Method and apparatus for modeling a neural synapse function by utilizing a single conventional MOSFET

[0002] This application claims the benefit of U.S. Provisional Application No. 60/237,144 filed on Oct. 02, 2000.

[0003] Not Applicable

[0004] Reference to a “Microfiche Appendix”

[0005] Not Applicable

[0006] 1. Field of the Invention

[0007] The present invention relates to modeling the function of a neural synapse in hardware thus allowing for building of neural networks or alike learning and adaptive systems using low-power conventional MOSFETs integrated on-chip with other analog or digital application circuits.

[0008] 2. Description of the Related and Prior Art

[0009] In spite of the immense advance in the development of the modem VLSI technology, digital circuits or systems reach the critical point from its computational speed and integration. In implementing real-time digital signal processing applications, the conventional VLSI technology has many limitations with regard to chip area and its speed, due to complexity of both hardware and software processing algorithms. On the other hand, artificial neural networks offer great potential in many applications. This poses the need of a simple, fast and efficient solution for implementation of such neural networks in a conventional CMOS fabrication technology along with the rest of the integrated circuit application. Such characteristics can be most often satisfied by the utilization of simple analog signal processing elements, in particular MOSFETs.

[0010] Prior efforts for single-MOSFET synapse circuits largely include use of floating gate MOSFET devices (for example: U.S. Pat. No. 6,023,422; U.S. Pat. No. 5,986,927; U.S. Pat. No. 5,914,894; U.S. Pat. No. 5,864,242; U.S. Pat. No. 5,825,063; U.S. Pat. No. 5,818,081; U.S. Pat. No. 5,627,392; U.S. Pat. No. 5,621,336; U.S. Pat. No. 5,457,771; U.S. Pat. No. 5,336,936; U.S. Pat. No. 5,331,215; U.S. Pat. No. 5,253,196; U.S. Pat. No. 5,204,549; U.S. Pat. No. 5,027,171) which utilize various structures and methods to store/remove electrical charges on/from a floating gate or node through insulator by tunneling (Fowler-Nordheim) or hot-electron-injection. Beside the many advantages that those structures offer, they rely on conditions that are hard to meet in a conventional CMOS fabrication process. For example, at the voltages and oxide thicknesses used in conventional silicon MOS processing, the tunneling probability is exceedingly small, likewise hot-electron-injection requires much higher electric fields and supply voltages than normal. The latter is in direct conflict with the tendency of lowering supply voltages with the constant decrease of the device geometries and increase of the scale of integration.

[0011] Other related prior art includes analog multipliers build by coupled current mirrors (U.S. Pat. No. 5,914,868), four-quadrant square-law circuits (U.S. Pat. No. 5,864,255) or pair of MOSFETs and a symmetrical voltage source (U.S. Pat. No. 5,254,889) all capable of removing non-linear current component in one form or another to improve multiplier linearity. Some solutions utilize voltage-current conversion circuits employing differential pair of MOS transistors (U.S. Pat. No. 5,704,014) or current controlled current conveyor circuits (U.S. Pat. No. 5,206,541). There are also solutions to use multiple-bit-split MOSFET gates (U.S. Pat. No. 5,442,209). It should be mentioned that this list is not in any way comprehensive or inclusive and does not represent the complete scope and class of search for prior art performed by the inventor. For sake of briefness, herein will not be mentioned quite innovative solutions for building artificial neural networks as, for example, “Information processing device capable of optically writing synapse strength matrix” (U.S. Pat. No. 5,546,504) in which a matrix of plurality of neurons is realized through a combination of a light-emitting and light-receiving functions of two overlapping molecular films. The above-related art is mentioned in order to point out that most of the solutions require special integrated circuit technology, show performance dependencies as to the quality or the technology parameters of the used fabrication process or require special ambient (for UV floating-gate programming for example). Therefore, in general practice, those solutions do not allow for easy on-chip integration with other integrated circuit applications implemented on most widely used conventional CMOS processes.

[0012] Naturally, it is desired to provide a simple single-transistor synapse for modeling neural synaptic connection function and for building artificial neural networks in VLSI integrated circuits, which offers following advantages and features:

[0013] 1. use of a single, conventional MOSFET to model a neural synapse function;

[0014] 2. low power consumption;

[0015] 3. independence of the model quality with regard to quality of the CMOS fabrication process;

[0016] 4. simplicity and feasibility to dense integration;

[0017] 5. preferred conventional CMOS implementation which allows for integration with conventional analog and digital IC applications;

[0018] 6. current signal input and output allowing for straightforward and easy multi-layer neural network interconnection, simple synapse-output summing, avoidance of parasitic capacitive effects on both input and output transient signals therefore allowing for faster processing in real-time applications;

[0019] This and other features of the invention will be apparent to a person of ordinary skill in the art from the description of the invention contained herein.

[0020] Specification description of the claimed invention and disclosure will be facilitated by the definition of the meaning of the following terms. Term definitions given herein are intended to help in limiting redundancy and unduly multiplication of terms in the disclosure and should be used to better comprehend the spirit and scope of the invention. The definitions given are not intended to limit and define the scope of the appended claims rather than to provide antecedent support of a claim in cases where such support can be more easily found by the interpretation of the terms given herein and used in the disclosure, or in cases where these definitions help avoid inconsistencies between claim and specification disclosure or prior art, should such arise.

[0021] Neural synapse—although ‘neural’ refers to a biological synaptic connection formed between a dendrite tree and axon terminal of a neuron (most often cerebral pyramidal cell), herein it should be most often interpreted as artificial synapse model, mathematical or functional abstract of its biological counterpart. Synapse, neural synapse or synaptic connection will most often be used interchangeably in the application.

[0022] Synapse strength or weight—the quantity that can be used to show the degree of proportion between the quantity used to represent pre-synaptic activity (input stimulus) and the quantity representing post-synaptic activity (weighted input stimulus).

[0023] Neural synapse function—although biological synapse function comprises functions of excitation or inhibition to effectively strengthen or weaken the transmission of a pre-synaptic signal to a post-synaptic signal and also learning functions (to keep or adjust its strength with respect to synaptic activity), herein, a synapse function should be interpreted as the multiplication function between the pre-synaptic signal quantity and synapse strength (or weight) quantity employed in the computational model most often used to describe the synapse.

[0024] Neuron—most often should be interpreted as functional abstract model of its biological counterpart. The latter model comprises of a linear combiner producing a sum of weighted input stimuli, further processed by a non-linear activation function, of sigmoidal or hard-limiting type, applied to limit the amplitude of the neuron output activity potential.

[0025] Neural network—a collection of interconnected neurons where a neuron input is either connected to previous layer neuron's output or receives input stimulus from an input node. Since the type or actual connectivity structure is immaterial to the present invention no further definition of neural network types and connectivity patterns will be given herein.

[0026] It is an object of the present invention to provide a method for modeling a neural synapse in hardware, using VLSI technology. More specifically, a method utilizing a single conventional MOSFET to model a neural synapse by effectively computing the product of an input signal (pre-synaptic activity) represented by gate-source voltage of latter MOSFET with synapse strength (or weight) represented by the drain-source voltage of same MOSFET.

[0027] Another object of the present invention is to provide a high-performance neural network synapse circuit operating in low voltage level range as a particular embodiment, allowing for variable weight setting (ν_DSvoltage) while keeping the latter independents within certain operational range, from the synapse output (post-synaptic) signal (i_Dcurrent).

[0028] In accordance with an aspect of the present invention, there is provided as prior art a first-order approximation of large-signal, low-frequency computational model describing a MOSFET in non-saturation region of operation and, as part of the object of the invention described herein, is presented the use of the above to model the multiplication function of a synapse. It should be noted that the presented model considers DC operating mode of operation or operation at analog signal frequencies as low as to keep the validity of relationships shown and practically render frequency dependent terms or effects insignificant. However, this does not limit the applicability of the model since in most cases this condition can be satisfied during consecutive short time periods of processing intervals.

[0029] In accordance with an aspect of the present invention, there is provided a neural network synapse comprising: a single conventional MOSFET with applied gate-source voltage as input signal, applied drain-source voltage as weight control signal; a preferred embodiment of an artificial neuron comprising a: synapse current input; synapse output current summing node; weight control circuit; neuron response current output.

[0030] The novel features believed characteristic of the present invention, as well as other features and advantages thereof, will become apparent to those of ordinary skill in the art and best understood by reference to the following detailed description of the particular embodiment, read in conjunction with the accompanying drawings listed herein:

[0031] FIG. 1 is a diagram of the most commonly used computational model of artificial neuron referred herein as prior art.

[0032] FIG. 2 is a view showing symbols of n-channel and p-channel MOSFETs along with the used herein positive current and voltages definition for applied terminal voltages;

[0033] FIG. 3 is a circuit block diagram of a MOSFET used as a synapse in the preferred embodiment of an artificial neuron capable of having any number of synaptic connections; a single MOSFET device is used to model each synaptic connection by effectively multiplying the input gate-source voltage signal and the drain-source voltage (synaptic weight value). Note: on this figure doted-line blocks show neighboring synapse means to illustrate the way the rest of synapses are connected following the same pattern.

[0034] FIG. 4 is a detailed circuit diagram displaying a neural network synapse, object of the invention, along with the accompanying circuits providing the current input means, weight control means, summing node and neuron's overall current output means according to the described embodiment of the present invention.

[0035] FIGS. 5 through 7 show results of computer simulations of an artificial neuron with two inputs and one output (two synapses) modeled by means of Eq. (1.6) trained and tested as linear classifier over a random sets of 2-D linearly separable data vectors.

[0036] FIGS. 8 through 10 show voltage and current plots of computer circuit simulation results of the circuit shown on FIG. 4. These plots serve to illustrate the essential behavior of the circuit disclosed in the specification as the best mode believed to carry out the invention.

[0037] The essence of the invention herein will be obvious to those of ordinary skill in the art after examining related computational equations on which the invention is based. Further below, the preferred embodiment of the present invention will be explained with reference to the accompanying drawings.

[0038] I. Method

[0039] The well-known in the art input-output relation of the “linear combiner” (20), essential part of the computational model of a neuron with N-number of synapses shown on FIG. 1 is given by: $\begin{array}{cc}\upsilon =\sum _{k=1}^N{w}_k{x}_k& \left(1.1\right)\end{array}$

[0040] where x_kis the k-th input vector component (representing pre-synaptic activity signal quantity for synapse k) and υ is the output of the linear combiner or so called “induced local field” or activation potential value. Synapse weights or strengths denoted with w_kfor each synapse k are shown on FIG. 1 as (11),(12) . . . (1N). Further, typically, such a model will have some type of limiting non-linear function (21) applied to limit neuron's output activity: $\begin{array}{cc}y=\varphi \left(\upsilon \right)=\varphi \left(\sum _{k=1}^N{w}_k{x}_k+\theta \right)& \left(1.2\right)\end{array}$

[0041] Since φ(υ), typically sigmoidal function, is most “sensitive” around the origin of the ν-axis, additional free parameter θ is used to “adjust” the neuron's induced local field to be in that vicinity at least during initial stages of training. This parameter is adjusted (“trained”) usually along with all of the free-parameters w_k(weights), which are adjusted according to the “error signal” computed at the output y. Parameter θ is often adjusted along with the rest of the weight parameters and is considered as an additional neuron synaptic connection with constant input value of +1. Therefore it will not be considered as a separate from weight coefficients entity in the remainder of the disclosure.

[0042] Referring now to FIG. 2 and the given as prior art first-order-approximated large-signal low-frequency model of a MOSFET drain current (assuming non-saturation region of operation) $\begin{array}{cc}\left|v_{\mathrm{GS}}\right|>\left|V_{\mathrm{TH}}\right|\mathrm{and}\left|v_{\mathrm{DS}}\right|\le \left|v_{\mathrm{GS}}-V_{\mathrm{TH}}\right|:i_D=\beta \left[\left(v_{\mathrm{GS}}-V_{\mathrm{TH}}\right)-\frac{v_{\mathrm{DS}}}{2}\right]v_{\mathrm{DS}}\left(1+\lambda v_{\mathrm{DS}}\right)& \left(1.3\right)\end{array}$

[0043] Wherein: $\beta \stackrel{△}{=}\mu ·C_{\mathrm{OX}}\frac{W}{L}$

[0044] is the process and geometry dependent transconductance parameter comprising:

[0045] μ—electron/hole channel carrier mobility,

[0046] C_OX—thin oxide layer gate unit capacitance per area, $\frac{W}{L}-$

[0047] MOSFET gate/channel geometry ratio; and,

[0048] λ—is channel-length modulation effect parameter of said MOSFET;

[0049] as is shown next, there is a way to model a neural synapse function described by the partial products w_kx_kin Eq. (1.1) by using relationship in Eq. (1.3).

[0050] By ignoring the last term in Eq. (1.3), due to very small values of λ (typical values of 0.004 to 0.01) and, as further seen, relatively small ν_DS, Eq. (1.3) is rewritten in the following form: $\begin{array}{cc}{i}_D\simeq \beta \left(v_{\mathrm{GS}}-V_{\mathrm{TH}}\right)v_{\mathrm{DS}}-\frac{1}{2}\beta v_{\mathrm{DS}}^2& \left(1.4\right)\end{array}$

[0051] Object of the described invention herein, the product of the gate and drain-source voltages is used to produce each of the partial products of relationship Eq. (1.1), then summing the output currents of those partial products for all synapses yields the complete “sum of weighted products” in Eq. (1.1).

[0052] Considering a single synapse k and denoting: ${\tilde{\upsilon }}_k\stackrel{△}{=}{i}_D,x_k\stackrel{△}{=}\beta \left(v_{\mathrm{GS}}-V_{\mathrm{TH}}\right),w_k\stackrel{△}{=}{v}_{\mathrm{DS}}$

[0053] a single synapse induced local field value can be written as:

[0054] {tilde over (υ)}=x_kw_k+ζw_k²  (1.5)

[0055] wherein ζ is constant, and $\zeta \stackrel{△}{=}-\frac{1}{2}\beta .$

[0056] It should be emphasized that several different notations can be used to re-write relationship in Eq. (1.3) into the form of Eq. (1.5), where ζ is constant, which all should be considered equivalent in the spirit of the invention as long as quantity x_kis directly proportional to ν_GS−V_TH, w_kis directly proportional to ν_DSand υ_kis directly proportional to i_D. For a neuron with N-number of synapses, Eq. (1.5) yields the overall induced local field value: $\begin{array}{cc}\tilde{\upsilon }=\sum _{k=1}^N{\tilde{\upsilon }}_k=\sum _{k=1}^N{x}_k{w}_k+\zeta \sum _{k=1}^N{w}_k^2& \left(1.6\right)\end{array}$

[0057] assuming ζ i.e. β is same for all synapse modeling MOSFETs.

[0058] Comparing Eq. (1.1) to Eq. (1.6), object of the present invention, it is found that the non-linearity error introduced by the square term in the latter equation can be considered insignificant with respect to the essential functional ability of the model described originally by Eq. (1.1) provided that following conditions are satisfied:

[0059] (a) synapse modeling MOSFET must be in non-saturation mode of operation,

[0060] (b) values of magnitude of quantity x are chosen in a range as larger as practical than the values of magnitude of quantity w.

[0061] To evaluate the above statement, examining the non-linearity error introduced by the square term in Eq. (1.6) will be very useful. The latter error, for a single synapse k, can be defined as: $\begin{array}{cc}{ϵ}_{\mathrm{lin}}=\frac{{\tilde{\upsilon }}_k-{\upsilon }_k}{{\upsilon }_k}=\zeta \frac{w_k}{x_k}=-\frac{1}{2}\frac{v_{\mathrm{DS}}}{v_{\mathrm{GS}}-V_{\mathrm{TH}}}& \left(1.7\right)\end{array}$

[0062] where ${\upsilon }_k\stackrel{△}{=}{w}_k{x}_k$

[0063] is the ideally linear local induced field value for the considered k-th synapse and {tilde over (υ)}_kis the value modeled by the merit of Eq. (1.5). By inspection following conclusions are drawn:

[0064] (a) the error is independent of β (independent of MOSFET geometry and technology process constants)

[0065] (b) the error could be minimized, theoretically, by minimizing ζ, except that in the case disclosed if β is decreased, ν_GS−V_THshould be increased accordingly to keep quantity x from decreasing as well.

[0066] (c) the error is minimized by choice of low threshold voltage for synapse modeling MOSFET.

[0067] (d) the smaller the drain-source voltage and the greater the “effective” gate-source voltage is, less the linearity error is and more linear relationship in Eq. (1.5) becomes,

[0068] (e) although relationship in Eq. (1.5) is squarely non-linear with respect to weight quantity it is linear with respect to input stimulus quantity, therefore by a choice of a low voltage range for weight quantity, the error is minimized.

[0069] It should be noted that the last two conditions are in perfect accord with the condition of non-saturation mode of operation of the synapse modeling MOSFET set for Eq. (1.3). In addition, examining a typical value for this error brings sense as to its relevance. Typical values of the quantities in Eq. (1.7): ν_DS≦100 mV, ν_GS−V_TH≅2 to 1V result in ∈_lin≦1 to 5%.

[0070] Consequently, by the merit of relationship in Eq. (1.5), a single MOSFET device offers good potential and yields a rather simple method for modeling a synapse function in hardware.

[0071] II. Apparatus

[0072] Further, a preferred embodiment, being another object of the current invention is explained by referring to FIG. 3. As described, the essence of the given hardware solution is a single conventional MOSFET device (41) to model each synaptic function of an artificial neuron. The voltage across the source and drain regions of (41) determines the weighting or the synaptic strength by means of weight control means (31) and signal (32), gate-source voltage of (41) represents the input stimulus (34) applied to that synaptic connection either by an input signal at that node or by previous-layer neuron's output and is controlled by input means (33). The resulting drain current through (41) representing the induced local field of that particular synaptic connection is then summed up along with all of the activity signals induced in the rest of the neuron's synapses at node (99). Finally, the overall activity signal (total activation potential) is processed through a non-linear (sigmoidal or hard-limiting) function (36) to generate neuron's output signal.

[0073] Latter described preferred embodiment of the present invention is shown next in more detail on FIG. 4. Herein, for the purpose of an example, an n-well CMOS process is considered. Since the n-channel MOSFETs (44),(45),(102) and (103) are inherently built in the p-substrate, their bulk terminals will be assumed to be all at ground potential and will not be drawn. Terminal voltages and currents for both n-channel and p-channel MOSFETs use positive sign convention shown as prior art on FIG. 2.

[0074] The embodiment shown on FIG. 4 comprises: a current-voltage converter input means (33) formed by capacitor C_Xbetween nodes (99) and (40) and a current switch (47); synapse modeling means (35) utilizing p-channel MOSFET (41); all-synaptic-activity current summing common node (99) and a common for all synapses active-resistor load (36′) by a p-channel MOSFET (100); weight control means (31) comprising a current mirror formed by n-channel MOSFETs (44) and (45), active-resistor load formed by p-channel MOSFET (42) matched with (100), a p-channel MOSFET (43) forming a current mirror with (100); a common for all synapses current output means (36) comprising p-channel MOSEFT (101) forming another current mirror with (100), and a current mirror sink source on n-channel MOSFETs (102) and (103). In the shown embodiment, (100), (42), (43) and (101) are all-matched-parameters MOSFETs. Herein, a circuit with one synapse connection (model) is considered, and then the applicable conclusions are generalized for a circuit having more than one synapse modeling means. This assumes means (33),(35) and (31) are implemented for each synaptic connection modeled while means (36) and (36′) remain common for all synapse connections.

[0075] The above-described circuit operates as follows. Constant with time input current i_X(produced by a current sink source of an output stage similar to (36) or formed in the neural network inputs) is integrated into a linearly time-dependent voltage (applied as gate-source voltage ν_SG41on (41)) for a certain period of time T_Cfor which the switch (47) is closed: $\begin{array}{cc}{v}_{\mathrm{SG41}}=v_{C_x}\left(T_C\right)=\frac{1}{C_X}{\int }_0^{T_C}{i}_{X}dt=\frac{1}{C_X}{i}_X·T_C& \left(1.8\right)\end{array}$

[0076] Therefore the resulting voltage in Eq. (1.8) is linearly proportional to the input current i_X. After period of time T_Cthe current switch (47) is opened and remains opened for the rest of the computational interval under consideration. The voltage on C_xapplied on the gate-source terminals of the MOSFET (41) remains essentially constant being subject to discharge only by the leakage currents of (41) and (47). The latter voltage forms said x_kquantity in Eq. (1.5). “Synapse” current i_D41of (41) will be finally determined by the applied drain-source ν_SD41between nodes (99) and (46) forming synapse weight w_kin Eq. (1.5). Said ν_SD41=V_A−V_Bis determined by the difference of √{square root over (i_D42)}−√{square root over (i_D100)} through matched active-resistor loads (42) and (100): $\begin{array}{cc}{V}_A=V_{\mathrm{SS}}-v_{\mathrm{SD100}}\approx V_{\mathrm{SS}}-\sqrt{\frac{2i_{\mathrm{D100}}}{{\beta }_{100}}}-V_{\mathrm{TH100}}& \left(1.9\right)\\ V_B=V_{\mathrm{SS}}-v_{\mathrm{SD42}}\approx V_{\mathrm{SS}}-\sqrt{\frac{2i_{\mathrm{D42}}}{{\beta }_{42}}}-V_{\mathrm{TH42}}& \left(1.10\right)\end{array}$

[0077] where V_SSis the most positive supply voltage potential applied at the sources of (100),(42),(43) and (100); V_TH42=V_TH100are the threshold voltages of MOSFETs (100) and (42) respectively, and β₄₂=β₁₀₀are the transconductance parameters of matched parameters pair (100) and (42).

[0078] Subtracting Eq. (1.10) from Eq. (1.9) results in:

[0079] V_A−V_B=√{square root over (2/β)}(√{square root over (i_D42)}−√{square root over (i  (1.11)

[0080] where $\beta \stackrel{△}{=}{\beta }_{42}={\beta }_{100}.$

[0081] Hence, by controlling said currents difference, V_A−V_Band respectively connection weight quantity w_kof the modeled k-th synapse is controlled. The resulting current i_D41of this synapse MOSFET (41) is then summed up at node (99) along with the drain currents of the remaining synapse modeling MOSFETs (not shown) connected to the common node (99) in the same way as MOSFET (41): $\begin{array}{cc}{i}_{\mathrm{D100}}=\sum _{k=1}^N{i}_k=i_{\mathrm{D41}}+\dots & \left(1.12\right)\end{array}$

[0082] where i_D100current represents total synaptic current output for all N-number of synapse-modeling MOSFETs like (41).

[0083] In order to provide constant difference of potentials V_Aand V_B, independent of both local synapse current (for example i_D41) and neuron's overall synapse current i_D100respectively, it is further shown that i_D42≈i_D100is required. The latter is achieved by weight control means (31) comprised of p-channel MOSFETs (42), (43) and coupled n-channel MOSFET (44) and (45). Means (31) build effectively a follower for changes in V_Aby tracking changes of i_D100. Since i_D43=i_D100by the virtue of current mirror (100)-(43), current i_D44results in:

[0084] i_D44=m·i_D45=m·i_D43=m·i_D100  (1.13)

[0085] where m is (44)-(45) current mirror ratio. Further, by expressing:

[0086] i_D41=p·i_D100  (1.14)

[0087] where p is a quantitative scalar number satisfying 0≦p≦1 which represents i_D41as fraction of i_D100, current i_D42is written as:

[0088] i_D42=i_D44−i_D41=m·i_D100−p·i_D100=(m−p)·i_D100  (1.15)

[0089] Thus, it is obvious to one of ordinary skill that, current i_D42is proportional to overall synaptic activity current i_D100. Circuit DC operating point and current mirror ratio m are chosen such that, within a certain region of operation, (m−p)≈1 i.e.

[0090] i_D42≈i_D100  (1.16)

[0091] This further leads to: $\begin{array}{cc}\frac{d{V}_A}{d{i}_{\mathrm{D100}}}\approx \frac{d{V}_B}{d{i}_{\mathrm{D42}}}& \left(1.17\right)\end{array}$

[0092] It is also fortunate that Eq. (1.16) leads to very small V_A−V_Bwhich is in perfect agreement with aforementioned requirement to minimize non-linearity error defined in Eq. (1.7).

[0093] Regarding the choice of m, it will become apparent to one of ordinary skill, that it should satisfy

[0094] 1<m≦2  (1.18)

[0095] and that it is dependent on the number of synapse connections modeled (MOSFETs connections to node (99)). For instance, for one synapse, apparently p=1, therefore m≈2 should be implemented so that Eq.(1.16) and Eq.(1.17) are true. As number of synapse connections increases (number of synapse modeling MOSFETs connected to (99) increases), obviously, p is becoming smaller for each synapse and m should decrease to keep m−p≈1. In the extreme case where number of synapses increases to infinity, p→0 and m→1 accordingly. Thus it is concluded that m is inversely proportional to the number of synaptic connections modeled and a possible general rule that governs the choice of m can be written as: $\begin{array}{cc}m\approx 1+\frac{1}{N}& \left(1.19\right)\end{array}$

[0096] where N is the number of synapses modeled by the circuit shown on FIG. 4.

[0097] Still, in the interest of the present invention is also the ability to offset V_B<V_Aby a small amount such that to produce the desired ν_SD41=V_A−V_Bi.e. quantity w_krespectively. The latter can be achieved, in the suggested embodiment, by offsetting the back-gate of (43), employing the body-effect to offset the threshold voltage V_TH43of (43) thus effectively offsetting also i_D43from i_D100This is done by the introduction of a small control voltage V_WSETwhich should satisfy V_WSET<<V_THSUBwhere V_THSUBis the threshold voltage at which the n-channel MOSFET bulk-substrate junction becomes forward-biased and significant current flows into the substrate.

[0098] Finally, the current output means (36) construct a current mirror between the neuron load (100) and (101) to provide output current proportional to the sum of all synaptic output currents summed at node (99) without affecting said synaptic currents (as i_D41or overall synaptic current i_D100). The latter also provide a current sink source (102 and 103) compatible with the design of the current input(s) (like 33) of the described synapse(s) to allow for easy interconnection. It should be noted that, although, means (36) do not implement any specific hard-limiting function, as shown in this embodiment, it is inherent property of the circuit implemented by (101),(102) and (103) that it will, in fact, limit the overall circuit output due to two main factors:

[0099] (a) devices (101) or (103) go out of saturation mode of operation, and

[0100] (b) the circuit node voltages are ultimately limited by the power supply voltage range.

[0101] It must be noted that the implementation of specific hard-limiting or sigmoidal type output processing means is not object of the disclosure herein neither specific output processing means, other that the one mentioned above, are claimed as part of the invention. Such means can be easily added and implemented by any person ordinarily skilled in the art without need to modify the circuit disclosed herein or depart from the spirit of the invention.

[0102] III. Experimental Validation Data

[0103] Data disclosed on FIGS. 5 through 11 is believed useful with respect to utility requirement of 35 U.S.C 101 and 112, first paragraph and with respect to credibility by establishing evidence of record of a working example as related to MPEP 2107 second section.

[0104] As mentioned in the brief description of the drawings, FIG. 5 through 7 show results of computer simulations of an artificial neuron with two inputs and one output (two synapses) modeled by means of (1.6) trained and tested as linear classifier over a random sets of 2-D linearly separable data vectors. Results given herein are based on 200 random data runs, for each of which first the original model of a neuron with ideally linear synaptic connections based on (1.1) is trained and tested (data designated with a circle), then another model of the same neuron employing a synaptic connections modeled with inherent non-linearity according to (1.6), object of the present invention, is trained and tested (data designates with a cross) and the results are plotted on common plots to facilitate their analysis and comparison. More specifically:

[0105] FIGS. 5A and 5B show each run Mean-Square-Error (MSE) of neuron's response while learning over the training set of data and the Final Learning Rate (FLR) parameter value. These two characteristics give a measure of how well the neuron is learning to classify the two sets of data. It is obvious that both neurons perform very much alike and very well with MSE of, typically, less than 0.05 and FLR of about 0.1.

[0106] FIG. 6A shows a measure of how quickly each of the tested neuron models is learning. Again, it is observed that the performance between the two models is, practically, the same and both models, typically, finish their learning in about or less than 200 epochs.

[0107] FIG. 6B shows the success rate of correct classification during a test-run over the learned set of data for each model. As seen on the plot, the success rate is either localized around complete failure/success or almost evenly distributed in-between this range. What is important to notice is that the two models again appear to have quite indistinguishable distributions i.e. their performance is practically indistinguishable.

[0108] FIG. 7 shows “Deviation from reference” error-measured as the relative difference between the response of a neuron simulated with synaptic connections as in Eq. (1.6) and the response of an ideally linear neuron model over the same set of data. As shown, typically, this error is very minimal.

[0109] What is construed from the simulation result log files (not included in the disclosure for briefness) and simulation plots (shown) is that the model including non-linearity error is performing not worse that the original model in most cases and even better in some cases with respect to faster convergence possibly due to larger updates to the weights without compromising stability.

[0110] FIG. 8 shows I-V curves of the synapse drain current (i_D41) through MOSFET (41) versa gate-source voltage on same MOSFET (representing synapse pre-synaptic/input stimulus) where the family of curves are plotted for different values of source-drain voltage (same MOSFET) representing synapse connection weight. Note that, this plot applies to the circuit on FIG. 4 which is a single-synapse neuron (as shown) and thus, the current shown i_D100=i_D41which does not limit the generality of the results. Shown transient data is in response to a linear-dependent increase in source-gate voltage as shown on the lower half diagram on FIG. 8.

[0111] FIG. 9 depicts curves of voltage difference on nodes (99) and (46)—voltage V_A−V_B, determining synapse connection weight, versa pre-synaptic stimulus represented by gate-source voltage on MOSFET (41). The family of three curves are for three different V_WSETvoltages which control the absolute value of V_A−V_B. It is shown how the mentioned voltage difference remains, essentially, constant over a certain range (between markers M1-M2).

[0112] FIG. 10 shows voltage potentials V_Aand V_B, this time separately, where the family of curves are shown again for different values of weight-control signal V_WSET. This diagram demonstrates the operation of weight-control means (31) and the ability to compensate for changes in drain current (i_D41) and voltage V_Arespectfully by keeping V_SD41=V_A−V_Bessentially constant over a certain range (between markers M5-M6).

[0113] IV. Conclusion

[0114] As apparent from the above description and considerations, the present invention provides a method and apparatus to model a neural network synapse multiplication function, by using low supply voltages and utilizing conventional VLSI CMOS fabrication technology. Thus, the present invention provides for a simplification and on-chip integration of the neural network applications with other analog or digital applications, by means of only five conventional MOSFETs per synapse, while the synapse function itself, more specifically, is modeled by means of only a single MOSFET device.

[0115] It should be emphasized that the present invention is not limited to the particular embodiment disclosed herein as the believed best mode contemplated for carrying out the present invention, but rather that the disclosed method to use a single conventional MOSFET to model a neural synapse multiplication function may have many variations within the spirit and the scope of this invention except as limited and defined in the appended claims.