG. 1. The system 100 may be capable of changing of “learning” its internal parameters based on the input 102, output 104 signals, and/or an external influence 106. The system 100 may be commonly described using a function 110 that depends (including probabilistic dependence) on the history of inputs and outputs of the system and/or on some external signal r that is related to the inputs and outputs. The function F_x,y,rmay be referred to as a “performance function”. The purpose of adaptation (or learning) may be to optimize the input-output transformation according to some criteria, where learning is described as minimization of an average value of the performance function F.

[0007] Although there are numerous models of adaptive systems, these typically implement a specific set of learning rules (e.g., supervised, unsupervised, reinforcement). Supervised learning may be the machine learning task of inferring a function from supervised (labeled) training data. Reinforcement learning may refer to an area of machine learning concerned with how an agent ought to take actions in an environment so as to maximize some notion of reward (e.g., immediate or cumulative). Unsupervised learning may refer to the problem of trying to find hidden structure in unlabeled data. Because the examples given to the learner are unlabeled, there is no external signal to evaluate a potential solution.

[0008] When the task changes, the learning rules (typically effected by adjusting the control parameters w={w_i, w₂, . . . , w_n}) may need to be modified to suit the new task. Hereinafter, the boldface variables and symbols with arrow superscripts denote vector quantities, unless specified otherwise. Complex control applications, such as for example, autonomous robot navigation, robotic object manipulation, and/or other applications may require simultaneous implementation of a broad range of learning tasks. Such tasks may include visual recognition of surroundings, motion control, object (face) recognition, object manipulation, and/or other tasks. In order to handle these tasks simultaneously, existing implementations may rely on a partitioning approach, where individual tasks are implemented using separate controllers, each implementing its own learning rule (e.g., supervised, unsupervised, reinforcement).

[0009] One conventional implementation of a multi-task learning controller is illustrated in FIG. 1A. The apparatus 120 comprises several blocks 120, 124, 130, each implementing a set of learning rules tailored for the particular task (e.g., motor control, visual recognition, object classification and manipulation, respectively). Some of the blocks (e.g., the signal processing block 130 in FIG. 1A) may further comprise sub-blocks (e.g., the blocks 132, 134) targeted at different learning tasks. Implementation of the apparatus 120 may have several shortcomings stemming from each block having a task specific implementation of learning rules. By way of example, a recognition task may be implemented using supervised learning while object manipulator tasks may comprise reinforcement learning. Furthermore, a single task may require use of more than one rule (e.g., signal processing task for block 130 in FIG. 1A) thereby necessitating use of two separate sub-blocks (e.g., blocks 132, 134) each implementing different learning rule (e.g., unsupervised learning and supervised learning, respectively).

[0010] Artificial neural networks may be used to solve some of the described problems. An artificial neural network (ANN) may include a mathematical and/or computational model inspired by the structure and/or functional aspects of biological neural networks. A neural network comprises a group of artificial neurons (units) that are interconnected by synaptic connections. Typically, an ANN is an adaptive system that is configured to change its structure (e.g., the connection configuration and/or neuronal states) based on external or internal information that flows through the network during the learning phase.

[0011] A spiking neuronal network (SNN) may be a special class of ANN, where neurons communicate by sequences of spikes. SNN may offer improved performance over conventional technologies in areas which include machine vision, pattern detection and pattern recognition, signal filtering, data segmentation, data compression, data mining, system identification and control, optimization and scheduling, and/or complex mapping. Spike generation mechanism may be a discontinuous process (e.g., as illustrated by the pre-synaptic spikes sx(t) 220, 222, 224, 226, 228, and post-synaptic spike train sy(t) 230, 232, 234 in FIG. 2) and a classical derivative of function F(s(t)) with respect to spike trains sx(t), sy(t) is not defined.

[0012] Even when a neural network is used as the computational engine for these learning tasks, individual tasks may be performed by a separate network partition that implements a task-specific set of learning rules (e.g., adaptive control, classification, recognition, prediction rules, and/or other rules). Unused portions of individual partitions (e.g., motor control when the robotic device is stationary) may remain unavailable to other partitions of the network that may require increased processing resources (e.g., when the stationary robot is performing face recognition tasks). Furthermore, when the learning tasks change during system operation, such partitioning may prevent dynamic retargeting (e.g., of the motor control task to visual recognition task) of the network partitions. Such solutions may lead to expensive and/or over-designed networks, in particular when individual portions are designed using the “worst possible case scenario” approach. Similarly, partitions designed using a limited resource pool configured to handle an average task load may be unable to handle infrequently occurring high computational loads that are beyond a performance capability of the particular partition, even when other portions of the networks have spare capacity.

[0013] By way of illustration, consider a mobile robot controlled by a neural network, where the task of the robot is to move in an unknown environment and collect certain resources by the way of trial and error. This can be formulated as reinforcement learning tasks, where the network is supposed to maximize the reward signals (e.g., amount of the collected resource). While in general the environment is unknown, there may be possible situations when the human operator can show to the network desired control signal (e.g., for avoiding obstacles) during the ongoing reinforcement learning. This may be formulated as a supervised learning task. Some existing learning rules for the supervised learning may rely on the gradient of the performance function. The gradient for reinforcement learning part may be implemented through the use of the adaptive critic; the gradient for supervised learning may be implemented by taking a difference between the supervisor signal and the actual output of the controller. Introduction of the critic may be unnecessary for solving reinforcement learning tasks, because direct gradient-based reinforcement learning may be used instead. Additional analytic derivation of the learning rules may be needed when the loss function between supervised and actual output signal is redefined.

[0014] While different types of learning may be formalized as a minimization of the performance function F, an optimal minimization solution often cannot be found analytically, particularly when relationships between the system's behavior and the performance function are complex. By way of example, nonlinear regression applications generally may not have analytical solutions. Likewise, in motor control applications, it may not be feasible to analytically determine the reward arising from external environment of the robot, as the reward typically may be dependent on the current motor control command and state of the environment. Moreover, analytic determination of a performance function F derivative may require additional operations (often performed manually) for individual new formulated tasks that are not suitable for dynamic switching and reconfiguration of the tasks described before.

[0015] Although some adaptive controller implementations may describe reward-modulated unsupervised learning algorithms, these implementations of unsupervised learning algorithms may be multiplicatively modulated by reinforcement learning signal and, therefore, may require the presence of reinforcement signal for proper operation.

[0016] Many presently available implementations of stochastic adaptive apparatuses may be incapable of learning to perform unsupervised tasks while being influenced by additive reinforcement (and vice versa). Many presently available adaptive implementations may be task-specific and implement one particular learning rule (e.g., classifier unsupervised learning), and such devices may be retargeted (e.g., reprogrammed) in order to implement different learning rules. Furthermore, presently available methodologies may not be capable of implementing dynamic re-tasking and use the same set of network resources to implement a different combination of learning rules.

[0017] Accordingly, there is a salient need for machine learning apparatus and methods to implement generalized stochastic learning configured to handle simultaneously any learning rule combination (e.g., reinforcement, supervised, unsupervised, online, batch) and is capable of, inter alia, dynamic reconfiguration using the same set of network resources.

Summary

[0018] The present disclosure satisfies the foregoing needs by providing, inter alia, apparatus and methods for implementing generalized probabilistic learning configured to handle simultaneously various learning rule combinations.

[0019] One aspect of the disclosure relates to one or more computerized apparatus, and/or computer-implemented methods for effectuating a spiking network stochastic signal processing system configured to implement task-specific learning. In one implementation, the apparatus may comprise a storage medium, the storage medium comprising a plurality of instructions to operate a network, comprising a plurality of spiking neurons, the instructions configured to, when executed: based at least in part on receiving a task indication, select first group and second group from the plurality of spiking neurons; operate the first group in accordance with first learning rule, based at least in part on an input signal and training signal; and operate the second group in accordance with second learning rule, based at least in part on input signal.

[0020] In some implementations, the task indication may comprise at least the first and the second rules. the first rule may comprise at least reinforcement learning rule; and the second rule may comprise at least unsupervised learning rule.

[0021] In some implementations the first rule further may comprise first combination of at least the reinforcement learning rule and supervised learning rule, the first combination further may comprise unsupervised learning rule; and the second rule further may comprise second combination of reinforcement, supervised and unsupervised learning rules, the second combination being different from the first combination.

[0022] In some implementations neurons in at least the first group are selected from the plurality, based at least in part on a random parameter associated with spatial coordinate of the plurality of neurons within the network; and at least one of the first and the second group may be characterized by a finite life span, the life span configured during the selecting.

[0023] In some implementations, neurons in at least the first group are selected using high level neuromorphic description language (HNLD) statement comprising a tag, configured to identify the neurons, and the first group and the second group comprise disjoint set pair characterized by an empty intersect.

[0024] In some implementations the first group and the second group comprise overlapping set pair, neurons in at least the first group are selected using high level neuromorphic description language (HNLD) statement comprising a tag, and the tag may comprise an alphanumeric identifiers adapted to identify a spatial coordinate of neurons within respective groups.

[0025] In some implementations the first rule having target performance associated therewith, and the operate the first group in accordance with the first rule may be configured to produce actual output having actual performance associated therewith such that the actual performance being closer to the target performance, as compared to another actual performance associated with another actual output being generated by the first group operated in absence of the first learning rule.

[0026] In some implementations, the training signal further may comprise a desired output, comparison of the actual performance to the target performance may be based at least in part on a distance measure between the desired output and actual output such that the actual performance may be being closer to the target performance may be characterized by a value of the distance measure, determined using the desired output and the actual output, being smaller compared to another value of the distance measure, determined using the desired output and the another actual output.

[0027] In some implementations the distance measure may comprise instantaneous mutual information.

[0028] In some implementations the distance measure may comprise a squared error between (i) a convolution of the actual output with first convolution kernel α and (ii) a convolution of the desired output with second convolution kernel β.

[0029] In some implementations, the operation of the first group in accordance with first learning rule may be based at least in part on first input signal, and operate the second group in accordance with second learning rule may be based at least in part on second input signal, the second signal being different from the first signal.

[0030] In some implementations the operation of the first group in accordance with first learning rule may be based at least in part on input signal, and operate the second group in accordance with second learning rule may be based at least in part on the input signal.

[0031] In one implementation a computer readable apparatus may comprise a storage medium, the storage medium comprising a plurality of instructions to operate a processing apparatus, the instructions configured to, when executed: based at least in part on first task indication at first instance, operate the processing apparatus in accordance with first stochastic hybrid learning rule configured to produce first learning signal based at least in part on first input signal and first training signal, associated with the first task indication; and based at least in part on second task indication at second instance, subsequent to first instance operate the processing apparatus in accordance with second stochastic hybrid learning rule configured to produce second learning signal based at least in part on second input signal and second training signal, associated with the second task indication, and the first hybrid learning rule may be configured to effectuate first rule combination; and the second hybrid learning rule may be configured to effect second rule combination, the second combination being different from the first combination.

[0032] In some implementations, the second task indication may be configured based at least in part on a parameter, associated with the operating the processing apparatus in accordance with the first stochastic hybrid learning rule, exceeding a threshold.

[0033] In some implementations, the parameter may be selected from the group consisting of: (i) peak power consumption associated with operating the processing apparatus; (ii) power consumption associated with operating the processing apparatus, averaged over an interval associated with producing the first learning signal; (iii) memory utilization associated with operating the processing apparatus; and (iv) logic resource utilization associated with operating the processing apparatus.

[0034] In some implementations the second task indication may be configured based at least in part on detecting a change in number if input channels associated with the first input signal.

[0035] In some implementations the second task indication may be configured based at least in part on detecting a change in composition of the first training signal, the change comprising any one or more of (i) addition of reinforcement signal; (ii) removal of reinforcement signal; (iii) addition of supervisor signal; and (iv) removal of supervisory signal.

[0036] In one or more implementations, a computer-implemented method of operating a computerized spiking network, comprising a plurality of nodes, may comprise based at least in part on first task indication at a first instance, operating the plurality of nodes in accordance with a first stochastic hybrid learning rule configured to produce first learning signal based at least in part on first input signal and first training signal, associated with the first task indication, and based at least in part on second task indication at second instance, subsequent to first instance: operating first portion of the plurality of nodes in accordance with second stochastic hybrid learning rule configured to produce second learning signal based at least in part on second input signal and second training signal, associated with the second task indication; and operating second portion of the plurality of nodes in accordance with third stochastic learning rule configured to produce third learning signal based at least in part on second input signal associated with the second task indication, and the first hybrid learning rule may be configured to effect first rule combination; of reinforcement learning rule and supervised learning rule, and the second hybrid learning rule may be configured to effect second rule combination, the second combination substantially different from the first combination.

[0037] In some implementations, the first hybrid learning rule may comprise first rule having first combination coefficient associated therewith and second rule having second combination coefficient associated therewith, the second hybrid learning rule may comprise the first rule having third combination coefficient associated therewith and the second rule having fourth combination coefficient associated therewith; and at the first coefficient different from the third coefficient.

[0038] In some implementations, the first rule may be selected from the group consisting of reinforcement and supervised learning rules, the first rule being configured in accordance with the first training and the second training signal, respectively.

[0039] In some implementations, the first hybrid learning rule may comprise first rule and second rule, and the second hybrid learning rule may comprise the first rule and at least third rule, the third rule different from at least one of the first rule and the second rule.

[0040] In some implementations, the third learning signal may be based at least in part on the second learning signal.

[0041] In some implementations, the first hybrid learning rule may be configured to implement reinforcement and supervised rule combination, and the second hybrid learning rule may be configured to implement at least supervised and unsupervised rule combination.

[0042] In some implementations, the second task indication may be based at least in part one or more of (i) a detected a change in network processing configuration; and (ii) a detected change in configuration of the first input signal.

[0043] In some implementations, the change in network processing configuration may comprise any of (i) a failure of one or more of the plurality of nodes; (ii) an addition of one or more failure of one or more nodes; and (iii) a failure of one or more of input-output interface associated with the plurality of nodes.

[0044] These and other objects, features, and characteristics of the present disclosure, as well as the methods of operation and functions of the related elements of structure and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the disclosure. As used in the specification and in the claims, the singular form of “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise.

Brief Description of the Drawings

[0045] FIG. 1 is a block diagram illustrating a typical architecture of an adaptive system according to prior art.

[0046] FIG. 1A is a block diagram illustrating multi-task learning controller apparatus according to prior art.

[0047] FIG. 2 is a graphical illustration of typical input and output spike trains according to prior art.

[0048] FIG. 3 is a block diagram illustrating generalized learning apparatus, in accordance with one or more implementations.

[0049] FIG. 4 is a block diagram illustrating learning block apparatus of FIG. 3, in accordance with one or more implementations.

[0050] FIG. 4A is a block diagram illustrating exemplary implementations of performance determination block of the learning block apparatus of FIG. 4, in accordance with the disclosure.

[0051] FIG. 5 is a block diagram illustrating generalized learning apparatus, in accordance with one or more implementations.

[0052] FIG. 5A is a block diagram illustrating generalized learning block configured for implementing different learning rules, in accordance with one or more implementations.

[0053] FIG. 5B is a block diagram illustrating generalized learning block configured for implementing different learning rules, in accordance with one or more implementations.

[0054] FIG. 5C is a block diagram illustrating generalized learning block configured for implementing different learning rules, in accordance with one or more implementations.

[0055] FIG. 6A is a block diagram illustrating a spiking neural network, comprising three dynamically configured partitions, configured to effectuate generalized learning block of FIG. 4, in accordance with one or more implementations.

[0056] FIG. 6B is a block diagram illustrating a spiking neural network, comprising two dynamically configured partitions, adapted to effectuate generalized learning, in accordance with one or more implementations.

[0057] FIG. 6C is a block diagram illustrating a spiking neural network, comprising three partitions, configured to effectuate hybrid learning rules in accordance with one or more implementations.

[0058] FIG. 7 is a block diagram illustrating spiking neural network configured to effectuate multiple learning rules, in accordance with one or more implementations.

[0059] FIG. 8A is a logical flow diagram illustrating generalized learning method for use with the apparatus of FIG. 5A, in accordance with one or more implementations.

[0060] FIG. 8B is a logical flow diagram illustrating dynamic reconfiguration method for use with the apparatus of FIG. 5A, in accordance with one or more implementations.

[0061] FIG. 9A is a plot presenting simulations data illustrating operation of the neural network of FIG. 7 prior to learning, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network before learning; (iii) supervisor spike pattern; (iv) positive reinforcement spike pattern; and (v) negative reinforcement spike pattern.

[0062] FIG. 9B is a plot presenting simulations data illustrating supervised learning operation of the neural network of FIG. 7, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network before learning; (iii) supervisor spike pattern; (iv) positive reinforcement spike pattern; and (v) negative reinforcement spike pattern.

[0063] FIG. 9C is a plot presenting simulations data illustrating reinforcement learning operation of the neural network of FIG. 7, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network after learning; (iii) supervisor spike pattern; (iv) positive reinforcement spike pattern; and (v) negative reinforcement spike pattern.

[0064] FIG. 9D is a plot presenting simulations data illustrating operation of the neural network of FIG. 7, comprising reinforcement learning aided with small portion of supervisor spikes, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network after learning; (iii) supervisor spike pattern; (iv) positive reinforcement spike pattern; and (v) negative reinforcement spike pattern.

[0065] FIG. 9E is a plot presenting simulations data illustrating operation of the neural network of FIG. 7, comprising an equal mix of reinforcement and supervised learning signals, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network after learning; (iii) supervisor spike pattern; (iv) positive reinforcement spike pattern; and (v) negative reinforcement spike pattern.

[0066] FIG. 9F is a plot presenting simulations data illustrating operation of the neural network of FIG. 7, comprising supervised learning augmented with a 50% fraction of reinforcement spikes, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network after learning; (iii) supervisor spike pattern; (iv) positive reinforcement spike pattern; and (v) negative reinforcement spike pattern.

[0067] FIG. 10A is a plot presenting simulations data illustrating supervised learning operation of the neural network of FIG. 7, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network before learning; (iii) supervisor spike pattern.

[0068] FIG. 10B is a plot presenting simulations data illustrating operation of the neural network of FIG. 7, comprising supervised learning augmented by a small amount of unsupervised learning, modeled as 15% fraction of randomly distributed (Poisson) spikes, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network after learning, (iii) supervisor spike pattern.

[0069] FIG. 10C is a plot presenting simulations data illustrating operation of the neural network of FIG. 7, comprising supervised learning augmented by a substantial amount of unsupervised learning, modeled as 80% fraction of Poisson spikes, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network after learning, (iii) supervisor spike pattern.

[0070] FIG. 11 is a plot presenting simulations data illustrating operation of the neural network of FIG. 7, comprising supervised learning and reinforcement learning, augmented by a small amount of unsupervised learning, modeled as 15% fraction of Poisson spikes, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network after learning, (iii) supervisor spike pattern; (iv) positive reinforcement spike pattern; and (v) negative reinforcement spike pattern.

[0071] FIG. 12 is a plot presenting simulations data illustrating operation of the neural network of FIG. 7, comprising supervised learning and reinforcement learning, augmented by a small amount of unsupervised learning, modeled as 15% fraction of Poisson spikes, in accordance with one or more implementations, where data in the panels from top to bottom comprise: (i) input spike pattern; (ii) output activity of the network after learning, (iii) supervisor spike pattern; (iv) positive reinforcement spike pattern; and (v) negative reinforcement spike pattern.

[0072] FIG. 13 is a graphic illustrating a node subset tagging, in accordance with one or more implementations.

Detailed Description

[0074] Exemplary implementations of the present disclosure will now be described in detail with reference to the drawings, which are provided as illustrative examples so as to enable those skilled in the art to practice the disclosure. Notably, the figures and examples below are not meant to limit the scope of the present disclosure to a single implementation, but other implementations are possible by way of interchange of or combination with some or all of the described or illustrated elements. Wherever convenient, the same reference numbers will be used throughout the drawings to refer to same or similar parts.

[0075] Where certain elements of these implementations can be partially or fully implemented using known components, only those portions of such known components that are necessary for an understanding of the present disclosure will be described, and detailed descriptions of other portions of such known components will be omitted so as not to obscure the disclosure.

[0076] In the present specification, an implementation showing a singular component should not be considered limiting; rather, the disclosure is intended to encompass other implementations including a plurality of the same component, and vice-versa, unless explicitly stated otherwise herein.

[0077] Further, the present disclosure encompasses present and future known equivalents to the components referred to herein by way of illustration.

[0078] As used herein, the term “bus” is meant generally to denote all types of interconnection or communication architecture that is used to access the synaptic and neuron memory. The “bus” may be optical, wireless, infrared, and/or another type of communication medium. The exact topology of the bus could be for example standard “bus”, hierarchical bus, network-on-chip, address-event-representation (AER) connection, and/or other type of communication topology used for accessing, e.g., different memories in pulse-based system.

[0079] As used herein, the terms “computer”, “computing device”, and “computerized device” may include one or more of personal computers (PCs) and/or minicomputers (e.g., desktop, laptop, and/or other PCs), mainframe computers, workstations, servers, personal digital assistants (PDAs), handheld computers, embedded computers, programmable logic devices, personal communicators, tablet computers, portable navigation aids, J2ME equipped devices, cellular telephones, smart phones, personal integrated communication and/or entertainment devices, and/or any other device capable of executing a set of instructions and processing an incoming data signal.

[0080] As used herein, the term “computer program” or “software” may include any sequence of human and/or machine cognizable steps which perform a function. Such program may be rendered in a programming language and/or environment including one or more of C/C++, C#, Fortran, COBOL, MATLAB™, PASCAL, Python, assembly language, markup languages (e.g., HTML, SGML, XML, VoXML), object-oriented environments (e.g., Common Object Request Broker Architecture (CORBA)), Java™ (e.g., J2ME, Java Beans), Binary Runtime Environment (e.g., BREW), and/or other programming languages and/or environments.

[0081] As used herein, the terms “connection”, “link”, “transmission channel”, “delay line”, “wireless” may include a causal link between any two or more entities (whether physical or logical/virtual), which may enable information exchange between the entities.

[0082] As used herein, the term “memory” may include an integrated circuit and/or other storage device adapted for storing digital data. By way of non-limiting example, memory may include one or more of ROM, PROM, EEPROM, DRAM, Mobile DRAM, SDRAM, DDR/2 SDRAM, EDO/FPMS, RLDRAM, SRAM, “flash” memory (e.g., NAND/NOR), memristor memory, PSRAM, and/or other types of memory.

[0083] As used herein, the terms “integrated circuit”, “chip”, and “IC” are meant to refer to an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material. By way of non-limiting example, integrated circuits may include field programmable gate arrays (e.g., FPGAs), a programmable logic device (PLD), reconfigurable computer fabrics (RCFs), application-specific integrated circuits (ASICs), and/or other types of integrated circuits.

[0084] As used herein, the terms “microprocessor” and “digital processor” are meant generally to include digital processing devices. By way of non-limiting example, digital processing devices may include one or more of digital signal processors (DSPs), reduced instruction set computers (RISC), general-purpose (CISC) processors, microprocessors, gate arrays (e.g., field programmable gate arrays (FPGAs)), PLDs, reconfigurable computer fabrics (RCFs), array processors, secure microprocessors, application-specific integrated circuits (ASICs), and/or other digital processing devices. Such digital processors may be contained on a single unitary IC die, or distributed across multiple components.

[0085] As used herein, the term “network interface” refers to any signal, data, and/or software interface with a component, network, and/or process. By way of non-limiting example, a network interface may include one or more of FireWire (e.g., FW400, FW800, etc.), USB (e.g., USB2), Ethernet (e.g., 10/100, 10/100/1000 (Gigabit Ethernet), 10-Gig-E, etc.), MoCA, Coaxsys (e.g., TVnet™), radio frequency tuner (e.g., in-band or OOB, cable modem, etc.), Wi-Fi (802.11), WiMAX (802.16), PAN (e.g., 802.15), cellular (e.g., 3G, LTE/LTE-A/TD-LTE, GSM, etc.), IrDA families, and/or other network interfaces.

[0086] As used herein, the terms “node”, “neuron”, and “neuronal node” are meant to refer, without limitation, to a network unit (e.g., a spiking neuron and a set of synapses configured to provide input signals to the neuron) having parameters that are subject to adaptation in accordance with a model.

[0087] As used herein, the terms “state” and “node state” is meant generally to denote a full (or partial) set of dynamic variables used to describe node state.

[0088] As used herein, the term “synaptic channel”, “connection”, “link”, “transmission channel”, “delay line”, and “communications channel” include a link between any two or more entities (whether physical (wired or wireless), or logical/virtual) which enables information exchange between the entities, and may be characterized by a one or more variables affecting the information exchange.

[0089] As used herein, the term “Wi-Fi” includes one or more of IEEE-Std. 802.11, variants of IEEE-Std. 802.11, standards related to IEEE-Std. 802.11 (e.g., 802.11a/b/g/n/s/v), and/or other wireless standards.

[0090] As used herein, the term “wireless” means any wireless signal, data, communication, and/or other wireless interface. By way of non-limiting example, a wireless interface may include one or more of Wi-Fi, Bluetooth, 3G (3GPP/3GPP2), HSDPA/HSUPA, TDMA, CDMA (e.g., IS-95A, WCDMA, etc.), FHSS, DSSS, GSM, PAN/802.15, WiMAX (802.16), 802.20, narrowbandlFDMA, OFDM, PCS/DCS, LTE/LTE-A/TD-LTE, analog cellular, CDPD, satellite systems, millimeter wave or microwave systems, acoustic, infrared (i.e., IrDA), and/or other wireless interfaces.

Overview

[0091] The present disclosure provides, among other things, a computerized apparatus and methods for dynamically configuring generalized learning rules in an adaptive signal processing apparatus given multiple cost measures. In one implementation of the disclosure, the framework may be used to enable adaptive signal processing system to flexibly combine different learning rules (e.g., supervised, unsupervised, reinforcement learning, and/or other learning rules) with different methods (e.g., online, batch, and/or other learning methods). The generalized learning apparatus of the disclosure may employ, in some implementations, modular architecture where learning tasks are separated from control tasks, so that changes in one of the blocks do not necessitate changes within the other block. By separating implementation of learning tasks from the control tasks, the framework may further allow dynamic reconfiguration of the learning block in response to a task change or learning method change in real time. The generalized learning apparatus may be capable of implementing several learning rules concurrently based on the desired control task and without requiring users to explicitly identify the required learning rule composition for that application.

[0092] The generalized learning framework described herein advantageously provides for learning implementations that do not affect regular operation of the signal system (e.g., processing of data). Hence, a need for a separate learning stage may be obviated so that learning may be turned off and on again when appropriate.

[0093] One or more generalized learning methodologies described herein may enable different parts of the same network to implement different adaptive tasks. The end user of the adaptive device may be enabled to partition network into different parts, connect these parts appropriately, and assign cost functions to each task (e.g., selecting them from predefined set of rules or implementing a custom rule). A user may not be required to understand detailed implementation of the adaptive system (e.g., plasticity rules, neuronal dynamics, etc.) nor may be be required to be able to derive the performance function and determine its gradient for each learning task. Instead, a user may be able to operate generalized learning apparatus of the disclosure by assigning task functions and connectivity map to each partition.

Generalized Learning Apparatus

[0094] Detailed descriptions of various implementations of apparatuses and methods of the disclosure are now provided. Although certain aspects of the disclosure may be understood in the context of robotic adaptive control system comprising a spiking neural network, the disclosure is not so limited. Implementations of the disclosure may also be used for implementing a variety of learning systems, such as, for example, signal prediction (e.g., supervised learning), finance applications, data clustering (e.g., unsupervised learning), inventory control, data mining, and/or other applications that do not require performance function derivative computations.

[0095] Implementations of the disclosure may be, for example, deployed in a hardware and/or software implementation of a neuromorphic computer system. In some implementations, a robotic system may include a processor embodied in an application specific integrated circuit, which can be adapted or configured for use in an embedded application (e.g., a prosthetic device).

[0096] FIG. 3 illustrates one exemplary learning apparatus useful to the disclosure. The apparatus 300 shown in FIG. 3 comprises the control block 310, which may include a spiking neural network configured to control a robotic arm and may be parameterized by the weights of connections between artificial neurons, and learning block 320, which may implement learning and/or calculating the changes in the connection weights. The control block 310 may receive an input signal x, and may generate an output signal y. The output signal y may include motor control commands configured to move a robotic arm along a desired trajectory. The control block 310 may be characterized by a system model comprising system internal state variables S. An internal state variable q may include a membrane voltage of the neuron, conductance of the membrane, and/or other variables. The control block 310 may be characterized by learning parameters w, which may include synaptic weights of the connections, firing threshold, resting potential of the neuron, and/or other parameters. In one or more implementations, the parameters w may comprise probabilities of signal transmission between the units (e.g., neurons) of the network.

[0097] The input signal x(t) may comprise data used for solving a particular control task. In one or more implementations, such as those involving a robotic arm or autonomous robot, the signal x(t) may comprise a stream of raw sensor data (e.g., proximity, inertial, terrain imaging, and/or other raw sensor data) and/or preprocessed data (e.g., velocity, extracted from accelerometers, distance to obstacle, positions, and/or other preprocessed data). In some implementations, such as those involving object recognition, the signal x(t) may comprise an array of pixel values (e.g., RGB, CMYK, HSV, HSL, grayscale, and/or other pixel values) in the input image, and/or preprocessed data (e.g., levels of activations of Gabor filters for face recognition, contours, and/or other preprocessed data). In one or more implementations, the input signal x(t) may comprise desired motion trajectory, for example, in order to predict future state of the robot on the basis of current state and desired motion.

[0098] The control block 310 of FIG. 3 may comprise a probabilistic dynamic system, which may be characterized by an analytical input-output (x→y) probabilistic relationship having a conditional probability distribution associated therewith:
P=p(y|x,w) (Eqn. 1)
In Eqn. 1, the parameter w may denote various system characteristics including connection efficacy, firing threshold, resting potential of the neuron, and/or other parameters. The analytical relationship of Eqn. 1 may be selected such that the gradient of ln[p(y|x,w)] with respect to the system parameter w exists and can be calculated. The framework shown in FIG. 3 may be configured to estimate rules for changing the system parameters (e.g., learning rules) so that the performance function F(x,y,r) is minimized for the current set of inputs and outputs and system dynamics S.

[0099] In some implementations, the control performance function may be configured to reflect the properties of inputs and outputs (x,y). The values F(x,y,r) may be calculated directly by the learning block 320 without relying on external signal r when providing solution of unsupervised learning tasks.

[0100] In some implementations, the value of the function F may be calculated based on a difference between the output y of the control block 310 and a reference signal y^dcharacterizing the desired control block output. This configuration may provide solutions for supervised learning tasks, as described in detail below.

[0101] In some implementations, the value of the performance function F may be determined based on the external signal r. This configuration may provide solutions for reinforcement learning tasks, where r represents reward and punishment signals from the environment.

Learning Block

[0102] The learning block 320 may implement learning framework according to the implementation of FIG. 3 that enables generalized learning methods without relying on calculations of the performance function F derivative in order to solve unsupervised, supervised, reinforcement, and/or other learning tasks. The block 320 may receive the input x and output y signals (denoted by the arrow 302_1, 308_1, respectively, in FIG. 3), as well as the state information 305. In some implementations, such as those involving supervised and reinforcement learning, external teaching signal r may be provided to the block 320 as indicated by the arrow 304 in FIG. 3. The teaching signal may comprise, in some implementations, the desired motion trajectory, and/or reward and punishment signals from the external environment.

[0103] In one or more implementations the learning block 320 may optimize performance of the control system (e.g., the system 300 of FIG. 3) that is characterized by minimization of the average value of the performance function F(x,y,r) as described in detail below.

[0104] In some implementations, the average value of the performance function may depend only on current values of input x, output y, and external signal r as follows:
<F>_x,y,r=Σ_x,y,rP(x,y,r)F(x,y,r)→min (Eqn. 2)
where P(x,y,r) is a joint probability of receiving inputs x, r and generating output y.

[0105] The performance function of EQN. 2 may be minimized using, for example, gradient descend algorithms. By way of example, derivative of the average value of the function F_x,y,rwith respect to the system control parameters w_imay be found as:

[0106]

(Eqn . 3)

\frac{\partial}{\partial w_{i}} {〈 F (x, y, r) 〉}_{x, y, r} = \sum_{r} p (r ❘ x, y) \frac{\partial}{\partial w_{i}} \sum_{x} p (x) \sum_{y} F (x, y, r) p (y ❘ x, w) = \sum_{r} p (r ❘ x, y) \sum_{x} p (x) \sum_{y} F (x, y, r) \frac{\partial}{\partial w_{i}} p (y ❘ x, w) = \sum_{r} p (r ❘ x, y) \sum_{x} p (x) \sum_{y} F (x, y, r) p (y ❘ x, w) \frac{\partial}{\partial w_{i}} \ln (p (y ❘ x, w)) = \sum_{r} p (r ❘ x, y) \sum_{x, y} p (x, y) F (x, y, r) \frac{\partial}{\partial w_{i}} \ln (p (y ❘ x, w)) = {〈 {〈 F (x, y, r) \frac{\partial}{\partial w_{i}} \ln (p (y ❘ x, w)) 〉}_{x, y} 〉}_{r}

where :

(Eqn . 4) - \ln (p (y ❘ x, w)) = h (y ❘ x, w)

is the per-stimulus entropy of the system response (or ‘surprisal’). The probability of the external signal p(r|x, y) may be characteristic of the external environment and may changed due to adaptation by the system. That property may allow an omission of averaging over external signals r in subsequent consideration of learning rules. In the online version of the algorithm, the changes in the i^thparameter w_imay be made after sampling from inputs x and outputs y and receiving the value of F in this point (x,y) using the following equation:

[0107]

\begin{matrix} Δ w_{i} = γ F (x, y, r) \frac{\partial h (x ❘ y)}{\partial w_{i}} & (Eqn . 5) \end{matrix}

where: γ is a step size of a gradient descent, or a “learning rate”; and

[0108]

\frac{\partial h (x ❘ y)}{\partial w_{i}}

is derivative of the per-stimulus entropy with respect to the learning parameter w_i(also referred to as the score function).

[0109] If the value of F also depends on history of the inputs and the outputs, the SF/LR maybe extended to stochastic processes using, for example, frameworks developed for episodic Partially Observed Markov Decision Processes (POMDPs).

[0110] When performing reinforcement learning tasks, the adaptive controller 300 of FIG. 3 may be construed as an agent that performs certain actions (e.g., produces an output y) on the basis of sensory state (e.g., inputs x). The agent (i.e., the controller 300) may be provided with the reinforcement signal based on the sensory state and the output. The goal of the controller may be to determine outputs y(t) so as to increase total reinforcement.

[0111] Another extension, suitable for online learning, may comprise online algorithm (OLPOMDP) configured to calculate gradient traces that determine an effect of the history of the input on the output of the system for individual parameters as a discounted average of score function values for each time step t, as follows:

[0112]

\begin{matrix} z_{i} (t + Δ t) = β z_{i} (t) + \frac{\partial h (y (t) ❘ x (t))}{\partial w_{i}} & (Eqn . 6) \end{matrix}

where β is decay coefficient that may be typically based on memory depth required for the control task. In some implementations, control parameters w may be updated each time step according to the value of the performance function F and eligibility traces as follows:
Δw_i(t)=γF(x,y,r)z_i(t) (Eqn. 7)
where γ is a learning rate and F(t) is a current value of the performance function that may depend on previous inputs and outputs.

[0113] As illustrated in FIG. 3, the learning block may have access to the system's inputs and outputs, and/or system internal state S. In some implementations, the learning block may be provided with additional inputs 304 (e.g., reinforcement signals, desired output, current costs of control movements, and/or other inputs) that are related to the current task of the control block.

[0114] The learning block may estimate changes of the system parameters w that minimize the performance function F, and may provide the parameter adjustment information Δw to the control block 310, as indicated by the arrow 306 in FIG. 3. In some implementations, the learning block may be configured to modify the learning parameters w of the controller block. In one or more implementations (not shown), the learning block may be configured to communicate parameters w (as depicted by the arrow 306 in FIG. 3) for further use by the controller block 310, or to another entity (not shown).

[0115] By separating learning related tasks into a separate block (e.g., the block 320 in FIG. 3) from control tasks, the architecture shown in FIG. 3 may provide flexibility of applying different (or modifying) learning algorithms without requiring modifications in the control block model. In other words, the methodology illustrated in FIG. 3 may enable implementation of the learning process in such a way that regular functionality of the control aspects of the system 300 is not affected. For example, learning may be turned off and on again as required with the control block functionality being unaffected.

[0116] The detailed structure of the learning block 420 is shown and described with respect to FIG. 4. The learning block 420 may comprise one or more of gradient determination (GD) block 422, performance determination (PD) block 424 and parameter adaptation block (PA) 426, and/or other components. The implementation shown in FIG. 4 may decompose the learning process of the block 420 into two parts. A task-dependent/system independent part (i.e., the block 420) may implement a performance determination aspect of learning that is dependent only on the specified learning task (e.g., supervised). Implementation of the PD block 424 may not depend on particulars of the control block (e.g., block 310 in FIG. 3) such as, for example, neural network composition, neuron operating dynamics, and/or other particulars). The second part of the learning block 420, comprised of the blocks 422 and 426 in FIG. 4, may implement task-independent/system dependent aspects of the learning block operation. The implementation of the GD block 422 and PA block 426 may be the same for individual learning rules (e.g., supervised and/or unsupervised). The GD block implementation may further comprise particulars of gradient determination and parameter adaptation that are specific to the controller system 310 architecture (e.g., neural network composition, neuron operating dynamics, and/or plasticity rules). The architecture shown in FIG. 4 may allow users to modify task-specific and/or system-specific portions independently from one another, thereby enabling flexible control of the system performance. An advantage of the framework may be that the learning can be implemented in a way that does not affect the normal protocol of the functioning of the system (except of changing the parameters w). For example, there may be no need in a separate learning stage and learning may be turned off and on again when appropriate.

Gradient Determination Block

[0117] The GD block may be configured to determine the score function g by, inter alia, computing derivatives of the logarithm of the conditional probability with respect to the parameters that are subjected to change during learning based on the current inputs x, outputs y, and/or state variables S, denoted by the arrows 402, 408, 410, respectively, in FIG. 4. The GD block may produce an estimate of the score function g, denoted by the arrow 418 in FIG. 4 that is independent of the particular learning task (e.g., reinforcement, and/or unsupervised, and/or supervised learning). In some implementations, where the learning model comprises multiple parameters w_i, the score function g may be represented as a vector g comprising scores g_iassociated with individual parameter components w_i.

Performance Determination Block

[0118] The PD block may be configured to determine the performance function F based on the current inputs x, outputs y, and/or training signal r, denoted by the arrow 404 in FIG. 4. In some implementations, the external signal r may comprise the reinforcement signal in the reinforcement learning task. In some implementations, the external signal r may comprise reference signal in the supervised learning task. In some implementations, the external signal r comprises the desired output, current costs of control movements, and/or other information related to the current task of the control block (e.g., block 310 in FIG. 3). Depending on the specific learning task (e.g., reinforcement, unsupervised, or supervised) some of the parameters x,y,r may not be required by the PD block illustrated by the dashed arrows 402_1, 408_1, 404_1, respectively, in FIG. 4A The learning apparatus configuration depicted in FIG. 4 may decouple the PD block from the controller state model so that the output of the PD block depends on the learning task and is independent of the current internal state of the control block.

[0119] In some implementations, the PD block may transmit the external signal r to the learning block (as illustrated by the arrow 404_1) so that:
F(t)=r(t), (Eqn. 8)
where signal r provides reward and/or punishment signals from the external environment. By way of illustration, a mobile robot, controlled by spiking neural network, may be configured to collect resources (e.g., clean up trash) while avoiding obstacles (e.g., furniture, walls). In this example, the signal r may comprise a positive indication (e.g., representing a reward) at the moment when the robot acquires the resource (e.g., picks up a piece of rubbish) and a negative indication (e.g., representing a punishment) when the robot collides with an obstacle (e.g., wall). Upon receiving the reinforcement signal r, the spiking neural network of the robot controller may change its parameters (e.g., neuron connection weights) in order to maximize the function F (e.g., maximize the reward and minimize the punishment).

[0120] In some implementations, the PD block may determine the performance function by comparing current system output with the desired output using a predetermined measure (e.g., a distance d):
F(t)=d(y(t),y^d(t)), (Eqn. 9)
where y is the output of the control block (e.g., the block 310 in FIG. 3) and r=y^dis the external reference signal indicating the desired output that is expected from the control block. In some implementations, the external reference signal r may depend on the input x into the control block. In some implementations, the control apparatus (e.g., the apparatus 300 of FIG. 3) may comprise a spiking neural network configured for pattern classification. A human expert may present to the network an exemplary sensory pattern x and the desired output y^dthat describes the input pattern x class. The network may change (e.g., adapt) its parameters w to achieve the desired response on the presented pairs of input x and desired response y^d. After learning, the network may classify new input stimuli based on one or more past experiences.

[0121] In some implementations, such as when characterizing a control block utilizing analog output signals, the distance function may be determined using the squared error estimate as follows:
F(t)=(y(t)−y^d(t))² (Eqn. 10)

[0122] In some implementations, such as those applicable to control blocks using spiking output signals, the distance measure may be determined using the squared error of the convolved signals y, y^das follows:
F=[(y*α)−(y^d*β)]², (Eqn. 11)
where α, β are finite impulse response kernels. In some implementations, the distance measure may utilize the mutual information between the output signal and the reference signal.

[0123] In some implementations, the PD may determine the performance function by comparing one or more particular characteristic of the output signal with the desired value of this characteristic:
F=[ƒ(y)−ƒ¹(y)]², (Eqn. 12)
where ƒ is a function configured to extract the characteristic (or characteristics) of interest from the output signal y. By way of example, useful with spiking output signals, the characteristic may correspond to a firing rate of spikes and the function ƒ(y) may determine the mean firing from the output. In some implementations, the desired characteristic value may be provided through the external signal as
r=ƒ¹(y). (Eqn. 13)
In some implementations, the ƒ¹(y) may be calculated internally by the PD block.

[0124] In some implementations, the PD block may determine the performance function by calculating the instantaneous mutual information i between inputs and outputs of the control block as follows:
F=i(x,y)=−ln(p(y))+ln(p(y|x), (Eqn. 14)
where p(y) is an unconditioned probability of the current output. It is noteworthy that the average value of the instantaneous mutual information may equal the mutual information I(x,y). This performance function may be used to implement ICA (unsupervised learning).

[0125] In some implementations, the PD block may determines the performance function by calculating the unconditional instantaneous entropy h of the output of the control block as follows:
F=h(x,y)=−ln(p(y)). (Eqn. 15)
where p(y) is an unconditioned probability of the current output. It is noteworthy that the average value of the instantaneous unconditional entropy may equal the unconditional H(x,y). This performance function may be used to reduce variability in the output of the system for adaptive filtering.

[0126] In some implementations, the PD block may determine the performance function by calculating the instantaneous Kullback-Leibler divergence d_KL(p,∂) between the output probability distribution p(y|x) of the control block and some desired probability distribution ∂(y|x) as follows:
F=d_KL(x,y)=ln(p(y|x))−ln(∂(y|x)). (Eqn. 16)
It is noteworthy that the average value of the instantaneous Kulback-Leibler divergence may equal the d_KL(p,∂). This performance function may be applied in unsupervised learning tasks in order to restrict a possible output of the system. For example, if ∂(y) is a Poisson distribution of spikes with some firing rate R, then minimization of this performance function may force the neuron to have the same firing rate R.

[0127] In some implementations, the PD block may determine the performance function for the sparse coding. The sparse coding task may be an unsupervised learning task where the adaptive system may discover hidden components in the data that describes data the best with a constraint that the structure of the hidden components should be sparse:
F=∥x−A(y,w)∥²+∥y∥², (Eqn. 17)
where the first term quantifies how close the data x can be described by the current output y, where A(y,w) is a function that describes how to decode an original data from the output. The second term may calculate a norm of the output and may imply restrictions on the output sparseness.

[0128] A learning framework of the present innovation may enable generation of learning rules for a system, which may be configured to solve several completely different tasks-types simultaneously. For example, the system may learn to control an actuator while trying to extract independent components from movement trajectories of this actuator. The combination of tasks may be done as a linear combination of the performance functions for each particular problem:
F=C(F₁,F₂, . . . ,F_n), (Eqn. 18)
where: F₁, F₂, . . . , F_nare performance function values for different tasks; and C is a combination function.

[0129] In some implementations, the combined cost function C may comprise a weighted linear combination of individual cost functions corresponding to individual learning tasks:
C(F₁,F₁, . . . ,F₁)=Σ_ka_kF_k, (Eqn. 19)
where a_kare combination weights.

[0130] It is recognized by those killed in the arts that linear cost function combination described by Eqn. 19 illustrates one particular implementation of the disclosure and other implementations (e.g., a nonlinear combination) may be used as well.

[0131] In some implementations, the PD block may be configured to calculate the baseline of the performance function values (e.g., as a running average) and subtract it from the instantaneous value of the performance function in order to increase learning speed of learning. The output of the PD block may comprise a difference between the current value F(t)^curof the performance function and its time average custom character

:
F(t)=F(t)^cur− custom character

. (Eqn. 20)
In some implementations, the time average of the performance function may comprise an interval average, where learning occurs over a predetermined interval. A current value of the cost function may be determined at individual steps within the interval and may be averaged over all steps. In some implementations, the time average of the performance function may comprise a running average, where the current value of the cost function may be low-pass filtered according to:

[0132]

\begin{matrix} \frac{ⅆ F (t)}{ⅆ x} = - τ F (t) + {F (t)}^{cur}, & (Eqn . 21) \end{matrix}

thereby producing a running average output.

[0133] Referring now to FIG. 4A different implementations of the performance determination block (e.g., the block 424 of FIG. 4) are shown. The PD block implementation denoted 434, may be configured to simultaneously implement reinforcement, supervised and unsupervised (RSU) learning rules; and/or receive the input signal x(t) 412, the output signal y(t) 418, and/or the learning signal 436. The learning signal 436 may comprise the reinforcement component r(t) and the desired output (teaching) component y^d(t). In one or more implementations, the output performance function F_RSU 438 of the RSUPD block may be determined in accordance with Eqn. 38 described below.

[0134] The PD blocks 444, 445, may implement the reinforcement (R) learning rule. The output 448 of the block 444 may be determined based on the output signal y(t) 418 and the reinforcement signal r(t) 446. In one or more implementations, the output 448 of the RSUPD block may be determined in accordance with Eqn. 13. The performance function output 449 of the block 445 may be determined based on the input signal x(t), the output signal y(t), and/or the reinforcement signal r(t).

[0135] The PD block implementation denoted 454, may be configured to implement supervised (S) learning rules to generate performance function F_S 458 that is dependent on the output signal y(t) value 418 and the teaching signal y^d(t) 456. In one or more implementations, the output 458 of the PD 454 block may be determined in accordance with Eqn. 9-Eqn. 12.

[0136] The output performance function 468 of the PD block 464 implementing unsupervised learning may be a function of the input x(t) 412 and the output y(t) 418. In one or more implementations, the output 468 may be determined in accordance with Eqn. 14-Eqn. 17.

[0137] The PD block implementation denoted 474 may be configured to simultaneously implement reinforcement and supervised (RS) learning rules. The PD block 474 may not require the input signal x(t), and may receive the output signal y(t) 418 and the teaching signals r(t),y^d(t) 476. In one or more implementations, the output performance function F_RS 478 of the PD block 474 may be determined in accordance with Eqn. 18, where the combination coefficient for the unsupervised learning is set to zero. By way of example, in some implementations reinforcement learning task may be to acquire resources by the mobile robot, where the reinforcement component r(t) provides information about acquired resources (reward signal) from the external environment, while at the same time a human expert shows the robot what should be desired output signal y^d(t) to optimally avoid obstacles. By setting a higher coefficient to the supervised part of the performance function, the robot may be trained to try to acquire the resources if it does not contradict with human expert signal for avoiding obstacles.

[0138] The PD block implementation denoted 475 may be configured to simultaneously implement reinforcement and supervised (RS) learning rules. The PD block 475 output may be determined based the output signal 418, the learning signals 476, comprising the reinforcement component r(t) and the desired output (teaching) component y^d(t) and on the input signal 412, that determines the context for switching between supervised and reinforcement task functions. By way of example, in some implementations, reinforcement learning task may be used to acquire resources by the mobile robot, where the reinforcement component r(t) provides information about acquired resources (reward signal) from the external environment, while at the same time a human expert shows the robot what should be desired output signal y^d(t) to optimally avoid obstacles. By recognizing obstacles, avoidance context on the basis of some clues in the input signal, the performance signal may be switched between supervised and reinforcement. That may allow the robot to be trained to try to acquire the resources if it does not contradict with human expert signal for avoiding obstacles. In one or more implementations, the output performance function 479 of the PD 475 block may be determined in accordance with Eqn. 18, where the combination coefficient for the unsupervised learning is set to zero.

[0139] The PD block implementation denoted 484 may be configured to simultaneously implement reinforcement, and unsupervised (RU) learning rules. The output 488 of the block 484 may be determined based on the input and output signals 412, 418, in one or more implementations, in accordance with Eqn. 18. By way of example, in some implementations of sparse coding (unsupervised learning), the task of the adaptive system on the robot may be not only to extract sparse hidden components from the input signal, but to pay more attention to the components that are behaviorally important for the robot (that provides more reinforcement after they can be used).

[0140] The PD block implementation denoted 494, which may be configured to simultaneously implement supervised and unsupervised (SU) learning rules, may receive the input signal x(t) 412, the output signal y(t) 418, and/or the teaching signal y^d(t) 436. In one or more implementations, the output performance function F_SU 438 of the SU PD block may be determined in accordance with Eqn. 37 described below.

[0141] By the way of example, the stochastic learning system (that is associated with the PD block implementation 494) may be configured to learn to implement unsupervised data categorization (e.g., using sparse coding performance function), while simultaneously receiving external signal that is related to the correct category of particular input signals. In one or more implementations such reward signal may be provided by a human expert.

Parameter Changing Block

[0142] The parameter changing PA block (the block 426 in FIG. 4) may determine changes of the control block parameters Δw_iaccording to a predetermined learning algorithm, based on the performance function F and the gradient g it receives from the PD block 424 and the GD block 422, as indicated by the arrows marked 428, 430, respectively, in FIG. 4. Particular implementations of the learning algorithm within the block 426 may depend on the type of the control signals (e.g., spiking or analog) used by the control block 310 of FIG. 3.

[0143] Several exemplary implementations of PA learning algorithms applicable with spiking control signals are described below. In some implementations, the PA learning algorithms may comprise a multiplicative online learning rule, where control parameter changes are determined as follows:

[0144]

\begin{matrix} Δ \vec{w} (t) = γ F (t) \vec{g} (t), & (Eqn . 22) \end{matrix}

where γ is the learning rate configured to determine speed of learning adaptation. The learning method implementation according to (Eqn. 22) may be advantageous in applications where the performance function F(t) depends on the current values of the inputs x, outputs y, and/or signal r.

[0145] In some implementations, the control parameter adjustment Δw may be determined using an accumulation of the score function gradient and the performance function values, and applying the changes at a predetermined time instance (corresponding to, e.g., the end of the learning epoch):

[0146]

\begin{matrix} Δ \overset{r}{w} (t) = \frac{γ}{N^{2}} \cdot \sum_{i = 0}^{N - 1} F (t - i Δ t) \cdot \sum_{i = 0}^{N - 1} \overset{r}{g} (t - i Δ t), & (Eqn . 23) \end{matrix}

where: T is a finite interval over which the summation occurs; N is the number of steps; and Δt is the time step determined as T/N. The summation interval T in Eqn. 23 may be configured based on the specific requirements of the control application. By way of illustration, in a control application where a robotic arm is configured to reaching for an object, the interval may correspond to a time from the start position of the arm to the reaching point and, in some implementations, may be about 1 s-50 s. In a speech recognition application, the time interval T may match the time required to pronounce the word being recognized (typically less than 1 s-2 s). In some implementations of spiking neuronal networks, Δt may be configured in range between 1 ms and 20 ms, corresponding to 50 steps (N=50) in one second interval.

[0147] The method of Eqn. 23 may be computationally expensive and may not provide timely updates. Hence, it may be referred to as the non-local in time due to the summation over the interval T. However, it may lead to unbiased estimation of the gradient of the performance function.

[0148] In some implementations, the control parameter adjustment Δw_imay be determined by calculating the traces of the score function e_i(t) for individual parameters w_i. In some implementations, the traces may be computed using a convolution with an exponential kernel β as follows:
{right arrow over (e)}(t+Δt)=β{right arrow over (z)}(t)+{right arrow over (g)}(t), (Eqn. 24)
where β is the decay coefficient. In some implementations, the traces may be determined using differential equations:

[0149]

\begin{matrix} \frac{ⅆ}{ⅆ t} \overset{->}{e} (t) = - τ \overset{->}{e} (t) + \overset{->}{g} (t) . & (Eqn . 25) \end{matrix}

The control parameter w may then be adjusted as:
{right arrow over (Δw)}(t)=γF(t){right arrow over (e)}(t), (Eqn. 26)
where γ is the learning rate. The method of Eqn. 24-Eqn. 26 may be appropriate when a performance function depends on current and past values of the inputs and outputs and may be referred to as the OLPOMDP algorithm. While it may be local in time and computationally simple, it may lead to biased estimate of the performance function. By way of illustration, the methodology described by Eqn. 24-Eqn. 26 may be used, in some implementations, in a rescue robotic device configured to locate resources (e.g., survivors, unexploded ordinance, and/or other resources) in a building. The input x may correspond to the robot current position in the building. The reward r (e.g., the successful location events) may depend on the history of inputs and on the history of actions taken by the agent (e.g., left/right turns, up/down movement, and/or other actions taken by the agent).

[0150] In some implementation, the control parameter adjustment Δw determined using methodologies of the Eqns. 16, 17, 19 may be further modified using a gradient with momentum according to:

[0151]

\begin{matrix} Δ \vec{w} (t) \Rightarrow μ Δ \vec{w} (t - Δ t) + Δ \vec{w} (t), & (Eqn . 27) \end{matrix}

where μ is the momentum coefficient. In some implementations, the sign of the gradient may be used to perform learning adjustments as follows:

[0152]

\begin{matrix} Δ w_{i} (t) \Rightarrow \frac{Δ w_{i} (t)}{\langle Δ w_{i} (t) \rangle} . & (Eqn . 28) \end{matrix}

In some implementations, the gradient descent methodology may be used for learning coefficient adaptation.

[0153] In some implementations, the gradient signal g, determined by the PD block 422 of FIG. 4, may be subsequently modified according to another gradient algorithm, as described in detail below. In some implementations, these modifications may comprise determining natural gradient, as follows:

[0154]

\begin{matrix} Δ \overset{r}{w} = {〈 \overset{r}{g} \cdot \overset{r_{T}}{g} 〉}_{x, y}^{- 1} \cdot {〈 \overset{r}{g} \cdot F 〉}_{x, y}, & (Eqn . 29) \end{matrix}

where

{right arrow over (g)}{right arrow over (g)}^T custom character

_x,yis the Fisher information metric matrix. Applying the following transformation to Eqn. 21:

[0155]

\begin{matrix} {〈 \overset{r}{g} (\overset{r_{T}}{g} Δ \overset{r}{w} - F) 〉}_{x, y} = 0, & (Eqn . 30) \end{matrix}

natural gradient from linear regression task may be obtained as follows:
GΔ{right arrow over (w)}={right arrow over (F)} (Eqn. 31)
where G=[{right arrow over (g₀^T)}, . . . , {right arrow over (g_n^T)}] is a matrix comprising n samples of the score function g, {right arrow over (F^T)}=[F₀, . . . , F_n] is the a vector of performance function samples, and n is a number of samples that should be equal or greater of the number of the parameters w_i. While the methodology of Eqn. 29-Eqn. 31 may be computationally expensive, it may help dealing with “plato”-like landscapes of the performance function.
Signal Processing Apparatus

[0156] In one or more implementations, the generalized learning framework described supra may enable implementing signal processing blocks with tunable parameters w. Using the learning block framework that provides analytical description of individual types of signal processing block may enable it to automatically calculate the appropriate score function

[0157]

\frac{\partial h (x ❘ y)}{\partial w_{i}}

for individual parameters of the block. Using the learning architecture described in FIG. 3, a generalized implementation of the learning block may enable automatic changes of learning parameters w by individual blocks based on high level information about the subtask for each block. A signal processing system comprising one or more of such generalized learning blocks may be capable of solving different learning tasks useful in a variety of applications without substantial intervention of the user. In some implementations, such generalized learning blocks may be configured to implement generalized learning framework described above with respect to FIGS. 3-4A and delivered to users. In developing complex signal processing systems, the user may connect different blocks, and/or specify a performance function and/or a learning algorithm for individual blocks. This may be done, for example, with the special graphical user interface (GUI), which may allow blocks to be connected using a mouse or other input peripheral by clicking on individual blocks and using defaults or choosing the performance function and a learning algorithm from a predefined list. Users may not need to re-create a learning adaptation framework and may rely on the adaptive properties of the generalized learning blocks that adapt to the particular learning task. When the user desires to add a new type of block into the system, he may need to describe it in a way suitable to automatically calculate a score functions for individual parameters.

[0158] FIG. 5 illustrates one exemplary implementation of a robotic apparatus 500 comprising adaptive controller apparatus 512. In some implementations, the adaptive controller 520 may be configured similar to the apparatus 300 of FIG. 3 and may comprise generalized learning block (e.g., the block 420), configured, for example according to the framework described above with respect to FIG. 4, supra, is shown and described. The robotic apparatus 500 may comprise the plant 514, corresponding, for example, to a sensor block and a motor block (not shown). The plant 514 may provide sensory input 502, which may include a stream of raw sensor data (e.g., proximity, inertial, terrain imaging, and/or other raw sensor data) and/or preprocessed data (e.g., velocity, extracted from accelerometers, distance to obstacle, positions, and/or other preprocessed data) to the controller apparatus 520. The learning block of the controller 520 may be configured to implement reinforcement learning, according to, in some implementations Eqn. 13, based on the sensor input 502 and reinforcement signal 504 (e.g., obstacle collision signal from robot bumpers, distance from robotic arm endpoint to the desired position), and may provide motor commands 506 to the plant. The learning block of the adaptive controller apparatus (e.g., the apparatus 520 of FIG. 5) may perform learning parameter (e.g., weight) adaptation using reinforcement learning approach without having any prior information about the model of the controlled plant (e.g., the plant 514 of FIG. 5). The reinforcement signal r(t) may inform the adaptive controller that the previous behavior led to “desired” or “undesired” results, corresponding to positive and negative reinforcements, respectively. While the plant 514 must be controllable (e.g., via the motor commands in FIG. 5) and the control system may be required to have access to appropriate sensory information (e.g., the data 502 in FIG. 5), detailed knowledge of motor actuator dynamics or of structure and significance of sensory signals may not be required to be known by the controller apparatus 520.

[0159] It will be appreciated by those skilled in the arts that the reinforcement learning configuration of the generalized learning controller apparatus 520 of FIG. 5 is used to illustrate one exemplary implementation of the disclosure and myriad other configurations may be used with the generalized learning framework described herein. By way of example, the adaptive controller 520 of FIG. 5 may be configured for: (i) unsupervised learning for performing target recognition, as illustrated by the adaptive controller 520_3 of FIG. 5A, receiving sensory input and output signals (x,y) 522_3; (ii) supervised learning for performing data regression, as illustrated by the adaptive controller 520_3 receiving output signal 522_1 and teaching signal 504_1 of FIG. 5A; and/or (iii) simultaneous supervised and unsupervised learning for performing platform stabilization, as illustrated by the adaptive controller 520_2 of FIG. 5A, receiving input 522_2 and learning 504_2 signals.

[0160] FIGS. 5B-5C illustrate dynamic tasking by a user of the adaptive controller apparatus (e.g., the apparatus 320 of FIG. 3A or 520 of FIG. 5, described supra) in accordance with one or more implementations.

[0161] A user of the adaptive controller 520_4 of FIG. 5B may utilize a user interface (textual, graphics, touch screen, etc.) in order to configure the task composition of the adaptive controller 520_4, as illustrated by the example of FIG. 5B. By way of illustration, at one instance for one application the adaptive controller 520_4 of FIG. 5B may be configured to perform the following tasks: (i) task 550_1 comprising sensory compressing via unsupervised learning; (ii) task 550_2 comprising reward signal prediction by a critic block via supervised learning; and (ii) task 550_3 comprising implementation of optimal action by an actor block via reinforcement learning. The user may specify that task 550_1 may receive external input {X} 542, comprising, for example raw audio or video stream, output 546 of the task 550_1 may be routed to each of tasks 550_2, 550_3, output 547 of the task 550_2 may be routed to the task 550_3; and the external signal {r} (544) may be provided to each of tasks 550_2, 550_3, via pathways 544_1, 544_2, respectively as illustrated in FIG. 5B. In the implementation illustrated in FIG. 5B, the external signal {r} may be configured as {r}={y^d(t), r(t)}, the pathway 544_1 may carry the desired output y^d(t), while the pathway 544_2 may carry the reinforcement signal r(t).

[0162] Once the user specifies the learning type(s) associated with each task (unsupervised, supervised and reinforcement, respectively) the controller 520_4 of FIG. 5B may automatically configure the respective performance functions, without further user intervention. By way of illustration, performance function F_uof the task 550_1 may be determined based on (i) ‘sparse coding’; and/or (ii) maximization of information. Performance function F_sof the task 550_2 may be determined based on minimizing distance between the actual output 547 (prediction pr) d(r, pr) and the external reward signal r 544_1. Performance function F_rof the task 550_3 may be determined based on maximizing the difference F=r−pr. In some implementations, the end user may select performance functions from a predefined set and/or the user may implement a custom task.

[0163] At another instance in a different application, illustrated in FIG. 5C, the controller 520_4 may be configured to perform a different set of task: (i) the task 550_1, described above with respect to FIG. 5B; and task 552_4, comprising pattern classification via supervised learning. As shown in FIG. 5C, the output of task 550_1 may be provided as the input 566 to the task 550_4.

[0164] Similarly to the implementation of FIG. 5B, once the user specifies the learning type(s) associated with each task (unsupervised and supervised, respectively) the controller 520_4 of FIG. 5C may automatically configure the respective performance functions, without further user intervention. By way of illustration, the performance function corresponding to the task 550_4 may be configured to minimize distance between the actual task output 568 (e.g., a class {Y} to which a sensory pattern belongs) and human expert supervised signal 564 (the correct class y^d).

[0165] Generalized learning methodology described herein may enable the learning apparatus 520_4 to implement different adaptive tasks, by, for example, executing different instances of the generalized learning method, individual ones configured in accordance with the particular task (e.g., tasks 550_1, 550_2, 550_3, in FIG. 5B, and 550_4, 550_5 in FIG. 5C). The user of the apparatus may not be required to know implementation details of the adaptive controller (e.g., specific performance function selection, and/or gradient determination). Instead, the user may ‘task’ the system in terms of task functions and connectivity.

Partitioned Network Apparatus

[0166] FIGS. 6A-6B illustrate exemplary implementations of reconfigurable partitioned neural network apparatus comprising generalized learning framework, described above. The network 600 of FIG. 6A may comprise several partitions 610, 620, 630, comprising one or more of nodes 602 receiving inputs 612 {X} via connections 604, and providing outputs via connections 608.

[0167] In one or more implementations, the nodes 602 of the network 600 may comprise spiking neurons (e.g., the neurons 730 of FIG. 9, described below), the connections 604, 608 may be configured to carry spiking input into neurons, and spiking output from the neurons, respectively. The neurons 602 may be configured to generate post-synaptic spikes (as described in, for example, U.S. patent application Ser. No. 13/152,105 filed on Jun. 2, 2011, and entitled “APPARATUS AND METHODS FOR TEMPORALLY PROXIMATE OBJECT RECOGNITION”, incorporated by reference herein in its entirety) which may be propagated via feed-forward connections 608.

[0168] In some implementations, the network 600 may comprise artificial neurons, such as for example, spiking neurons described by U.S. patent application Ser. No. 13/152,105 filed on Jun. 2, 2011, and entitled “APPARATUS AND METHODS FOR TEMPORALLY PROXIMATE OBJECT RECOGNITION”, incorporated supra, artificial neurons with sigmoidal activation function, binary neurons (perceptron), radial basis function units, and/or fuzzy logic networks.

[0169] Different partitions of the network 600 may be configured, in some implementations, to perform specialized functionality. By way of example, the partition 610 may adapt raw sensory input of a robotic apparatus to internal format of the network (e.g., convert analog signal representation to spiking) using for example, methodology described in U.S. patent application Ser. No. 13/314,066, filed Dec. 7, 2001, entitled “NEURAL NETWORK APPARATUS AND METHODS FOR SIGNAL CONVERSION”, incorporated herein by reference in its entirety. The output {Y1} of the partition 610 may be forwarded to other partitions, for example, partitions 620, 630, as illustrated by the broken line arrows 618, 618_1 in FIG. 6A. The partition 620 may implement visual object recognition learning that may require training input signal y^d_j(t) 616, such as for example an object template and/or a class designation (friend/foe). The output {Y2}) of the partition 620 may be forwarded to another partition (e.g., partition 630) as illustrated by the dashed line arrow 628 in FIG. 6A. The partition 630 may implement motor control commands required for the robotic arm to reach and grasp the identified object, or motor commands configured to move robot or camera to a new location, which may require reinforcement signal r(t) 614. The partition 630 may generate the output {Y} 638 of the network 600 implementing adaptive controller apparatus (e.g., the apparatus 520 of FIG. 5). The homogeneous configuration of the network 600, illustrated in FIG. 6A, may enable a single network comprising several generalized nodes of the same type to implement different learning tasks (e.g., reinforcement and supervised) simultaneously.

[0170] In one or more implementations, the input 612 may comprise input from one or more sensor sources (e.g., optical input {Xopt} and audio input {Xaud}) with each modality data being routed to the appropriate network partition, for example, to partitions 610, 630 of FIG. 6A, respectively.

[0171] The homogeneous nature of the network 600 may enable dynamic reconfiguration of the network during its operation. FIG. 6B illustrates one exemplary implementation of network reconfiguration in accordance with the disclosure. The network 640 may comprise partition 650, which may be configured to perform unsupervised learning task, and partition 660, which may be configured to implement supervised and reinforcement learning simultaneously. As shown in FIG. 6B, the partitions 650, 660 are configured to receive input signal {X1}. In some implementations, the network configuration of FIG. 6B may be used to perform signal separation tasks by the partition 650 and signal classification tasks by the partition 660. The partition 650 may be operated according to unsupervised learning rule and may generate output {Y3} denoted by the arrow 658 in FIG. 6B. The partition 660 may be operated according to a combined reinforcement and supervised rule, may receive supervised and reinforcement input 656, and/or may generate the output {Y4} 668.

[0172] FIG. 6C illustrates an implementation of dynamically configured neuronal network 660. The network 660 may comprise partitions 670, 680, 690. The partition 670 may be configured to process (e.g., to perform compression, encoding, and/or other processes) the input signal 662 via an unsupervised learning task and to generate processed output {Y5}. The partition 680 may be configured to receive the output 678 of the partition 670 and to further process it, e.g., perform object recognition via supervised learning. Operation of the partition 680 during learning may be aided by training signal 674 r(t), comprising supervisory signal y^d(t), such as for example, examples of desired object to be recognized.

[0173] The partition 690 may be configured to receive the output 688 of the partition 680 and to further process it (e.g., perform adaptive control) via a combination of reinforcement and supervised learning. In one or more implementations, the learning rule employed by the partition 690 may comprise a hybrid learning rule. The hybrid learning rule may comprise reinforcement and supervised learning combination, as described, for example, by Eqn. 34 below. Operation of the partition 690 during learning in this implementation may be aided by teaching signal 694 r(t). The teaching signal 694 r(t) may comprise (1) supervisory signal y^d(t), which may provide, for example, desired locations (waypoints) for an autonomous robotic apparatus; and (2) reinforcement signal r(t), which may provide, for example, how close the apparatus navigates with respect to these waypoints.

[0174] The dynamic network learning reconfiguration illustrated in FIGS. 6A-6C may be used, for example, in an autonomous robotic apparatus performing exploration tasks (e.g., a pipeline inspection autonomous underwater vehicle (AUV), or space rover, explosive detection, and/or mine exploration). When certain functionality of the robot is not required (e.g., the arm manipulation function) the available network resources (i.e., the nodes 602) may be reassigned to perform different tasks. Such reuse of network resources may be traded for (i) smaller network processing apparatus, having lower cost, size and consuming less power, as compared to a fixed pre-determined configuration; and/or (ii) increased processing capability for the same network capacity.

[0175] As is appreciated by those skilled in the arts, the reconfiguration methodology described supra may comprise a static reconfiguration, where particular node populations are designated in advance for specific partitions (tasks); a dynamic reconfiguration, where node partitions are determined adaptively based on the input information received by the network and network state; and/or a semi-static reconfiguration, where static partitions are assigned predetermined life-span.

Spiking Network Apparatus

[0176] Referring now to FIG. 7, one implementation of spiking network apparatus for effectuating the generalized learning framework of the disclosure is shown and described in detail. The network 700 may comprise at least one stochastic spiking neuron 730, operable according to, for example, a Spike Response Model, and configured to receive n-dimensional input spiking stream X(t) 702 via n− input connections 714. In some implementations, the n− dimensional spike stream may correspond to n-input synaptic connections into the neuron. As shown in FIG. 7, individual input connections may be characterized by a connection parameter 712 w_ijthat is configured to be adjusted during learning. In one or more implementations, the connection parameter may comprise connection efficacy (e.g., weight). In some implementations, the parameter 712 may comprise synaptic delay. In some implementations, the parameter 712 may comprise probabilities of synaptic transmission.

[0177] The following signal notation may be used in describing operation of the network 700, below:

[0178]

y (t) = \sum_{i} δ (t - t_{i})

denotes the output spike pattern, corresponding to the output signal 708 produced by the control block 710 of FIG. 3, where t_idenotes the times of the output spikes generated by the neuron;

[0179]

y^{d} (t) = \sum_{t_{i}} δ (t - t_{i}^{d})

denotes the teaching spike pattern, corresponding to the desired (or reference) signal that is part of external signal 404 of FIG. 4, where t_i^ddenotes the times when the spikes of the reference signal are received by the neuron;

[0180]

y^{+} (t) = \sum_{t_{i}} δ (t - t_{i}^{+}); y^{-} (t) = \sum_{t_{i}} δ (t - t_{i}^{-})

denotes the reinforcement signal spike stream, corresponding to signal 304 of FIG. 3. and external signal 404 of FIG. 4, where t_i⁺,t_i⁻ denote the spike times associated with positive and negative reinforcement, respectively.

[0181] In some implementations, the neuron 730 may be configured to receive training inputs, comprising the desired output (reference signal) y^d(t) via the connection 704. In some implementations, the neuron 730 may be configured to receive positive and negative reinforcement signals via the connection 704.

[0182] The neuron 730 may be configured to implement the control block 710 (that performs functionality of the control block 310 of FIG. 3) and the learning block 720 (that performs functionality of the control block 320 of FIG. 3, described supra.) The block 710 may be configured to receive input spike trains X(t), as indicated by solid arrows 716 in FIG. 7, and to generate output spike train y(t) 708 according to a Spike Response Model neuron which voltage v(t) is calculated as:

[0183]

v (t) = \sum_{i, k} w_{i} \cdot α (t - t_{i}^{k}),

where w_iw_irepresents weights of the input channels, t_i^krepresents input spike times, and α(t)=(t/τ_α)e^1−(t/τ^α⁾represents an alpha function of postsynaptic response, where τ_α represents time constant (e.g., 3 ms and/or other times). A probabilistic part of a neuron may be introduced using the exponential probabilistic threshold. Instantaneous probability of firing λ(t) may be calculated as λ(t)=e^{(v(t)−Th)κ}, where Th represents a threshold value, and κ represents stochasticity parameter within the control block. State variables q (probability of firing λ(t) for this system) associated with the control model may be provided to the learning block 720 via the pathway 705. The learning block 720 of the neuron 730 may receive the output spike train y(t) via the pathway 708_1. In one or more implementations (e.g., unsupervised or reinforcement learning), the learning block 720 may receive the input spike train (not shown). In one or more implementations (e.g., supervised or reinforcement learning) the learning block 720 may receive the learning signal, indicated by dashed arrow 704_1 in FIG. 7. The learning block determines adjustment of the learning parameters w, in accordance with any methodologies described herein, thereby enabling the neuron 730 to adjust, inter alia, parameters 712 of the connections 714.
Exemplary Methods

[0184] Referring now to FIG. 8A one exemplary implementation of the generalized learning method of the disclosure for use with, for example, the learning block 420 of FIG. 4, is described in detail. The method 800 of FIG. 8A may allow the learning apparatus to: (i) implement different learning rules (e.g., supervised, unsupervised, reinforcement, and/or other learning rules); and (ii) simultaneously support more than one rule (e.g., combination of supervised, unsupervised, reinforcement rules described, for example by Eqn. 18) using the same hardware/software configuration.

[0185] At step 802 of method 800 the input information may be received. In some implementations (e.g., unsupervised learning) the input information may comprise the input signal x(t), which may comprise raw or processed sensory input, input from the user, and/or input from another part of the adaptive system. In one or more implementations, the input information received at step 802 may comprise learning task identifier configured to indicate the learning rule configuration (e.g., Eqn. 18) that should be implemented by the learning block. In some implementations, the indicator may comprise a software flag transited using a designated field in the control data packet. In some implementations, the indicator may comprise a switch (e.g., effectuated via a software commands, a hardware pin combination, or memory register).

[0186] At step 804, learning framework of the performance determination block (e.g., the block 424 of FIG. 4) may be configured in accordance with the task indicator. In one or more implementations, the learning structure may comprise, inter alia, performance function configured according to Eqn. 18. In some implementations, parameters of the control block, e.g., number of neurons in the network, may be configured as well.

[0187] At step 808, the status of the learning indicator may be checked to determine whether additional learning input may be provided. In some implementations, the additional learning input may comprise reinforcement signal r(t). In some implementations, the additional learning input may comprise desired output (teaching signal) y^d(t), described above with respect to FIG. 4.

[0188] If instructed, the external learning input may be received by the learning block at step 808.

[0189] At step 812, the value of the present performance may be computed using the performance function F(x,y,r) configured at the prior step. It will be appreciated by those skilled in the arts, that when performance function is evaluated for the first time (according, for example to Eqn. 10) and the controller output y(t) is not available, a pre-defined initial value of y(t) (e.g., zero) may be used instead.

[0190] At step 814, gradient g(t) of the score function (logarithm of the conditional probability of output) may be determined by the GD block (e.g., The block 422 of FIG. 4) according, for example, to methodology described in co-owned and co-pending U.S. patent application Ser. No. 13/487,533 entitled “STOCHASTIC SPIKING NETWORK LEARNING APPARATUS AND METHODS”, filed Jun. 4, 2012, incorporated supra.

[0191] At step 816, learning parameter w update may be determined by the Parameter Adjustment block (e.g., block 426 of FIG. 4) using the performance function F and the gradient g, determined at steps 812, 814, respectively. In some implementations, the learning parameter update may be implemented according to Eqns. 22-31.

[0192] At step 818, the control output y(t) of the controller may be updated using the input signal x(t) (received via the pathway 820) and the updated learning parameter Δw.

[0193] FIG. 8B illustrates a method of dynamic controller reconfiguration based on learning tasks, in accordance with one or more implementations.

[0194] At step 822 of method 830, the input information may be received. As described above with respect to FIG. 8A, in some implementations, the input information may comprise the input signal x(t) and/or learning task identifier configured to indicate the learning rule configuration (e.g., Eqn. 18) that should be implemented buy the learning block.

[0195] At step 834, the controller partitions (e.g., the partitions 520_6, 520_7, 520_8, 520_9, of FIG. 5B, and/or partitions 610, 620, 630 of FIG. 6A) may be configured in accordance with the learning rules (e.g., supervised, unsupervised, reinforcement, and/or other learning rules) corresponding to the task received at step 832. Subsequently, individual partitions may be operated according to, for example, the method 800 described with respect to FIG. 8A.

[0196] At step 836, a check may be performed as to whether the new task (or task assortment) is received. If no new tasks are received, the method may proceed to step 834. If new tasks are received that require controller repartitioning, such as for example, when exploration robotic device may need to perform visual recognition tasks when stationary, the method may proceed to step 838.

[0197] At step 838, current partition configuration (e.g., input parameter, state variables, neuronal composition, connection map, learning parameter values and/or rules, and/or other information associated with the current partition configuration) may be saved in a nonvolatile memory.

[0198] At step 840, the controller state and partition configurations may reset and the method proceeds to step 832, where a new partition set may be configured in accordance with the new task assortment received at step 836. Method 800 of FIG. 8B may enable, inter alia, dynamic partition reconfiguration as illustrated in FIGS. 5B, 6A-6B, supra.

Performance Results

[0199] FIGS. 9A through 11 present performance results obtained during simulation and testing by the Assignee hereof, of exemplary computerized spiking network apparatus configured to implement dynamic reconfiguration framework described above with respect to FIGS. 4-6B. The exemplary apparatus, in one implementation, comprises learning block (e.g., the block 420 of FIG. 4) that implemented using spiking neuronal network 700, described in detail with respect to FIG. 7, supra.

[0200] The average performance (e.g. the function custom character

_x,y,raverage of Eqn. 2) may be determined over a time interval Tav that is configured in accordance with the specific application. In one or more implementations, the Tav may be configured to exceed the rate of output y(t) by a factor of 5 to 10000. In one such implementation, the spike rate may comprise 70 Hz output, and the averaging time may be selected at about 100 s

Combined Supervised and Reinforcement Learning Tasks

[0201] In some implementations, in accordance with the framework described by, inter alia, Eqn. 18, the network 700 of the adaptive learning apparatus may be configured to implement supervised and reinforcement learning concurrently. Accordingly, the cost function F_sr, corresponding to a combination of supervised and reinforcement learning tasks, may be expressed as follows:
F_sr=aF_sup+bF_reinf,
where F_supand F_reinfare the cost functions for the supervised and reinforcement learning tasks, respectively, and a, b are coefficients determining relative contribution of each cost component to the combined cost function. By varying the coefficients a,b during different simulation runs of the spiking network, effects of relative contribution of each learning method on the network learning performance may be investigated.

[0202] In some implementations, such as those involving classification of spiking input patterns derived from speech data in order to determine speaker identity, the supervised learning cost function may comprise a product of the desired spiking pattern y^d(t) (belonging to a particular speaker) with filtered output spike train y(t). In some implementations, such as those involving a low pass exponential filter kernel, the F_supmay be computed using the following expression:

[0203]

\begin{matrix} F_{\sup} = \int_{- \infty}^{t} (y (s) ⅇ^{- (t - s) / τ_{d}} ⅆ s) (y^{d} (t) - C), & (Eqn . 32) \end{matrix}

where τ_dis the trace decay constant, and C is the bias constant configured to introduce penalty associated with extra activity of the neuron does not corresponding to the desired spike train.

[0204] The cost function for reinforcement learning may be determined as a sum of positive and negative reinforcement contributions that are received by the neuron via two spiking channels (y⁺(t) and y⁻(t)):
F_reinf=y⁺(t)−y⁻(t). (Eqn. 33)
Reinforcement may be generated according to the task that is being solved by the neuron.

[0205] A composite cost function for simultaneous reinforcement and supervised learning may be constructed using a linear combination of contributions provided by Eqns. 28-29:

[0206]

\begin{matrix} \begin{matrix} F = {aF}_{\sup} + {bF}_{reinf} \\ = a \int_{- \infty}^{t} (\sum_{i} δ (t t_{i}) ⅇ^{- (t - s) / τ_{d}} ⅆ s) (\sum_{i} δ (t - t_{i}^{d}) ⅆ t - C) + \\ b (\sum_{j} δ (t - t_{j}^{+}) ⅆ t - \sum_{j} δ (t - t_{j}^{-}) ⅆ t) \end{matrix} & (Eqn . 1) \end{matrix}

Using the description of Eqn. 34, the spiking neuron network (e.g., the network 700 of FIG. 7) may be configured to maximize the combined cost function F_srusing one or more of the methodologies described in a co-owned and co-pending U.S. patent application Ser. No. 13/487,499 entitled “STOCHASTIC APPARATUS AND METHODS FOR IMPLEMENTING GENERALIZED LEARNING RULES” filed contemporaneously herewith, and incorporated supra.

[0207] FIGS. 9A-9F present data related to simulation results of the spiking network (e.g., the network 700 of FIG. 7) configured in accordance with supervised and reinforcement rules described with respect to Eqn. 34, supra. The input into the network (e.g., the neuron 730 of FIG. 7) is shown in the panel 900 of FIG. 9A and may comprise a single 100-dimensional input spike stream of length 600 ms. The horizontal axis denotes elapsed time in milliseconds, the vertical axis denotes each input dimension (e.g., the connection 714 in FIG. 7), each row corresponds to the respective connection, and dots denote individual spikes within each row. The panel 902 in FIG. 9A, illustrates supervisor signal, comprising a sparse 600 ms-long stream of training spikes, delivered to the neuron 730 via the connection 704, in FIG. 7. Each dot in the panel 902 denotes the desired output spike y^d(t).

[0208] The reinforcement signal may be provided to the neuron according to the following protocol:

- [0209] If the network (e.g., the network 700 of FIG. 7) generates one spike within a [0,50 ms] time window from the onset of pre-synaptic input, then it receives the positive reinforcement spike, illustrated in the panel 904 in FIG. 9A.
- [0210] If the network does not generate outputs during that interval or generates more than one spike, then it receives negative reinforcement spike, illustrated in the panel 906 in FIG. 9A.
- [0211] If the network is active (generates output spikes) during time intervals [200 ms, 250 ms] and [400 ms, 450 ms], then it receives negative reinforcement spike.
- [0212] Reinforcement signals are not generated during all other intervals.
  A maximum reinforcement configuration may comprise (i) one positive reinforcement spike and (ii) no negative reinforcement spikes. A maximum negative reinforcement configuration may comprise (i) no positive reinforcement spikes and (ii) three negative reinforcement spikes.

[0213] The output activity (e.g., the post-synaptic spikes y(t)) of the network 660 prior to learning, illustrated in the panel 910 of FIG. 9A, shows that output 910 comprises few output spikes generated at random times that do not display substantial correlation with the supervisor input 902. The reinforcement signals 904, 906 show that the untrained neuron does not receive positive reinforcement (manifested by the absence of spikes in the panel 904) and receives two spikes of negative reinforcement (shown by the dots at about 50 ms and about 450 ms in the panel 906) because the neuron is quiet during [0 ms-50 ms] interval and it spikes during [400 ms-450 ms] interval.

[0214] FIG. 9B illustrates output activity of the network 700, operated according to the supervised learning rule, which may be effected by setting the coefficients (a,b) of Eqn. 34 as follows: a=1, b=0. Different panels in FIG. 9B present the following data: panel 900 depicts pre-synaptic input into the network 700 of FIG. 7; panel 912 depicts supervisor (training) spiking input; and panels 914, 916 depict positive and negative reinforcement input spike patterns, respectively.

[0215] The output of the network shown in the panel 910 displays a better correlation (compared to the output 910 in FIG. 9A) of the network with the supervisor input. Data shown in FIG. 9B confirm that while the network learns to repeat the supervisor spike pattern it fails to perform reinforcement task (receives 3 negative spikes−maximum possible reinforcement).

[0216] FIG. 9C illustrates output activity of the network, operated according to the reinforcement learning rule, which may be effected by setting the coefficients (a,b) of Eqn. 34 as follows: a=0, b=1. Different panels in FIG. 9C present the following data: panel 900 depicts pre-synaptic input into the network; panel 922 depicts supervisor (training) spiking input; panels 924, 926 depict positive and negative reinforcement input spike patterns, respectively.

[0217] The output of the network, shown in the panel 920, displays no visible correlation with the supervisor input, as expected. At the same time, network receives maximum possible reinforcement (one positive spike and no negative spikes) illustrated by the data in panels 924, 926 in FIG. 9C.

[0218] FIG. 9D illustrates output activity of the network 700, operated according to the reinforcement learning rule augmented by the supervised learning, effected by setting the coefficients (a,b) of Eqn. 34 as follows: a=0.5, b=1. Different panels in FIG. 9D present the following data: panel 900 depicts pre-synaptic input into the network; panel 932 depicts supervisor (training) spiking input; and panels 934, 936 depict positive and negative reinforcement input spike patterns, respectively.

[0219] The output of the network shown in the panel 930 displays a better correlation (compared to the output 910 in FIG. 9A) of the network with the supervisor input. Data presented in FIG. 9D show that network receives maximum possible reinforcement (panel 934, 936) and begins starts to reproduce some of the supervisor spikes (at around 400 ms and 470 ms) when these do not contradict with the reinforcement learning signals. However, not all of the supervised spikes are echoed in the network output 930, and additional spikes are present (e.g., the spike at about 50 ms), compared to the supervisor input 932.

[0220] FIG. 9E illustrates data obtained for an equal weighting of supervised and reinforcement learning: (a=1; b=1 in of Eqn. 34). The reinforcement traces 944, 946 of FIG. 9E show that the network receives maximum reinforcement. The network output (trace 940) contains spikes corresponding to a larger portion of the supervisor input (the trace 942) when compared to the data shown by the trace 930 of FIG. 9E, provided the supervisor input does not contradict the reinforcement input. However, not all of the supervised spikes of FIG. 9E are echoed in the network output 940, and additional spikes are present (e.g., the spike at about 50 ms), compared to the supervisor input 942.

[0221] FIG. 9F illustrates output activity of the network, operated according to the supervised learning rule augmented by the reinforcement learning, effected by setting the coefficients (a,b) of Eqn. 34 as follows: a=1, b=0.4. The output of the network shown in the panel 950 displays a better correlation with the supervisor input (the panel 952), as compared to the output 940 in FIG. 9E. The network output (950) is shown to repeat the supervisor input (952) event when the latter contradicts with the reinforcement learning signals (traces 954, 956). The reinforcement data (956) of FIG. 9F show that while the network receive maximum possible reinforcement (trace 954), it is penalized (negative spike at 450 ms on trace 956) for generating output that is inconsistent with the reinforcement rules.

Combined Supervised and Unsupervised Learning Tasks

[0222] In some implementations, in accordance with the framework described by, inter alia, Eqn. 18, the cost function F_su, corresponding to a combination of supervised and unsupervised learning tasks, may be expressed as follows:
F_su=aF_sup+c(−F_unsup). (Eqn. 35)
where F_supis described by, for example, Eqn. 9, F_unsupis the cost function for the unsupervised learning tasks, and a,c are coefficients determining relative contribution of each cost component to the combined cost function. By varying the coefficients a,c during different simulation runs of the spiking network, effects of relative contribution of individual learning methods on the network learning performance may be investigated.

[0223] In order to describe the cost function of the unsupervised learning, a Kullback-Leibler divergence between two point processes may be used:
F_unsup=ln(p(t))−ln(p^d(t)) (Eqn. 36)
where p(t) is the probability of the actual spiking pattern generated by the network, and p^d(t) is the probability of a spiking pattern generated by Poisson process. The unsupervised learning task in this implementation may serve to minimize the function of Eqn. 36 such that when the two probabilities p(t)=p^d(t) are equal at all times, then the network may generate output spikes according to Poisson distribution.

[0224] Accordingly, the composite cost function for simultaneous unsupervised and supervised learning may be expressed as a linear combination of Eqn. 35 and Eqn. 36:

[0225]

\begin{matrix} F = {aF}_{\sup} + c (- F_{unsup}) = a [\int_{\infty}^{t} (\int_{\infty}^{t} (\sum_{i} δ (t - t_{i}) ⅇ^{- \frac{t - s}{τ_{d}}} ⅆ s) \sum_{i} δ (t - t_{i}^{d}) ⅆ t) - C] + c (\ln (p^{d} (t)) - \ln (p (t))) & (Eqn . 37) \end{matrix}

[0226] Referring now to FIGS. 8A-8C, data related to simulation results of the spiking network 700 may be configured in accordance with supervised and unsupervised rules described with respect to Eqn. 37, supra. The input into the neuron 730 is shown in the panel 1000 of FIG. 10A-10C and may comprise a single 100-dimensional input spike stream of length 600 ms. The horizontal axis denotes elapsed time in ms, the vertical axis denotes each input dimension (e.g., the connection 714 in FIG. 7), and dots denote individual spikes.

[0227] FIG. 10A illustrates output activity of the network (e.g., network 700 of FIG. 7), operated according to the supervised learning rule, which is effected by setting the coefficients (a,c) of Eqn. 37 as follows: a=1, b=0. The panel 1002 in FIG. 10A, illustrates supervisor signal, comprising a sparse 600 ms-long stream of training spikes, delivered to the neuron 730 via the connection 704 of FIG. 7. Dots in the panel 1002 denotes the desired output spike y^d(t).

[0228] The output activity (the post-synaptic spikes y(t)) of the network, illustrated in the panel 1010 of FIG. 10A, shows that the network successfully repeats the supervisor spike pattern which does not behave as a Poisson process with 60 Hz firing rate.

[0229] FIG. 10B illustrates output of the network, where supervised learning rule is augmented by 15% fraction of Poisson spikes, effected by setting the coefficients (a,c) of Eqn. 37 as follows: a=1, c=0.15. The output activity of the network, illustrated in the panel 1020 of FIG. 10B, shows that the network successfully repeats the supervisor spike pattern 1022 and further comprises additional output spikes are randomly distributed and the total number of spikes is consistent with eh desired firing rate.

[0230] FIG. 10C illustrates output of the network 700, where supervised learning rule is augmented by 80% fraction of Poisson spikes, effected by setting the coefficients (a,c) of Eqn. 37 as follows: a=1, c=0.8. The output activity of the network 700, illustrated in the panel 1030 of FIG. 10B, shows that the network output is characterized by the desired Poisson distribution and the network tries to repeat the supervisor pattern, as shown by the spikes denoted with circles in the panel 1030 of FIG. 10C.

Combined Supervised, Unsupervised, and Reinforcement Learning Tasks

[0231] In some implementations, in accordance with the framework described by, inter alia, Eqn. 18, the cost function F_sur, representing a combination of supervised, unsupervised, and/or reinforcement learning tasks, may be expressed as follows:
F_sur=aF_sup+bF_reinf+c(−F_unsup) (Eqn. 38)

[0232] Referring now to FIG. 11, data related to simulation results of the spiking network configured in accordance with supervised, reinforcement, and unsupervised rules described with respect to Eqn. 38, supra. The network learning rules comprise equally weighted supervised and reinforcement rules augmented by a 15% fraction of Poisson spikes, representing unsupervised learning. Accordingly, the weight coefficients of Eqn. 38 are set as follows: a=1; b=1; c=0.1.

[0233] In FIG. 11, panel 1100 depicts the pre-synaptic input comprising a single 100-dimensional input spike stream of length 600 ms; panel 902 depicts the supervisor input; and panels 904, 906 depict positive and negative reinforcement inputs into the network 700 of FIG. 7, respectively.

[0234] The network output, presented in panel 1110 in FIG. 11, comprises spikes that generated based on (i) reinforcement learning (the first spike at 50 ms leads to the positive reinforcement spike at 60 ms in the panel 1104); (ii) supervised learning (e.g., spikes between 400 ms and 500 ms interval); and (iii) random activity spikes due to unsupervised learning (e.g., spikes between 100 ms and 200 ms interval).

Dynamic Reconfiguration and HLND

[0235] In some implementations, the dynamic reconfiguration methodology described herein may be effectuated using high level neuromorphic language description (HLND) described in detail in co-pending and co-owned U.S. patent application Ser. No. 13/385,938 entitled “TAG-BASED APPARATUS AND METHODS FOR NEURAL NETWORKS” filed on Mar. 15, 2012, incorporated supra.

[0236] In accordance with some implementations, individual elements of the network (i.e., nodes, extensions, connections, I/O ports) may be assigned at least one unique tag to facilitate the HLND operation and disambiguation. The tags may be used to identify and/or refer to the respective network elements (e.g., a subset of nodes of the network that is within a specified area).

[0237] In some implementations, tags may be used to form a dynamic grouping of the nodes so that these dynamically created node groups may be connected with one another. That is, a node group tag may be used to identify a subset of nodes and/or to create new connections within the network. These additional tags may not create new instances of network elements, but may add tags to existing instances so that the additional tags are used to identify the tagged instances.

[0238] In some implementations, tags may be used to form a dynamic grouping of the nodes so that these dynamically created node groups may be connected with one another. That is, a node group tag may be used to identify a subset of nodes and/or to create new connections within the network, as described in detail below in connection with FIG. 13. These additional tags may not create new instances of network elements, but may add tags to existing instances so that the additional tags are used to identify the tagged instances.

[0239] FIG. 13 illustrates an exemplary implementation of using additional tags to identify tagged instances. The network node population 1300 may comprise one or more nodes 1302 (tagged as ‘MyNodes’), one or more nodes 1304 (tagged as ‘MyNodes’ and ‘Subset’), and/or other nodes. The dark triangles in the node population 1300 of FIG. 13 may denote the nodes 1302 tagged as ‘MyNodes’, while the black and white triangles may correspond to a subset of nodes 1304 that are tagged as ‘MyNodes’, and ‘Subset’.

[0240] Using the tag ‘MyNodes’, a node collection 1310 may be selected. The node collection 1310 may comprise individual ones of nodes 1302 and/or 1304 (see, e.g., FIG. 13). The node collection 1320 may represent nodes tagged as <‘MyNodes’ NOT ‘Subset’>. The node collection 1320 may comprise individual ones of the nodes 1302. The node collection 1330 may represent the nodes tagged as ‘Subset’. The node collection 1330 may comprise individual ones of the nodes 1304 (see, e.g., FIG. 13).

[0241] In some implementations, the HLND framework may use two types of tags, which may include string tags, numeric tags, and/or other tags. In some implementations, the nodes may comprise arbitrary user-defined tags. Numeric tags may include numeric identifier (ID) tags, spatial tags, and/or other tags.

[0242] In some implementations, nodes may comprise position tags and/or may have zero default extension. Such nodes may connect to co-located nodes. Connecting nodes with spatial tags may require overlap so that overlapping nodes may be connected.

[0243] As shown in FIG. 13, the tags may be used to identify a subset of the network. To implement this functionality, one or more Boolean operations may be used on tags. In some implementations, mathematical logical operations may be used with numerical tags. The < . . . > notation may identify a subset of the network, where the string encapsulated by the chevrons < > may define operations configured to identify and/or select the subset. By way of non-limiting illustration, <‘MyTag’> may select individual nodes from the network that have the tag ‘MyTag’; <‘MyTag1’ AND ‘MyTag2’> may select individual members from the network that have both the ‘MyTag1’ and the ‘MyTag2’ string tags; <‘MyTag1’ OR ‘MyTag2’> may select individual members from the network that has the ‘MyTag1’ or the ‘MyTag2’ string tags; <‘MyTag1’ NOT ‘MyTag2’> may select individual members from the network that have the string tag ‘MyTag1’ but do not have the string tag ‘MyTag2’; and <‘MyTag1’ AND MyMathFunction(Spatial Tags)<NumericalValue1> may select individual nodes from the network that have the string tag ‘MyTag1’ and the output provided by MyMathFunction (as applied the spatial coordinates of the node) is smaller than NumericalValue1. Note that this example assumes the existence of spatial tags, which are not mandatory, in accordance with various implementations.

[0244] In some implementations, the HLND may comprise a Graphical User Interface (GUI). The GUI may be configured to translate user actions (e.g., commands, selections, etc.) into HLND statements using appropriate syntax. The GUI may be configured to update the GUI to display changes of the network in response to the HLND statements. The GUI may provide a one-to-one mapping between the user actions in the GUI and the HLND statements. Such functionality may enable users to design a network in a visual manner by, inter alia, displaying the HLND statements created in response to user actions. The GUI may reflect the HLND statements entered, for example, using a text editor module of the GUI, into graphical representation of the network.

[0245] This “one-to-one mapping” may allow the same or similar information to be unambiguously represented in multiple formats (e.g., the GUI and the HLND statement), as different formats are consistently updated to reflect changes in the network design. This development approach may be referred to as “round-trip engineering”.

Exemplary Uses and Applications of Certain Aspects of the Disclosure

[0246] Generalized learning framework apparatuses and methods of the disclosure may allow for an improved implementation of single adaptive controller apparatus system configured to simultaneously perform a variety of control tasks (e.g., adaptive control, classification, object recognition, prediction, and/or clasterisation). Unlike traditional learning approaches, the generalized learning framework of the present disclosure may enable adaptive controller apparatus, comprising a single spiking neuron, to implement different learning rules, in accordance with the particulars of the control task.

[0247] In some implementations, the network may be configured and provided to end users as a “black box”. While existing approaches may require end users to recognize the specific learning rule that is applicable to a particular task (e.g., adaptive control, pattern recognition) and to configure network learning rules accordingly, a learning framework of the disclosure may require users to specify the end task (e.g., adaptive control). Once the task is specified within the framework of the disclosure, the “black-box” learning apparatus of the disclosure may be configured to automatically set up the learning rules that match the task, thereby alleviating the user from deriving learning rules or evaluating and selecting between different learning rules.

[0248] Even when existing learning approaches employ neural networks as the computational engine, each learning task is typically performed by a separate network (or network partition) that operate task-specific (e.g., adaptive control, classification, recognition, prediction rules, etc.) set of learning rules (e.g., supervised, unsupervised, reinforcement). Unused portions of each partition (e.g., motor control partition of a robotic device) remain unavailable to other partitions of the network even when the respective functionality of not needed (e.g., the robotic device remains stationary) that may require increased processing resources (e.g., when the stationary robot is performing recognition/classification tasks).

[0249] When learning tasks change during system operation (e.g., a robotic apparatus is stationary and attempts to classify objects), generalized learning framework of the disclosure may allow dynamic re-tasking of portions of the network (e.g., the motor control partition) at performing other tasks (e.g., visual pattern recognition, or object classifications tasks). Such functionality may be effected by, inter alia, implementation of generalized learning rules within the network which enable the adaptive controller apparatus to automatically use a new set of learning rules (e.g., supervised learning used in classification), compared to the learning rules used with the motor control task. These advantages may be traded for a reduced network complexity, size and cost for the same processing capacity, or increased network operational throughput for the same network size.

[0250] Generalized learning methodology described herein may enable different parts of the same network to implement different adaptive tasks (as described above with respect to FIGS. 5B-5C). The end user of the adaptive device may be enabled to partition network into different parts, connect these parts appropriately, and assign cost functions to each task (e.g., selecting them from predefined set of rules or implementing a custom rule). The user may not be required to understand detailed implementation of the adaptive system (e.g., plasticity rules and/or neuronal dynamics) nor is he required to be able to derive the performance function and determine its gradient for each learning task. Instead, the users may be able to operate generalized learning apparatus of the disclosure by assigning task functions and connectivity map to each partition.

[0251] Furthermore, the learning framework described herein may enable learning implementation that does not affect normal functionality of the signal processing/control system. By way of illustration, an adaptive system configured in accordance with the present disclosure (e.g., the network 600 of FIG. 6A or 700 of FIG. 7) may be capable of learning the desired task without requiring separate learning stage. In addition, learning may be turned off and on, as appropriate, during system operation without requiring additional intervention into the process of input-output signal transformations executed by signal processing system (e.g., no need to stop the system or change signals flow.

[0252] In some implementations, the dynamic reconfiguration methodology of the disclosure may be utilized to facilitate processing of signals when input signal (e.g., the signal 602 in FIG. 6A) composition changes (i.e., additional input channels (e.g., the channels 604 in FIG. 6A) may become available, such as for example, when additional electromagnetic (e.g., CCD) or pressure sensors are added in a surveillance application.

[0253] In some implementations, the dynamic reconfiguration methodology of the disclosure may be utilized to facilitate processing of signals when rule and/or teaching signal configuration may change, such as, for example, when a reinforcement rule and a reward signal are added to signal processing system that is operated under supervised learning rule, in order to effectuate a combination of supervised and reinforcement learning.

[0254] In one or more implementations, the dynamic reconfiguration may be activated when learning convergences not sufficiently fast and/or when the residual error (e.g., a distance between training signal and system output in supervised learning, and/or a distance to target in reinforcement learning) is above desired level. In such implementations, the reconfiguration may comprise reconfiguring one or more network partitions to comprise (i) fewer or more computation blocks (e.g., neurons); (ii) configure a different learning rule set (e.g., from supervised to a combination of supervised and reinforcement or from unsupervised to a combination of unsupervised and reinforcement learning, and/or any other applicable combination.

[0255] In some implementations, the dynamic reconfiguration may be effectuated when, for example, resource use in the processing system exceeds a particular (pre-set or dynamically determined) level. By way of illustration, when computational load of one partition is high (e.g., >50% or any other applicable level), and another partition is less loaded (e.g., below 50% or any other practical level), a portion of computational and/or memory blocks from the less loaded partition may be dynamically reassigned to the highly loaded partition. In a cluster configuration, when power (e.g., thermal dissipation or available electrical) in one partition (executed on one or more nodes) approaches maximum (e.g., >130% or any other applicable level), and another partition (operable on other node(s)) is less loaded (e.g., below 50% or any other practical level), a portion of computational load from the first partition may be allocated to the second partition; and/or one or more nodes from the less loaded partition may be reassigned to the more loaded partition.

[0256] In some implementations, dynamic reconfiguration may be effectuated due to change in hardware/software configuration of the signal processing system, such as in an event of failure (when some of computational and/or memory blocks become unavailable) and/or an upgrade (when additional computational blocks become available). In some implementations, the failure may comprise a node failure, a network failure, etc.

[0257] In one or more implementations, the generalized learning apparatus of the disclosure may be implemented as a software library configured to be executed by a computerized neural network apparatus (e.g., containing a digital processor). In some implementations, the generalized learning apparatus may comprise a specialized hardware module (e.g., an embedded processor or controller). In some implementations, the spiking network apparatus may be implemented in a specialized or general purpose integrated circuit (e.g., ASIC, FPGA, and/or PLD). Myriad other implementations may exist that will be recognized by those of ordinary skill given the present disclosure.

[0258] Advantageously, the present disclosure can be used to simplify and improve control tasks for a wide assortment of control applications including, without limitation, industrial control, adaptive signal processing, navigation, and robotics. Exemplary implementations of the present disclosure may be useful in a variety of devices including without limitation prosthetic devices (such as artificial limbs), industrial control, autonomous and robotic apparatus, HVAC, and other electromechanical devices requiring accurate stabilization, set-point control, trajectory tracking functionality or other types of control. Examples of such robotic devices may include manufacturing robots (e.g., automotive), military devices, and medical devices (e.g., for surgical robots). Examples of autonomous navigation may include rovers (e.g., for extraterrestrial, underwater, hazardous exploration environment), unmanned air vehicles, underwater vehicles, smart appliances (e.g., ROOMBA®), and/or robotic toys. The present disclosure can advantageously be used in other applications of adaptive signal processing systems (comprising for example, artificial neural networks), including: machine vision, pattern detection and pattern recognition, object classification, signal filtering, data segmentation, data compression, data mining, optimization and scheduling, complex mapping, and/or other applications.

[0259] It will be recognized that while certain aspects of the disclosure are described in terms of a specific sequence of steps of a method, these descriptions are only illustrative of the broader methods of the invention, and may be modified as required by the particular application. Certain steps may be rendered unnecessary or optional under certain circumstances. Additionally, certain steps or functionality may be added to the disclosed implementations, or the order of performance of two or more steps permuted. All such variations are considered to be encompassed within the disclosure disclosed and claimed herein.

[0260] While the above detailed description has shown, described, and pointed out novel features of the disclosure as applied to various implementations, it will be understood that various omissions, substitutions, and changes in the form and details of the device or process illustrated may be made by those skilled in the art without departing from the disclosure. The foregoing description is of the best mode presently contemplated of carrying out the invention. This description is in no way meant to be limiting, but rather should be taken as illustrative of the general principles of the invention. The scope of the disclosure should be determined with reference to the claims.

Claims

What is claimed:

1. Apparatus comprising a storage medium, said storage medium comprising a plurality of instructions to operate a network, comprising a plurality of spiking neurons, the instructions configured to, when executed:

based at least in part on receiving a task indication, select first group and second group from said plurality of spiking neurons;

operate said first group in accordance with first learning rule, based at least in part on an input signal and training signal; and

operate said second group in accordance with second learning rule, based at least in part on input signal;

wherein:

said task indication comprises at least said first and said second rules;

said first rule comprises at least reinforcement learning rule;

said second rule comprises at least unsupervised learning rule; and

said first rule further comprises first combination of at least said reinforcement learning rule and supervised learning rule.

2. The apparatus of claim 1, wherein:

said first combination further comprises unsupervised learning rule; and

said second rule further comprises second combination of reinforcement, supervised and unsupervised learning rules, said second combination being distinctly different from said first combination.

3. The apparatus of claim 1, wherein neurons in at least said first group are selected from said plurality, based at least in part on a random parameter associated with spatial coordinate of said plurality of neurons within said network; and

at least one of said first and said second group is characterized by a finite life span, said life span configured during said selecting.

4. The apparatus of claim 1, wherein:

neurons in at least said first group are selected using high level neuromorphic description language (HNLD) statement comprising a tag, configured to identify said neurons; and

said first group and said second group comprise disjoint set pair characterized by an empty intersect.

5. The apparatus of claim 1, wherein:

said first group and said second group comprise overlapping set pair;

neurons in at least said first group are selected using high level neuromorphic description language (HNLD) statement comprising a tag; and

said tag comprises an alphanumeric identifiers adapted to identify a spatial coordinate of neurons within respective groups.

6. The apparatus of claim 1, wherein:

said first rule having target performance associated therewith; and

said operate said first group in accordance with said first rule is configured to produce actual output having actual performance associated therewith such that said actual performance being closer to said target performance, as compared to another actual performance associated with another actual output being generated by said first group operated in absence of said first learning rule.

7. The apparatus of claim 6, wherein:

said training signal further comprises a desired output;

comparison of said actual performance to said target performance is based at least in part on a distance measure between said desired output and actual output such that said actual performance is being closer to said target performance is characterized by a value of said distance measure, determined using said desired output and said actual output, being smaller compared to another value of said distance measure, determined using said desired output and said another actual output.

8. The apparatus of claim 7, wherein said distance measure comprises instantaneous mutual information.

9. The apparatus of claim 7, wherein said distance measure comprises a squared error between (i) a convolution of said actual output with first convolution kernel αand (ii) a convolution of said desired output with second convolution kernel β.

10. The apparatus of claim 1, wherein operate said first group in accordance with first learning rule is based at least in part on first input signal; and

operate said second group in accordance with second learning rule is based at least in part on second input signal, said second signal being different from said first signal.

11. The apparatus of claim 1, wherein operate said first group in accordance with first learning rule is based at least in part on input signal; and

operate said second group in accordance with second learning rule is based at least in part on said input signal.

12. Computer readable apparatus comprising a storage medium, said storage medium comprising a plurality of instructions to operate a processing apparatus, the instructions configured to, when executed:

based at least in part on first task indication at first instance, operate said processing apparatus in accordance with first stochastic hybrid learning rule configured to produce first learning signal based at least in part on first input signal and first training signal, associated with said first task indication; and

based at least in part on second task indication at second instance, subsequent to first instance operate said processing apparatus in accordance with second stochastic hybrid learning rule configured to produce second learning signal based at least in part on second input signal and second training signal, associated with said second task indication;

wherein:

said first hybrid learning rule is configured to effectuate first rule combination; and

said second hybrid learning rule is configured to effect second rule combination, said second combination distinctly different from said first combination.

13. The apparatus of claim 12, wherein said second task indication is configured based at least in part on a parameter, associated with said operating said processing apparatus in accordance with said first stochastic hybrid learning rule, exceeding a threshold.

14. The apparatus of claim 13, wherein said parameter is selected from the group consisting of: (i) peak power consumption associated with operating said processing apparatus; (ii) power consumption associated with operating said processing apparatus, averaged over an interval associated with producing said first learning signal; (iii) memory utilization associated with operating said processing apparatus; and (iv) logic resource utilization associated with operating said processing apparatus.

15. The apparatus of claim 12, wherein said second task indication is configured based at least in part on detecting a change in number if input channels associated with said first input signal.

16. The apparatus of claim 12, wherein said second task indication is configured based at least in part on detecting a change in composition of said first training signal, said change comprising any one or more of (i) addition of reinforcement signal; (ii) removal of reinforcement signal; (iii) addition of supervisor signal; and (iv) removal of supervisory signal.

17. A computer-implemented method of operating a computerized spiking network, comprising a plurality of nodes, the method comprising:

based at least in part on first task indication at a first instance, operating said plurality of nodes in accordance with a first stochastic hybrid learning rule configured to produce first learning signal based at least in part on first input signal and first training signal, associated with said first task indication; and

based at least in part on second task indication at second instance, subsequent to first instance:

operating first portion of said plurality of nodes in accordance with second stochastic hybrid learning rule configured to produce second learning signal based at least in part on second input signal and second training signal, associated with said second task indication; and

operating second portion of said plurality of nodes in accordance with third stochastic learning rule configured to produce third learning signal based at least in part on second input signal associated with said second task indication;

wherein:

said first hybrid learning rule is configured to effect first rule combination; and

said second hybrid learning rule is configured to effect second rule combination, said second combination substantially different from said first combination.

18. The method of claim 17, wherein:

said first hybrid learning rule comprises first rule having first combination coefficient associated therewith and second rule having second combination coefficient associated therewith;

said second hybrid learning rule comprises said first rule having third combination coefficient associated therewith and said second rule having fourth combination coefficient associated therewith; and

at said first coefficient different from said third coefficient.

19. The method of claim 17, wherein said first rule is selected from the group consisting of reinforcement and supervised learning rules, said first rule being configured in accordance with said first training and said second training signal, respectively.

20. The method of claim 17, wherein:

said first hybrid learning rule comprises first rule and second rule; and

said second hybrid learning rule comprises said first rule and at least third rule, said third rule different from at least one of said first rule and said second rule.

21. The method of claim 17, wherein said third learning signal is based at least in part on said second learning signal.

22. The method of claim 17, wherein:

said first hybrid learning rule is configured to implement reinforcement and supervised rule combination; and

said second hybrid learning rule is configured to implement at least supervised and unsupervised rule combination.

23. The method of claim 17, wherein said second task indication is based at least in part one or more of (i) a detected a change in network processing configuration; and (ii) a detected change in configuration of said first input signal.

24. The method of claim 23, wherein said change in network processing configuration comprises any of (i) a failure of one or more of said plurality of nodes; (ii) an addition of one or more failure of one or more nodes; and (iii) a failure of one or more of input-output interface associated with said plurality of nodes.

Patent Citations (86)

Patent	Date	Inventor	Cited By
US5063603(A)	1991-11-01	Burt	Applicant
US5092343(A)	1992-03-01	Spitzer	Applicant
US5245672(A)	1993-09-01	Wilson	Applicant
US5355435(A)	1994-10-01	DeYong	Applicant
US5388186(A)	1995-02-01	Bose	Applicant
US5408588(A)	1995-04-01	Ulug	Applicant
US5467428(A)	1995-11-01	Ulug	Applicant
US5638359(A)	1997-06-01	Peltola	Applicant
US5673367(A)	1997-09-01	Buckley	Applicant
US5875108(A)	1999-02-01	Hoffberg	Applicant
US6009418(A)	1999-12-01	Cooper	Applicant
US6014653(A)	2000-01-01	Thaler	Applicant
US6363369(B1)	2002-03-01	Liaw	Applicant
US6458157(B1)	2002-10-01	Suaning	Applicant
US6545705(B1)	2003-04-01	Sigel	Applicant
US6545708(B1)	2003-04-01	Tamayama	Applicant
US6546291(B2)	2003-04-01	Merfeld	Applicant
US6581046(B1)	2003-06-01	Ahissar	Applicant
US6601049(B1)	2003-07-01	Cooper	Applicant
US6643627(B2)	2003-11-01	Liaw	Applicant
US7395251(B2)	2008-07-01	Linsker	Applicant
US7426501(B2)	2008-09-01	Nugent	Applicant
US7672920(B2)	2010-03-01	Ito	Applicant
US7849030(B2)	2010-12-01	Ellingsworth	Applicant
US8015130(B2)	2011-09-01	Matsugu	Applicant
US8103602(B2)	2012-01-01	Izhikevich	Applicant
US8315305(B2)	2012-11-01	Petre	Applicant
US8467623(B2)	2013-06-01	Izhikevich	Applicant
US8655815(B2)	2014-02-01	Palmer	Applicant
US2002/0038294(A1)	2002-03-01	Matsugu	Applicant
US2003/0050903(A1)	2003-03-01	Liaw	Applicant
US2004/0193670(A1)	2004-09-01	Langan	Applicant
US2005/0015351(A1)	2005-01-01	Nugent	Applicant
US2005/0036649(A1)	2005-02-01	Yokono	Applicant
US2005/0283450(A1)	2005-12-01	Matsugu	Applicant
US2006/0161218(A1)	2006-07-01	Danilov	Applicant
US2007/0022068(A1)	2007-01-01	Linsker	Applicant
US2007/0176643(A1)	2007-08-01	Nugent	Applicant
US2007/0208678(A1)	2007-09-01	Matsugu	Applicant
US2008/0024345(A1)	2008-01-01	Watson	Applicant
US2008/0162391(A1)	2008-07-01	Izhikevich	Applicant
US2009/0043722(A1)	2009-02-01	Nugent	Applicant
US2009/0287624(A1)	2009-11-01	Rouat	Applicant
US2010/0086171(A1)	2010-04-01	Lapstun	Applicant
US2010/0166320(A1)	2010-07-01	Paquier	Applicant
US2010/0198765(A1)	2010-08-01	Fiorillo	Applicant
US2011/0016071(A1)	2011-01-01	Guillen	Applicant
US2011/0119214(A1)	2011-05-01	Breitwisch	Applicant
US2011/0119215(A1)	2011-05-01	Elmegreen	Applicant
US2011/0160741(A1)	2011-06-01	Asano	Applicant
US2012/0011090(A1)	2012-01-01	Tang	Applicant
US2012/0011093(A1)	2012-01-01	Aparin	Applicant
US2012/0036099(A1)	2012-02-01	Venkatraman	Applicant
US2012/0109866(A1)	2012-05-01	Modha	Applicant
US2012/0303091(A1)	2012-11-01	Izhikevich	Applicant
US2012/0308076(A1)	2012-12-01	Piekniewski	Applicant
US2012/0308136(A1)	2012-12-01	Izhikevich	Applicant
US2013/0073080(A1)	2013-03-01	Ponulak	Applicant
US2013/0073491(A1)	2013-03-01	Izhikevich	Applicant
US2013/0073493(A1)	2013-03-01	Modha	Applicant
US2013/0073496(A1)	2013-03-01	Szatmary	Applicant
US2013/0073500(A1)	2013-03-01	Szatmary	Applicant
US2013/0151448(A1)	2013-06-01	Ponulak	Examiner
US2013/0151449(A1)	2013-06-01	Ponulak	Applicant
US2013/0151450(A1)	2013-06-01	Ponulak	Applicant
US2013/0218821(A1)	2013-08-01	Szatmary	Applicant
US2013/0251278(A1)	2013-09-01	Izhikevich	Applicant
US2013/0297541(A1)	2013-11-01	Piekniewski	Applicant
US2013/0325766(A1)	2013-12-01	Petre	Applicant
US2013/0325768(A1)	2013-12-01	Sinyavskiy	Applicant
US2013/0325773(A1)	2013-12-01	Sinyavskiy	Applicant
US2013/0325774(A1)	2013-12-01	Sinyavskiy	Applicant
US2013/0325775(A1)	2013-12-01	Sinyavskiy	Applicant
US2013/0325776(A1)	2013-12-01	Ponulak	Applicant
US2013/0325777(A1)	2013-12-01	Petre	Applicant
US2014/0016858(A1)	2014-01-01	Richert	Applicant
US2014/0025613(A1)	2014-01-01	Ponulak	Applicant
US2014/0032458(A1)	2014-01-01	Sinyavskiy	Applicant
US2014/0193066(A1)	2014-07-01	Richert	Applicant
CN102226740	2011-10-01		Applicant
EP1089436	2001-04-01		Applicant
JP4087423	1992-03-01		Applicant
RU2108612	1998-10-01		Applicant
RU2406105(C2)	2010-12-01		Applicant
WO2008083335	2008-07-01		Applicant
WO2008132066(A1)	2008-11-01		Applicant

Non-Patent Literature (112)

PCT International Search Report for International Application PCT/US2013/060352 dated Jan. 16, 2014.Applicant
Izhikevich et al., ‘Relating STDP to BCM’, Neural Computation (2003) 15, 1511-1523.Applicant
Sjostrom et al., ‘Spike-Timing Dependent Plasticity’ Scholarpedia, 5(2):1362 (2010), pp. 1-18.Applicant
Szatmary et al., ‘Spike-timing Theory of Working Memory’ PLoS Computational Biology, vol. 6, Issue 8, Aug. 19, 2010 [retrieved on Dec. 30, 2013]. Retrieved from the Internet: <URL: http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371 %2Fjournal.pcbi.10008 79#>.Applicant
PCT International Search Report for PCT/US2013/052136 dated Nov. 30, 2013.Applicant
Froemke et al., Temporal modulation of spike-timing-dependent plasticity, Frontiers in Synaptic Neuroscience, vol. 2, Article 19, pp. 1-16 [online] Jun. 2010 [retrieved on Dec. 16, 2013]. Retrieved from the internet: <frontiersin.org>.Applicant
Seung, H. “Learning in spiking neural networks by reinforcement of stochastic synaptic transmission.” Neuron vol. 40 No. 6 (2003): pp. 1063-1073.Applicant
Weber, C. et al. ‘Robot docking with neural vision and reinforcement.’ Knowledge-Based Systems vol. 17 No. 2 (2004): pp. 165-172.Applicant
Baras, D. et al. “Reinforcement learning, spike-time-dependent plasticity, and the BCM rule.” Neural Computation vol. 19 No. 8 (2007): pp. 2245-2279.Applicant
de Queiroz, M. et al. “Reinforcement learning of a simple control task using the spike response model.” Neurocomputing vol. 70 No. 1 (2006): pp. 14-20.Applicant
PCT International Search Report and Written Opinion for International Application No. PCT/US2013/044124 dated Sep. 12, 2013.Applicant
Bennett (1999), The early history of the synapse: from Plato to Sherrington. Brain Res. Bull., 50(2): 95-118.Applicant
Haykin, (1999), Neural Networks: A Comprehensive Foundation (Second Edition), Prentice-Hall.Applicant
“In search of the artificial retina” [online], Vision Systems Design, Apr. 1, 2007.Applicant
Kenji, (2000), Reinforcement Learning in Continuous Time and Space, Neural Computation, 12:1, 219-245.Applicant
Klute et al., (2002). Artificial Muscles: Actuators for Biorobotic Systems. The International Journal 0./ Robotics Research 21 :295-309.Applicant
Lendek et al., (2006) State Estimation under Uncertainty: A Survey. Technical report 06-004, Delft Center for Systems and Control Delft University of Technology.Applicant
Legenstein et al., (2008), A learning theory for reward-modulated spike timing-dependent plasticity with application to biofeedback. PLoS Computational Biology, 4(10): 1-27.Applicant
Nikolic et al., (2011) High-sensitivity silicon retina for robotics and prosthetics.Applicant
Ponulak, (2005), ReSuMe—New supervised learning method for Spiking Neural Networks. Technical Report, Institute of Control and Information Engineering, Poznan University of Technology.Applicant
Ponulak et al., (2010) Supervised Learning in Spiking Neural Networks with ReSuMe: Sequence Learning, Classification and Spike-Shifting. Neural Comp., 22(2): 467-510.Applicant
Sutton et al., (1998), Reinforcement Learning, an Introduction. MIT Press.Applicant
Schreiber et al., (2003), A new correlation-based measure of spike timing reliability. Neurocomputing, 52-54, 925-931.Applicant
Sutton, (1988). Learning to predict by the methods of temporal differences. Machine Learning 3(1), 9-44.Applicant
Stein, (1967). Some models of neural variability. Biophys. J., 7: 37-68.Applicant
Werbos, (1992), or Prokhorov D.V and Wunsch D.C. (1997) Adaptive Critic Designs, IEEE Trans Neural Networks, vol. 8, No. 5, pp. 997-1007.Applicant
White et al., (Eds.) (1992) Handbook of Intelligent Control: Neural, Fuzzy and Adaptive Approaches. Van Nostrand Reinhold, New York.Applicant
Widrow et al., (1960) Adaptive Switching Circuits. IRE WESCON Convention Record 4: 96-104.Applicant
Ponulak (2006) Supervised Learning in Spiking Neural Networks with ReSuMe Method. Doctoral Dissertation Poznan, Poland.Applicant
Florian (2007) Reinforcement Learning Through Modulation of Spike-Timing-Dependent Synaptic Plasticity, Neural Computation 19, 1468-1502 Massachusetts Institute of Technology.Applicant
Morrison, (2008)Phenomenological models of synaptic plasticity based on spike timing.Applicant
Bouganis et al., (2010) “Training a Spiking Neural Network to Control a 4-DoF Robotic Arm based on Spike Timing-Dependent Plasticity”, Proceedings of WCCI201 0 IEEE World Congress on Computational Intelligence, CCIB, Barcelona, Spain, Jul. 18-23, 2010, pp. 4104-4111.Applicant
Xie et al., (2004) “Learning in neural networks by reinforcement of irregular spiking”, Physical Review E, vol. 69, letter 041909, pp. 1-10.Applicant
Floreano et al., (2008) Floreano et al. Neuroevolution: From Architectures to learning Evol. Intel. Jan. 2008 1:47-62 (retrieved online on Apr. 24, 2013 from http://infoscience.epfl.ch/record/112676/files/FloreanoDuerrMattiussi2008pdf).Applicant
D'Cruz (1998) Reinforcement Learning in Intelligent Control: A Biologically-Inspired Approach to the Re/earning Problem Brendan May 1998.Applicant
Aleksandrov (1968), Stochastic optimization, Engineering Cybernetics, 5, 11-16.Applicant
Amari (1998), Why natural gradient?, Acoustics, Speech and Signal Processing, (pp. 1213-1216). Seattle, WA, USA.Applicant
Bartlett et al., (2000) “A Biologically Plausible and Locally Optimal Learning Algorithm for Spiking Neurons” Retrieved from http://arp.anu.edu.au/ftp/papers/jon/brains.pdf.gz.Applicant
Baxter et al. (2000.). Direct gradient-based reinforcement learning. In Proceedings of the International Symposium on Circuits.Applicant
Bohte et al., “A Computational Theory of Spike-Timing Dependent Plasticity: Achieving Robust Neural Responses via Conditional Entropy Minimization” 2004.Applicant
Bohte, (2000). SpikeProp: backpropagation for networks of spiking neurons. In Proceedings of ESANN'2000, (pp. 419-424).Applicant
Booij (Jun. 2005). A Gradient Descent Rule for Spiking Neurons Emitting Multiple Spikes. Information Processing Letters n. 6, v.95 , 552-558.Applicant
Breiman et al., “Random Forests” 33pgs, Jan. 2001.Applicant
Capel, “Random Forests and Ferns” LPAC, Jan. 11, 2012, 40 pgs.Applicant
El-Laithy (2011), A reinforcement learning framework for spiking networks with dynamic synapses, Comput Intell Neurosci.Applicant
Fletcher (1987), Practical methods of optimization, New York, NY: Wiley-Interscience.Applicant
Florian (2005), A reinforcement learning algorithm for spiking neural networks SYNASC '05 Proceedings of the Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.Applicant
Fremaux et al., “Functional Requirements for Reward-Modulated Spike-Timing-Dependent Plasticity”, The Journal of Neuroscience, Oct. 6, 2010, 30 (40):13326-13337.Applicant
Fu (2005) Stochastic Gradient Estimation, Technical Research Report.Applicant
Fu (2008), What You Should Know About Simulation and Derivatives Naval Research Logistics, vol. 55, No. 8 , 723-736.Applicant
Fyfe et al., (2007), Reinforcement Learning Reward Functions for Unsupervised Learning, ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks.Applicant
Gerstner (2002), Spiking neuron models: single neurons, populations, plasticity, Cambridge, U.K.: Cambridge University Press.Applicant
Glynn (1995), Likelihood ratio gradient estimation for regenerative stochastic recursions, Advances in Applied Probability, 27, 4, 1019-1053.Applicant
Ho, “Random Decision Forests” Int'l Conf. Document Analysis and Recognition, 1995, 5 pgs.Applicant
Izhikevich (2007), Solving the distal reward problem through linkage of STDP and dopamine signaling, Cerebral Cortex, vol. 17, pp. 2443-2452.Applicant
Kalal et al. “Online learning of robust object detectors during unstable tracking” published on 3rd On-line Learning for Computer Vision Workshop 2009, Kyoto, Japan, IEEE CS.Applicant
Kiefer (1952), Stochastic Estimation of the Maximum of a Regression Function, Annals of Mathematical Statistics 23, #3, 462-466.Applicant
Klampfl (2009), Spiking neurons can learn to solve information bottleneck problems and extract independent components, Neural Computation, 21(4), pp. 911-959.Applicant
Kleijnen et al., Optimization and sensitivity analysis of computer simulation models by the score function method Invited Review European Journal of Operational Research, Mar. 1995.Applicant
Larochelle et al., (2009), Exploring Strategies for Training Deep Neural Networks, J. of Machine Learning Research, v. 10, pp. 1-40.Applicant
Ojala et al., “Performance Evaluation of Texture Measures with Classification Based on Kullback Discrimination of Distributions” 1994 IEEE, pp. 582-585.Applicant
Ozuysal et al., “Fast Keypoint Recognition in Ten Lines of Code” CVPR 2007.Applicant
Ozuysal et al., “Fast Keypoint Recognition Using Random Ferns” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, No. 3, Mar. 2010, pp. 448-461.Applicant
Pfister (2003), Optimal Hebbian Learning: A Probabilistic Point of View, In ICANN Proceedings. Springer, pp. 92-98.Applicant
Pfister (2006), Optimal Spike-Timing Dependent Plasticity for Precise Action Potential Firing in Supervised Learning, Neural computation ISSN 0899-7667, 18 (6).Applicant
Reiman et al. (1989). Sensitivity analysis for simulations via likelihood ratios. Oper Res 37, 830-844.Applicant
Robbins (1951), A Stochastic Approximation Method, Annals of Mathematical Statistics 22, #3, 400-407.Applicant
Rosenstein et al., (2002), Supervised learning combined with an actor-critic architecture, Technical Report 02-41, Department of Computer Science, University of Massachusetts, Amherst.Applicant
Kleijnen et al., “Optimization and sensitivity analysis of computer simulation models by the score function method”, Invited Review European Journal of Operational Research, Mar. 1995.Applicant
Rumelhart et al., (1986), Learning representations by back-propagating errors, Nature 323 (6088) , pp. 533-536.Applicant
Rumelhart (1986), Learning internal representations by error propagation, Parallel distributed processing, vol. 1 (pp. 318-362), Cambridge, MA: MIT Press.Applicant
Sinyavskiy, et al. “Generalized Stochatic Spiking Neuron Model and Extended Spike Response Model in Spatial-Temporal Impulse Pattern Detection Task”, Optical Memory and Neural Networks (Information Optics), 2010, vol. 19, No. 4, pp. 300-309, 2010.Applicant
Tishby et al., (1999), The information bottleneck method, In Proceedings of the 37th Annual Allerton Conference on Communication, Control and Computing, B Hajek & RS Sreenivas, eds., pp. 368-377, University of Illinois.Applicant
Toyoizumi (2007), Optimality Model of Unsupervised Spike-Timing Dependent Plasticity: Synaptic Memory and Weight Distribution, Neural Computation, 19 (3).Applicant
Toyoizumi et al., (2005), Generalized Bienenstock-Cooper-Munro rule for spiking neurons that maximizes information transmission, Proc. Natl. Acad. Sci. USA, 102, (pp. 5239-5244).Applicant
Vasilaki et al., “Spike-Based Reinforcement Learning in Continuous State and Action Space: When Policy Gradient Methods Fail” PLoS, vol. 5, Issue 12, Dec. 2009.Applicant
Vasilaki, et al., “Learning flexible sensori-motor mappings in a complex network” Biol Cybern (2009) 100:147-158.Applicant
Weaver (2001), The Optimal Reward Baseline for Gradient-Based Reinforcement Learning, UAI 01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence (pp. 538-545). Morgan Kaufmann Publishers.Applicant
Weber et al., (2009), Goal-Directed Feature Learning, In: Proc, International Joint Conference on Neural Networks, 3319-3326.Applicant
Williams (1992), Simple Statistical Gradient-Following Algorithms for Connectionist Reinforcement Learning, Machine Learning 8, 229-256.Applicant
Yi (2009), Stochastic search using the natural gradient, ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning. New York, NY, USA.Applicant
Sherrington , (1897); The Central Nervous System. A Textbook of Physiology, 7th ed., part III, Ed. by Foster M. Macmillian and Co. Ltd., London, p. 929.Applicant
Sinyavskiy O. Yu.: ‘Obuchenic s podkrepleniem spaikovoy neiroiniy seti v zadache upravleniya agentom v diskretnoy virtualnoy srede.’ Nelineinaya Dinamika vol. T. 7., No. 24, 2011, pp. 859-875.Applicant
Bohte, “Spiking Nueral Networks” Doctorate at the University of Leiden, Holland, Mar. 5, 2003, pp. 1-133 [retrieved on Nov. 14, 2012]. Retrieved from the internet: <URL: http://homepages.ewi.nl/-sbohte/publication/phdthesis.pdf>.Applicant
Brette et al., Brian: a simple and flexible simulator for spiking neural networks, The Neuromorphic Engineer, Jul. 1, 2009, pp. 1-4, doi: 10.2417/1200906.1659.Applicant
Cuntz et al., “One Rule to Grow Them All: A General Theory of Neuronal Branching and Its Paractical Application” PLoS Computational Biology, 6 (8), Published Aug. 5, 2010.Applicant
Davison et al., PyNN: a common interface for neuronal network simulators, Frontiers in Neuroinformatics, Jan. 2009, pp. 1-10, vol. 2, Article 11.Applicant
Djurfeldt, Mikael, The Connection-set Algebra: a formalism for the representation of connectivity structure in neuronal network models, implementations in Python and C++, and their use in simulators BMC Neuroscience Jul. 18, 2011 p. 1 12(Suppl 1):P80.Applicant
Fidjeland et al., Accelerated Simulation of Spiking Neural Networks Using GPUs [online], 2010 [retrieved on Jun. 15, 2013], Retrieved from the Internet: URL:http://ieeexplore.ieee.org/xpls/abs—all.jsp?arnmber=5596678&tag=1.Applicant
Floreano et al., “Neuroevolution: from architectures to learning” Evol. Intel. Jan. 2008 1:47-62, [retrieved Dec. 30, 2013] [retrieved online from URL:<http://inforscience.epfl.ch/record/112676/files/FloreanoDuerrMattiussi2008.pdf>.Applicant
Gewaltig et al., NEST (Neural Simulation Tool), Scholarpedia, 2007, pp. 1-15, 2( 4 ): 1430, doi: 1 0.4249/scholarpedia.1430.Applicant
Gleeson et al., ) NeuroML: A Language for Describing Data Driven Models of Neurons and Networks with a High Degree of Biological Detail, PLoS Computational Biology, Jun. 2010, pp. 1-19 vol. 6 Issue 6.Applicant
Goodman et al., Brian: a simulator for spiking neural networks in Python, Frontiers in Neuroinformatics, Nov. 2008, pp. 1-10, vol. 2, Article 5.Applicant
Gorchetchnikov et al., NineML: declarative, mathematically-explicit descriptions of spiking neuronal networks, Frontiers in Neuroinformatics, Conference Abstract: 4th INCF Congress of Neuroinformatics, doi: 1 0.3389/conf.fninf.2011.08.00098.Applicant
Graham, Lyle J., The Surf-Hippo Reference Manual, http://www.neurophys.biomedicale.univparis5. fr/-graham/surf-hippo-files/Surf-Hippo%20Reference%20Manual.pdf, Mar. 2002, pp. 1-128.Applicant
Izhikevich, “Polychronization: Computation with Spikes”, Neural Computation, 25, 2006, 18, 245-282.Applicant
Izhikevich, “Simple Model of Spiking Neurons”, IEEE Transactions on Neural Networks, vol. 14, No. 6, Nov. 2003, pp. 1569-1572.Applicant
Karbowski et al., “Multispikes and Synchronization in a Large Neural Network with Temporal Delays”, Neural Computation 12, 1573-1606 (2000).Applicant
Khotanzad, “Classification of invariant image representations using a neural network” IEEF. Transactions on Acoustics, Speech, and Signal Processing, vol. 38, No. 6, Jun. 1990, pp. 1028-1038 [online], [retrieved on Dec. 10, 2013]. Retrieved from the Internet <URL: http://www-ee.uta.edu/eeweb/IP/Courses/SPR/Reference/Khotanzad.pdf>.Applicant
Laurent, “The Neural Network Query Language (NNQL) Reference” [retrieved on Nov. 12, 2013]. Retrieved from the Internet: URL:http://nnql.org/nnql.org.Applicant
Laurent, “Issue 1—nnql—Refactor Nucleus into its own file—Neural Network Query Language” [retrieved on Nov. 12, 2013]. Retrieved from the Internet: URL:https://code.google.com/p/nnql/issues/detail?id=1.Applicant
Nichols, A Reconfigurable Computing Architecture for Implementing Artificial Neural Networks on FPGA, Master's Thesis, The University of Guelph, 2003, pp. 1-235.Applicant
Pavlidis et al. Spiking neural network training using evolutionary algorithms. In: Proceedings 2005 IEEE International Joint Conference on Neural Networkds, 2005. IJCNN'05, vol. 4, pp. 2190-2194 Publication Date Jul. 31, 2005 [online] [Retrieved on Dec. 10, 2013] Retrieved from the Internet <URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.5.4346&rep=rep1&type=pdf.Applicant
Paugam-Moisy et al., “Computing with spiking neuron networks” G. Rozenberg T. Back, J. Kok (Eds.), Handbook of Natural Computing, Springer-Verlag (2010) [retrieved Dec. 30, 2013], [retrieved online from link.springer.com].Applicant
Schemmel et al., Implementing synaptic plasticity in a VLSI spiking neural network model in Proceedings of the 2006 International Joint Conference on Neural Networks (IJCNN'06), IEEE Press (2006) Jul. 16-21, 2006, pp. 1-6 [online], [retrieved on Dec. 10, 2013]. Retrieved from the Internet <URL: http://www.kip.uni-heidelberg.de/veroeffentlichungen/download.cgi/4620/ps/1774.pdf>.Applicant
Simulink® model [online], [Retrieved on Dec. 10, 2013] Retrieved from <URL: http://www.mathworks.com/products/simulink/index.html>.Applicant
Sinyavskiy et al. “Reinforcement learning of a spiking neural network in the task of control of an agent in a virtual discrete environment” Rus. J. Nonlin. Dyn., 2011, vol. 7, No. 4 (Mobile Robots), pp. 859-875, chapters 1-8 (Russian Article with English Abstract).Applicant
Hagras, Hani et al., “Evolving Spiking Neural Network Controllers for Autonomous Robots”, IEEE 2004.Applicant
Masakazu et al, “Convolutional Spiking Neural Network Model for Robust Face Detection”, 2002 Proceedings of the 9th International Conference on Neural Information Processing (ICONIP'02), vol. 2.Applicant
Jesper Tegner, et al., 2002 “An adaptive spike-timing-dependent plasticity rule” Elsevier Science B.V.Applicant
Schrauwen et al., “Improving SpikeProp: Enhancements to an Error-Backpropagation Rule for Spiking Neural Networks”, ProsRISC workshop, 2004, pp. 301-305.Applicant
Ponulak, “Analysis of the Resume learning Process for Spiking Neural Networks,” International Journal of Applied Mathematics & Computer Science: Jun. 2008, vol. 18, Issue 2, p. 117.Applicant

Abstract