Inertial neuron implementation circuit

Abstract

The invention belongs to the field of circuit design technology and application, and particularly relates to a circuit for realizing inertial neurons, which comprises a first circuit channel for realizing a first circuit equation and a second circuit channel for realizing a second circuit equation, and the first circuit equation and the second circuit equation are used for realizing an inertial neuron model. By constructing the first circuit channel for realizing the first circuit equation and the second circuit channel for realizing the second circuit equation, the inertial neuron circuit is realized, and typical nonlinear behaviors of neurons can be realized only by adjusting external excitation; in addition, the circuit is simple in structure, low in manufacturing cost and convenient to integrate, and has an important value for hardware engineering and application of a future large-scale brain-like neural network.

Description

Technical Field

[0001] The invention belongs to the field of circuit design technology and application, and particularly relates to a circuit for realizing inertial neurons. Background Art

[0002] As the basic computing unit of neural networks, the circuit implementation technology of neuron models is one of the core research to promote the progress of artificial intelligence and brain-like computing systems. In the fields of brain-like computing, intelligent perception and complex system simulation, the hardware circuit design of neuron models directly affects the performance of neural network computing and the efficiency of system integration. Traditional neuron circuits are mostly based on complex mathematical models, such as the Hodgkin-Huxley model and the Izhikevich model. These models need to process multivariable dynamic equations and involve functions such as exponential terms and cubic terms, which leads to complex circuit structures during hardware implementation and is difficult to meet the design requirements of large-scale integrated circuits and low-power computing units.

[0003] In this context, studying neuron models with simple mathematical forms has become a cutting-edge technical direction for the hardware implementation of artificial neural networks. The inertial neuron model is a new type of artificial neuron model. It has gradually attracted widespread attention from researchers due to its simple mathematical expression, low computational complexity and easy circuit implementation. Compared with traditional complex neuron models, inertial neurons can significantly reduce the difficulty of circuit design and implementation while maintaining the chaotic dynamics effect. The core idea is to describe the excitation behavior of neurons through simple mathematical expressions, thereby greatly simplifying the circuit design process, improving implementation efficiency, and having higher circuit integration and flexibility.

[0004] Based on this, the present invention proposes an inertial neuron implementation circuit scheme, which realizes the chaotic and periodic behaviors of inertial neurons through analog circuit design methods, providing a more efficient and flexible neuron hardware implementation approach for the new generation of brain-like chips and intelligent computing systems. Summary of the invention

[0005] The purpose of the present invention is to provide an inertial neuron implementation circuit to solve the problems raised in the above background technology. The present invention provides the following technical solutions:

[0006] An inertial neuron implementation circuit, characterized in that it includes: a first circuit channel for implementing a first circuit equation and a second circuit channel for implementing a second circuit equation, wherein the first circuit equation and the second circuit equation are used to implement an inertial neuron model.

[0007] Furthermore, the first circuit channel includes a resistor R1, a capacitor C1, an operational amplifier U1 and an inverse hyperbolic tangent function circuit F1, one end of the resistor R1 is connected to the inverting input end of the operational amplifier U1 and connected to one end of the capacitor C1, the output end of the operational amplifier U1 is connected to the other end of the capacitor C1, and connected to the input end of the inverse hyperbolic tangent function circuit F1; the non-inverting input end of the operational amplifier U1 is connected to the "ground", and the output end voltage is recorded as the first state variable v x .

[0008] Furthermore, the second circuit channel includes a capacitor C2, resistors R3 to R7, and operational amplifiers U2 and U3; the output end of the reverse hyperbolic tangent function circuit F1 is connected to the inverting input end of the operational amplifier U2 via a resistor R4, and is connected to resistors R2, R3, R5 and one end of the capacitor C2; the other end of the resistor R3 is connected to the output end of the operational amplifier U1; the other end of the resistor R5 is connected to the input AC excitation -v AC The other end of the resistor R2 is connected to the other end of the capacitor C2 and connected to the output end of the operational amplifier U2; the output end of the operational amplifier U2 is connected to the inverting input end of the operational amplifier U3 via the resistor R6, and the inverting input end of the amplifier U3 is connected to its output end via the resistor R7 and connected to the other end of the resistor R1; the non-inverting input ends of the operational amplifiers U2 and U3 are connected to the "ground", and the output end voltage of the operational amplifier U2 is recorded as the second state variable v y .

[0009] Furthermore, the first circuit equation and the second circuit equation are:

[0010]

[0011] Furthermore, the parameter settings of the first circuit channel and the second circuit channel include R1=R2=R5=R6=R7=10kΩ, R3=R / 1.8=5.5556kΩ, R4=R / 3.5=2.8571kΩ; AC is the AC excitation, the formula is v AC =Asin(2πFt), where the amplitude A=3V and F is the physical frequency of AC excitation.

[0012] Furthermore, the reverse hyperbolic tangent function circuit F1 includes a resistor R8 with one end as an output end, and the other end of the resistor R8 is connected to the reverse input end of the operational amplifier U4; the positive input end of the operational amplifier U4 is connected to the "ground", and its reverse input end is connected to the "ground" through the resistor R F Connected to its output terminal and connected to the base set of transistor T1; the collector of T1 is connected to the resistor R c1 One end of the resistor R c1 The other end is connected to the power supply E; the power supply E is also connected to Rc2 One end, R c2 The other end is connected to the collector of transistor T2, the emitters of transistors T1 and T2 are connected, and connected to the collector of transistor T3; the base of transistor T4 is connected to the base of transistor T3, and the collector of transistor T4 is connected to its own base and also connected to resistor R w One end of the resistor R w The other end of the transistor T3 and T4 are connected to the ground through the resistor R T1 , R T2 The collector of transistor T1 is also connected to one end of resistor R9, and the other end of resistor R9 is also connected to resistor R 12 One end and the inverting input end of the operational amplifier U5, the resistor R 12 The other end is connected to the output end of the operational amplifier U5 as the output end of the reverse hyperbolic tangent function circuit; the collector and base of the transistor T2 are connected through resistors R 10 , R 11 Connect the positive input terminal of operational amplifier U5, and the base of transistor T2 is connected to the ground.

[0013] Furthermore, the parameters of the hyperbolic tangent function circuit F1 are set to include R8=R9=R 10 =R 11 =R 12 =10kΩ, R T1 =R T2 =10kΩ, R C1 =R C2 =1kΩ, R F =520Ω, R w =9.8kΩ, E=15V.

[0014] Beneficial effects of the present invention: The present invention realizes an inertial neuron circuit by constructing a first circuit channel for realizing a first circuit equation and a second circuit channel for realizing a second circuit equation, and only adjusting external excitation can realize typical nonlinear behavior of neurons. In addition, the circuit structure is simple, the manufacturing cost is low, and it is easy to integrate, which is of great value to the hardware engineering and application of future large-scale brain-like neural networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Implementing circuits for inertial neurons;

[0016] Figure 2 Implement a circuit for the inverse hyperbolic tangent function;

[0017] Figure 3 When the input AC excitation angular frequency is ω=1.3, the phase diagram of the double vortex chaotic attractor of the inertial neuron is realized on the xy plane simulated by MATLAB;

[0018] Figure 4 The two-phase diagram of the coexistence period of inertial neurons realized on the xy plane of MATLAB simulation when the input AC excitation angular frequency is ω=1.5;

[0019] Figure 5 When the input AC excitation angular frequency is ω=1.6, the phase diagram of the inertial neuron coexistence period limit cycle is realized on the xy plane simulated by MATLAB;

[0020] Figure 6 When the input AC excitation physical frequency is F = 2069.01Hz, the oscilloscope on the hardware captures v x -v y The phase diagram of the double-vortex chaotic attractor of inertial neurons is realized on the plane;

[0021] Figure 7 When the input AC excitation physical frequency is F = 2387.32Hz, the oscilloscope on the hardware captures v x -v y Realize the two-phase diagram of the coexistence period of inertial neurons on the plane;

[0022] Figure 8 When the input AC excitation physical frequency is F = 2556.08Hz, the oscilloscope on the hardware captures v x -v y Phase diagram of the limit cycle of the coexistence period of inertial neurons realized on the plane. DETAILED DESCRIPTION

[0023] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0024] Embodiment 1:

[0025] This embodiment is based on an inertial neuron model, aiming to realize the rich dynamics of neurons. When the frequency of external stimulation of neurons is changed, neurons will exhibit brain-like neuron dynamic phenomena such as chaos and periodic attractors. The inertial neuron model can be expressed by a first-order differential equation as follows:

[0026]

[0027] Where x is the average value of the neuron cell potential, y is the internal state variable of the neuron system, and tanh(x) is the activation function of the inertial neuron. Inertial neurons have a continuous S-shaped transfer characteristic or input-output relationship. The hyperbolic tangent corresponds perfectly to this functional relationship and can be used as a nonlinear function to construct neurons. AC=Asin(ωt) refers to the simulation of external time-varying stimulation, A is the amplitude of the stimulation, and ω is the adjustable angular frequency.

[0028] When A is a typical parameter of 3, the dynamic behavior of neurons under different ω can be manifested as chaos, coexistence chaotic state, coexistence period-2 state and coexistence limit cycle.

[0029] Based on the first-order differential equation of the above-mentioned inertial neuron model, this embodiment provides an inertial neuron implementation circuit including a first circuit channel and a second circuit channel. Figure 1 As shown, the first circuit channel includes a resistor R1, a capacitor C1, an operational amplifier U1 and an inverse hyperbolic tangent function circuit F1, one end of the resistor R1 is connected to the inverting input end of the operational amplifier U1 and connected to one end of the capacitor C1, the output end of the operational amplifier U1 is connected to the other end of the capacitor C1, and connected to the input end of the inverse hyperbolic tangent function circuit F1; the non-inverting input end of the operational amplifier U1 is connected to the "ground", and the output end voltage is recorded as the first state variable v x The second circuit channel includes capacitor C2, resistors R3 to R7, operational amplifiers U2 and U3; the output end of the reverse hyperbolic tangent function circuit F1 is connected to the inverting input end of the operational amplifier U2 via resistor R4, and is connected to resistors R2, R3, R5 and one end of the capacitor C2; the other end of the resistor R3 is connected to the output end of the operational amplifier U1; the other end of the resistor R5 is connected to the input AC excitation -v AC ; The other end of the resistor R2 is connected to the other end of the capacitor C2 and connected to the output end of the operational amplifier U2; the output end of the operational amplifier U2 is connected to the inverting input end of the operational amplifier U3 via the resistor R6, and the inverting input end of the amplifier U3 is connected to its output end via the resistor R7 and connected to the other end of the resistor R1; the non-inverting input ends of the operational amplifiers U2 and U3 are connected to the "ground", and the output end voltage of the operational amplifier U2 is recorded as the second state variable v y When the time scale of the circuit satisfies t = RCτ (R = 10kΩ, C = 10nF), according to Figure 1 The schematic diagram can be used to derive the circuit equation of the circuit of this embodiment:

[0030]

[0031] v x and v y are the two state variables of (2). By changing v AC =Asin(2πFt) can realize the dynamic behavior of inertial neurons in the circuit. According to model (2), the corresponding resistor configuration is R1=R2=R5=R6=R7=10kΩ, R3=R / 1.8=5.5556kΩ, R4=R / 3.5=2.8571kΩ, and the AC stimulation amplitude is fixed at A=3V.

[0032] Embodiment 2:

[0033] This embodiment provides an inverse hyperbolic tangent function circuit F1 for a first circuit channel. Figure 2 As shown, a resistor R8 is included, one end of which is used as an input end, and the other end of the resistor R8 is connected to the reverse input end of the operational amplifier U4; the positive input end of the operational amplifier U4 is connected to the "ground", and its reverse input end is connected to the "ground" through the resistor R F Connected to its output terminal and connected to the base of transistor T1; the collector of T1 is connected to the resistor R c1 One end of the resistor R c1 The other end is connected to power supply E; power supply E is also connected to R c2 One end, R c2 The other end is connected to the collector of transistor T2, the emitters of transistors T1 and T2 are connected, and connected to the collector of transistor T3; the base of transistor T4 is connected to the base of transistor T3, and the collector of transistor T4 is connected to its own base and also connected to resistor R w One end of the resistor R w The other end of the transistor T3 and T4 are connected to the ground through resistors R T1 , R T2 The collector of transistor T1 is also connected to one end of resistor R9, and the other end of resistor R9 is also connected to resistor R 12 One end and the inverting input end of the operational amplifier U5, the resistor R 12 The other end is connected to the output end of the operational amplifier U5 as the output end of the reverse hyperbolic tangent function circuit; the collector and base of the transistor T2 are connected through resistors R 10 , R 11 Connect the positive input terminal of operational amplifier U5, and the base of transistor T2 is connected to the ground.

[0034] In the inverse hyperbolic tangent function circuit module provided in this embodiment, the element value is fixed to R8=R9=R 10 =R 11 =R 12 =10kΩ, R T1 =R T2 =10kΩ, R C1 =R C2 =1kΩ, R F =520Ω, R w =9.8kΩ, E=15V.

[0035] Embodiment 3:

[0036] In this embodiment, the ODE23 algorithm is used in MATLAB software to perform numerical simulation on the model (1) in the embodiment 1. Taking A=3 as an example, the dynamic behavior of the numerical simulation of the inertial neuron under different ω is as follows: Figures 3 to 5 shown.

[0037] like Figure 3 As shown, when ω is 1.3, model (1) behaves as a chaotic double-vortex attractor.

[0038] like Figure 4 As shown, when ω is 1.5, model (1) behaves as a coexisting periodic two-attractor.

[0039] like Figure 5 As shown, when ω is 1.6, model (1) behaves as a periodic limit cycle.

[0040] Therefore, the numerical simulation results of the three sets of phase diagrams indicate the existence of chaotic attractors as well as coexisting periodic chaotic attractors.

[0041] Embodiment 4:

[0042] This embodiment is based on the inertial neuron implementation circuit provided in Examples 1 and 2, and the circuit experiment is verified. The electronic devices include a precision potentiometer with a ±15V power supply, a metal film resistor, a monolithic ceramic capacitor, and operational amplifiers AD711KN and TL082CP, thereby realizing the electronic neuron circuit without a multiplier as provided in Examples 1 and 2. The above resistance is measured using a Tonghui TH2830 LCR meter, the AC signal is provided by a Tektronix AFG3022C, and the experimental phase diagram is collected by a Tektronix TDS3054C digital oscilloscope in XY mode.

[0043] In circuit simulation, the resistance value is very accurate. However, in hardware experiments, since the analog circuit will have a certain percentage of change and will change with the temperature and power supply, the accuracy of the resistance value cannot be guaranteed. Therefore, this embodiment uses a precision instrument LCR meter device to measure the resistance value to ensure its accuracy and feasibility.

[0044] The experimental attractor for physically implementing the simple inertial neuron model (2) is as follows Figures 6 to 8 By adjusting the frequency of the input signal, v can be captured experimentally. x -v y Phase diagram projected onto a plane. Note that the initial voltage in the simulated hardware experiment was achieved by turning the power of the breadboard on and off.

[0045] like Figure 6As shown, when the input AC excitation physical frequency is F = 2069.01 Hz, model (2) behaves as a chaotic double-scroll attractor.

[0046] like Figure 7 As shown, when the input AC excitation physical frequency is F = 2387.32 Hz, model (2) behaves as a coexisting periodic two-attractor.

[0047] like Figure 8 As shown, when the input AC excitation physical frequency is F = 2556.08 Hz, model (2) behaves as a periodic limit cycle.

[0048] It can be seen that, ignoring some experimental errors, there are coexisting attractors, and they are basically consistent with the numerical simulation results, which illustrates the effectiveness and correctness of the circuit design.

[0049] In addition to the above embodiments, the present application also includes other implementation methods. Any technical solutions formed by equivalent transformation or equivalent replacement should fall within the protection scope of the claims of the present invention.

Claims

1. An inertial neuron implementation circuit, characterized in that: include: A first circuit path for implementing a first circuit equation and a second circuit path for implementing a second circuit equation, wherein the first circuit equation and the second circuit equation are used to implement an inertial neuron model.

2. The inertial neuron implementation circuit according to claim 1, characterized in that: The first circuit path includes a resistor R1, a capacitor C1, an operational amplifier U1 and an inverse hyperbolic tangent function circuit F1. One end of the resistor R1 is connected to the inverting input end of the operational amplifier U1 and to one end of the capacitor C1. The output end of the operational amplifier U1 is connected to the other end of the capacitor C1 and to the input end of the inverse hyperbolic tangent function circuit F1. The non-inverting input end of the operational amplifier U1 is connected to the "ground", and the output end voltage is recorded as the first state variable v x .

3. The inertial neuron implementation circuit according to claim 2, characterized in that: The second circuit path includes capacitor C2, resistors R3-R7, operational amplifiers U2 and U3; the output end of the reverse hyperbolic tangent function circuit F1 is connected to the inverting input end of the operational amplifier U2 via resistor R4, and is connected to resistors R2, R3, R5 and one end of the capacitor C2; the other end of the resistor R3 is connected to the output end of the operational amplifier U1; the other end of the resistor R5 is connected to the input AC excitation -v AC The other end of the resistor R2 is connected to the other end of the capacitor C2 and connected to the output end of the operational amplifier U2; the output end of the operational amplifier U2 is connected to the inverting input end of the operational amplifier U3 via the resistor R6, and the inverting input end of the amplifier U3 is connected to its output end via the resistor R7 and connected to the other end of the resistor R1; the non-inverting input ends of the operational amplifiers U2 and U3 are connected to "ground", and the output end voltage of the operational amplifier U2 is recorded as the second state variable v y .

4. The inertial neuron implementation circuit according to claim 3, characterized in that: The first circuit equation and the second circuit equation are:

5. An inertial neuron implementation circuit according to claim 3 or 4, characterized in that: The parameter settings of the first circuit channel and the second circuit channel include R=R1=R2=R5=R6=R7=10kΩ, R3=R / 1.8=5.5556kΩ, R4=R / 3.5=2.8571kΩ; the v AC is the AC excitation, the formula is v AC =Asin(2πFt), where the amplitude A=3V and F is the physical frequency of AC excitation.

6. An inertial neuron implementation circuit according to any one of claims 2 to 4, characterized in that: The reverse hyperbolic tangent function circuit F1 includes a resistor R8 at one end as an input end, and the other end of the resistor R8 is connected to the reverse input end of the operational amplifier U4; the positive input end of the operational amplifier U4 is connected to the "ground", and its reverse input end is connected to the "ground" through the resistor R F Connected to its output terminal and connected to the base set of transistor T1; the collector of T1 is connected to the resistor R c1 One end of the resistor R c1 The other end is connected to the power supply E; the power supply E is also connected to R c2 One end, R c2 The other end is connected to the collector of transistor T2, the emitters of transistors T1 and T2 are connected, and connected to the collector of transistor T3; the base of transistor T4 is connected to the base of transistor T3, and the collector of transistor T4 is connected to its own base and also connected to resistor R w One end of the resistor R w The other end of the transistor T3 and T4 are connected to the ground through the resistor R T1 , R T2 The collector of transistor T1 is also connected to one end of resistor R9, and the other end of resistor R9 is also connected to resistor R 12 One end and the inverting input end of the operational amplifier U5, the resistor R 12 The other end of the transistor T2 is connected to the output end of the operational amplifier U5 as the output end of the inverse hyperbolic tangent function circuit; the collector and base of the transistor T2 are connected to the output end of the operational amplifier U5 as the output end of the inverse hyperbolic tangent function circuit; 10 , R 11 Connect the positive input terminal of operational amplifier U5, and the base of transistor T2 is connected to "ground".

7. The inertial neuron implementation circuit according to claim 6, characterized in that: The parameters of the inverse hyperbolic tangent function circuit F1 are set to include R8=R9=R 10 =R 11 =R 12 =10kΩ, R T1 =R T2 =10kΩ, R C1 =R C2 =1kΩ, R F =520Ω, R w =9.8kΩ, E=15V.

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