WO2022249308A1 - 設計方法および記録媒体 - Google Patents

設計方法および記録媒体 Download PDF

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WO2022249308A1
WO2022249308A1 PCT/JP2021/019903 JP2021019903W WO2022249308A1 WO 2022249308 A1 WO2022249308 A1 WO 2022249308A1 JP 2021019903 W JP2021019903 W JP 2021019903W WO 2022249308 A1 WO2022249308 A1 WO 2022249308A1
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step size
firing
mathematical model
time
firing time
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French (fr)
Japanese (ja)
Inventor
悠介 酒見
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NEC Corp
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NEC Corp
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Priority to PCT/JP2021/019903 priority patent/WO2022249308A1/ja
Priority to US18/561,041 priority patent/US20240256826A1/en
Publication of WO2022249308A1 publication Critical patent/WO2022249308A1/ja
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/049—Temporal neural networks, e.g. delay elements, oscillating neurons or pulsed inputs
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/06—Physical realisation, i.e. hardware implementation of neural networks, neurons or parts of neurons
    • G06N3/063—Physical realisation, i.e. hardware implementation of neural networks, neurons or parts of neurons using electronic means
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/06—Physical realisation, i.e. hardware implementation of neural networks, neurons or parts of neurons
    • G06N3/063—Physical realisation, i.e. hardware implementation of neural networks, neurons or parts of neurons using electronic means
    • G06N3/065—Analogue means
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods

Definitions

  • the present invention relates to design methods and recording media.
  • a spiking neural network is one of neural networks (see, for example, Patent Document 1).
  • a spiking neural network is expected to be a neural network with high power efficiency in that information is transmitted between spiking neurons using binary signals called spikes.
  • a circuit with discretized firing times may be advantageous in terms of manufacturability and power efficiency.
  • models with discretized time tend to have low learning accuracy.
  • An example of the object of the present invention is to provide a design method and a recording medium that can solve the above problems.
  • the design method is such that the product of the step size of the firing time in the mathematical model and the step size of the weight in the mathematical model is the step size of the firing time of the spike generator and the synapse
  • the spike generator so that the product of the output current value of the circuit and the minimum step size is divided by the product of the firing threshold voltage in the spike generator and the capacitance of the capacitor that simulates the membrane potential the step size of the firing time, the minimum step size of the output current value of the synapse circuit, the firing threshold voltage of the spike generator, the capacitance of the capacitor, the step size of the firing time in the mathematical model, or the weight in the mathematical model; Determining at least one of the step sizes.
  • the recording medium stores in the computer that the product of the step size of the firing time in the mathematical model and the step size of the weight in the mathematical model is the step size of the firing time by the spike generator. and the minimum step size of the output current value of the synapse circuit, divided by the product of the firing threshold voltage in the spike generator and the capacitance of the capacitor that simulates the membrane potential.
  • the step size of the firing time by the generator, the minimum step size of the output current value of the synapse circuit, the firing threshold voltage in the spike generator, the capacitance of the capacitor, the step size of the firing time in the mathematical model, or the mathematical model is a recording medium for recording a program for determining at least one of the step sizes of the weights in .
  • the firing time can be discretized, and the learning accuracy is relatively high.
  • FIG. 4 is a diagram showing an example of a mathematical model of a spiking neuron to be discretized according to the embodiment;
  • FIG. 4 is a diagram showing an example of temporal evolution of membrane potential of a spiking neuron according to the embodiment;
  • FIG. 4 is a diagram showing an example of a circuit model of a spiking neuron according to the embodiment;
  • FIG. 5 is a diagram showing an example of firing times in the spiking neural network according to the embodiment; It is a figure which shows the example of the processing procedure in the design method which concerns on embodiment. 6 is a flow chart showing an example of processing in the design method according to the embodiment;
  • 1 is a schematic block diagram showing a configuration of a computer according to at least one embodiment;
  • FIG. 1 is a diagram showing an example of a mathematical model of a spiking neuron to be discretized.
  • a hierarchical neural network is assumed and the i-th spiking neuron of the l-th layer is shown.
  • the structure of the spiking neural network is not limited to a hierarchical structure.
  • a spiking neuron outputs a spike when the membrane potential v i (l) (t) reaches the firing threshold V th .
  • FIG. 2 is a diagram showing an example of time evolution of the membrane potential of a spiking neuron.
  • the horizontal axis of the graph in FIG. 2 indicates time.
  • the vertical axis indicates the membrane potential.
  • the membrane potential is denoted as v i (l) .
  • the spiking neuron in FIG . A spike input is being received. After the spike is input, the membrane potential continues to change at a rate corresponding to the weight set for each spiking neuron that outputs the spike. Also, the rate of change in membrane potential for each spike input is added linearly.
  • the membrane potential of the spiking neuron in FIG. 2 reaches the firing threshold V th and the spiking neuron is firing.
  • the membrane potential becomes 0 due to firing, and after that the membrane potential does not change even if a spike input is received.
  • the time when a spiking neuron fires is called firing time.
  • the firing time is also called spike time.
  • the firing time, the spike output time of the spike output side spiking neuron, and the spike input time of the spike input side spiking neuron are the same.
  • the delay time may be indicated in the formula.
  • the membrane potential after ignition is not limited to one that does not change from the potential 0 described above.
  • the membrane potential may change according to the spike input.
  • a change in membrane potential before firing in a mathematical model of a spiking neuron can be expressed as a differential equation of Equation (1).
  • v i (l) (t) denotes the membrane potential of the i-th spiking neuron in the l-th layer at time t.
  • w ij (l) represents the weight for the spike from the jth spiking neuron in the l ⁇ 1th layer to the ith spiking neuron in the lth layer.
  • .theta. represents a step function and is expressed as in Equation (2).
  • t j *(l ⁇ 1) indicates the firing time of the jth spiking neuron in the l ⁇ 1th layer.
  • FIG. 3 is a diagram showing an example of a circuit model of a spiking neuron.
  • a circuit model here is a circuit that implements the model.
  • the synapse circuit when a spike due to a pulse signal or step signal is input to a synapse circuit, the synapse circuit continues to output a weighted current.
  • the currents output by the synaptic circuits are summed up and stored in capacitors, creating a potential across the capacitors.
  • the potential of this capacitor simulates the membrane potential.
  • a Spike Generator compares the potential of the capacitor to a predetermined firing threshold. The spike generator outputs a spike when the potential of the capacitor reaches the firing threshold.
  • One spike generator may output a spike only once.
  • one spike generator may fire multiple times by, for example, resetting the potential of a capacitor when a spike occurs.
  • a change in membrane potential before firing in a circuit model of a spiking neuron can be expressed as a differential equation of Equation (3).
  • I ij (l) (t) represents a current value for simulating a change in membrane potential caused by a spike from the j-th spiking neuron in the l ⁇ 1-th layer to the i-th spiking neuron in the l-th layer.
  • Equation (3) is transformed into Equation (4).
  • I ij (l) represents the current value when the synaptic circuit outputs current. Since switching between ON and OFF of the current is indicated by " ⁇ (t ⁇ t j *(l ⁇ 1) )", the current value I ij (l) is treated as a constant whose value can be updated by learning. Therefore, unlike the expression (3), in the expression (4), "(t)" is not added to “I ij (l) ".
  • Equation (5) time is represented by time steps, and t takes an integer value of 0, 1, 2, . . .
  • the membrane potential “v i (l) (t)” at time t is obtained by multiplying the membrane potential “v i (l) (t ⁇ 1)” at time t ⁇ 1 by the amount of change “ ⁇ j (w ij (l) ⁇ (t ⁇ t j *(l ⁇ 1) ))”.
  • Equation (6) is obtained.
  • Equation (6) the charge on the capacitor between time t ⁇ 1 and time t is calculated by “ ⁇ j (I ij (l) (t))” obtained by multiplying the total current value by unit time “1”. is shown.
  • the accuracy of the spiking neural network's calculations will differ depending on how long the unit time in the time step is set to be the time width in the non-discretized time. It is considered that the shorter the time width of the unit time, the higher the accuracy of calculation.
  • the step width of the firing time is adjusted to the time width of the unit time in the time step, if the time width of the unit time is shortened, the spike with a short firing time step width will occur. utensil is required. Therefore, in this case, there is a trade-off between the accuracy of the spiking neural network's calculations and the required specifications for the spike generator.
  • the step width of the firing time is constant regardless of the time width of the unit time in the time step, shortening the time width of the unit time reduces the time step required for calculation It is conceivable that the number of steps in As the number of steps increases, the calculation time becomes longer and the power consumption becomes larger. Therefore, in this case, there is a trade-off between the accuracy of the calculation of the spiking neural network and the calculation time and power consumption.
  • FIG. 4 is a diagram showing an example of firing times in a spiking neural network.
  • the horizontal axis of the graph in FIG. 4 indicates the time elapsed since the input layer spiking neuron first fired.
  • the unit of time on the horizontal axis is milliseconds (ms).
  • the vertical axis indicates the identification number of the spiking neuron in each of the input layer, hidden layer, and output layer.
  • the time is expressed in time steps, and the unit time is 2 milliseconds. Six steps after the input layer spiking neuron fires first, the output layer spiking neuron fires first.
  • the mathematical model with discretized time is configured with a time step unit time of 2 milliseconds as shown in FIG. Assume that the step size is configured as 2 milliseconds. From this state, consider the case where the unit time of the time step in the mathematical model is set to 1 millisecond.
  • a circuit model spike generator it is conceivable to use a spike generator whose firing time interval is 2 milliseconds as it is. In this case, there is no need to prepare a new spike generator or replace the spike generator.
  • the calculation time in the circuit model will be double the calculation time in the mathematical model because the step size of the firing time is double the unit time of the time step. Further, when the electric charge stored in the capacitor exceeds the storage capacity of the capacitor due to the longer operation time, it becomes necessary to replace the capacitor or the synapse circuit.
  • the time width of the unit time There are merits and demerits regarding the merits and demerits of . If the time width of the unit time is changed after learning using a discretized circuit model, re-learning is required, which places a burden on the person in charge of learning. Re-learning is also required when changing the time span of the unit time after performing learning using a discretized mathematical model, which places a burden on the person in charge of learning.
  • FIG. 5 is a diagram illustrating an example of a processing procedure in the design method according to the embodiment;
  • a device such as a computer may automatically or semi-automatically perform the processing of FIG.
  • a person may perform the processing of FIG. 5, such as a designer of a spiking neural network performing the processing of FIG. 5 using a computer.
  • the device or person learns the non-discretized model of the spiking neural network (step S11).
  • the learning of the model here means adjusting the parameter values of the model by machine learning.
  • the device or person determines parameter values for implementing the learned model in the discretized circuit (step S12).
  • the parameter ⁇ of the ignition threshold scale is introduced into the equation (1), the equation (7) is obtained.
  • parameter ⁇ plays a role of a coefficient that adjusts the rate of change of membrane potential.
  • a parameter ⁇ can be used as a parameter for adjusting the scale of the membrane potential illustrated in FIG.
  • the value of the parameter ⁇ can be set according to the firing threshold set for the spike generator.
  • the value of parameter ⁇ is It can be set to 5.
  • Equation (8) is obtained by discretizing weight W ij (l) and firing time t j *(l ⁇ 1) for equation (7).
  • W (min) indicates the step size of the weight.
  • W ij (level, l) indicates an integer multiplied by the weight step width W (min) .
  • W (min) W ij (level, l) indicates a value obtained by rounding the weight W ij (l) shown in Equation (7) by discretization.
  • ⁇ t (model) indicates the step size of the ignition time in the mathematical model.
  • t j (step, l ⁇ 1) indicates an integer that is multiplied by the step size ⁇ t (model) of the firing time.
  • t j (step, l ⁇ 1) t (model) indicates a value obtained by rounding the firing time t j *(l ⁇ 1) shown in Equation (7) by discretization.
  • Formula (8) is further subjected to scale conversion that converts the time scale of the mathematical model to the time scale of the circuit model. This scale conversion is shown as Equation (9).
  • Equation (10) the time in the mathematical model is denoted by t, and the time in the circuit model is denoted by t'.
  • ⁇ t (Circuit) indicates the step size of the firing time in the circuit model.
  • Equation (11) is obtained by converting the time scale of Equation (8) from the time scale in the mathematical model to the time scale in the circuit model using Equations (9) and (10).
  • equation (12) is obtained. be done.
  • I (min) indicates the step size of the current value.
  • I ij (level, l) represents an integer that is multiplied by the step size I (min) of the current value.
  • I (min) I ij (level, l) indicates a value obtained by rounding the current value I ij (l) (t) shown in Equation (4) by discretization.
  • the device or person determines the value of each parameter so as to satisfy equation (15). For example, a device or a person may determine parameter values such that recognition performance and power efficiency of the spiking neural network are as high as possible under the constraint of Equation (15).
  • a device or a person inputs the hardware specifications into Equation (15) to determine the parameter values for discretization of the mathematical model. good too. For example, consider a case where hardware specifications are determined as follows.
  • ⁇ t (model) and W (min) may be determined.
  • the discretization parameter values of the mathematical model are, for example, the value of ⁇ t (model) and the value of w (min) .
  • Hardware specifications are, for example, the value of I (min) , the value of ⁇ , the value of C, and the value of ⁇ t (circuit) .
  • the device or person converts the learned spiking neural network into a mathematical model in which weights and firing times are discretized (step S13). Specifically, the device or person sets each of the spiking neuron models included in the learned spiking neural network to satisfy the values of ⁇ t (model) and w (min) obtained in step S12. Replace with a discretized model of spiking neurons.
  • the connection relationships between spiking neuron models are the same as in the spiking neural network before conversion.
  • the device or person designs the circuit model of the spiking neural network by converting the mathematical model in which the weights and firing times are discretized into a circuit model in which the current values and firing times are discretized (step S14). Specifically, the device or person uses I (min) , ⁇ , C, and ⁇ t (circuit ) to the circuit model of the spiking neuron. The connection relationships between spiking neuron models are the same as in the spiking neural network before conversion. After step S14, the person or device ends the processing of FIG.
  • the device automatically or semi-automatically generates a circuit model of the spiking neural network designed by the process of FIG. 5, so that the learned spiking neural network is implemented in hardware. good too.
  • a person may use a device to generate a circuit model of the spiking neural network designed by the process of FIG. 5, thereby implementing the learned spiking neural network in hardware.
  • the product of the step size of the firing time in the mathematical model and the step size of the weight in the mathematical model is the difference between the step size of the firing time of the spike generator and the minimum step size of the output current value of the synapse circuit.
  • the step size of the firing time by the spike generator and the output current value of the synaptic circuit are adjusted to be equal to the value obtained by dividing the product by the product of the firing threshold voltage in the spike generator and the capacitance of the capacitor that simulates the membrane potential. At least one of the minimum step size, the firing threshold voltage in the spike generator, the capacitance of the capacitor, the firing time step size in the mathematical model, or the weight step size in the mathematical model is determined.
  • a trained spiking neural network with undiscretized firing times and weights is transformed into a spiking neural network with a numerical model with discretized firing times and weights, Furthermore, it can be converted into a spiking neural network by a circuit model in which current values and weights are discretized.
  • the accuracy of learning is relatively high in that learning can be performed with a spiking neural network in which the firing time and weights are not discretized, and the firing time in the trained neural network can be discretized. can be done.
  • the firing time in the mathematical model Determine the step size and the step size of the weights in the mathematical model.
  • the design parameter values of the mathematical model of the spiking neural network are adjusted so as to match the specifications of the circuit model of the spiking neural network. can decide.
  • the step size of the firing time by the spike generator the minimum step size of the output current value of the synapse circuit, Determine the firing threshold voltage in the spike generator and the capacitance of the capacitor.
  • a circuit model of the spiking neural network is created so as to match the required specifications. specifications can be determined.
  • the design method further includes learning a spiking neural network using a spiking neuron model in which neither the firing time nor the weight is discretized.
  • the step size of the firing time in the mathematical model and the step size of the weight in the mathematical model are used to fire a trained spiking neural network using a spiking neuron model in which neither the firing time nor the weight is discretized. It is a design value for conversion to a spiking neural network using a mathematical model of spiking neurons in which time and weights are discretized.
  • the step size of the firing time by the spike generator, the minimum step size of the output current value of the synaptic circuit, the firing threshold voltage in the spike generator, and the capacitance of the capacitor that simulates the membrane potential are discretized in the firing time and weight.
  • a trained spiking neural network with undiscretized firing times and weights is transformed into a spiking neural network with a numerical model with discretized firing times and weights, Furthermore, it can be converted into a spiking neural network by a circuit model in which current values and weights are discretized.
  • the accuracy of learning is relatively high in that learning can be performed with a spiking neural network in which the firing time and weights are not discretized, and the firing time in the trained neural network can be discretized. can be done.
  • FIG. 6 is a flow chart showing an example of processing in the design method according to the embodiment.
  • the design method shown in FIG. 6 includes determining parameter values (step S611).
  • the product of the step size of the firing time in the mathematical model and the step size of the weight in the mathematical model is the step size of the firing time of the spike generator and the output current of the synapse circuit.
  • the step size of the firing time by the spike generator to be equal to the product of the minimum step size of the value divided by the product of the firing threshold voltage in the spike generator and the capacitance of the capacitor that simulates the membrane potential, At least one of the minimum step size of the output current value of the synapse circuit, the firing threshold voltage of the spike generator, the capacity of the capacitor, the firing time step size in the mathematical model, or the weight step size in the mathematical model is determined.
  • a trained spiking neural network with undiscretized firing times and weights is replaced with a spiking neural network based on a numerical model with discretized firing times and weights. Furthermore, it can be transformed into a spiking neural network by a circuit model in which the current values and weights are discretized.
  • the accuracy of learning is relatively high in that learning can be performed with a spiking neural network in which the firing time and weights are not discretized, and the firing time in the trained neural network can be discretized.
  • FIG. 7 is a schematic block diagram showing the configuration of a computer according to at least one embodiment.
  • a computer 700 includes a CPU (Central Processing Unit) 710 , a main memory device 720 , an auxiliary memory device 730 and an interface 740 .
  • CPU Central Processing Unit
  • each process described above is stored in the auxiliary storage device 730 in the form of a program.
  • the CPU 710 reads out the program from the auxiliary storage device 730, develops it in the main storage device 720, and executes the above processing according to the program. Further, the CPU 710 secures a storage area for the above-described processing in the main storage device 720 according to the program.
  • Communication for the above-described processing is performed by the interface 740 having a communication function and performing communication under the control of the CPU 710 .
  • interface 740 which includes a display device and an input device, displays various images under the control of CPU 710, and receives user operations.
  • each process of steps S11 to S14 is stored in the auxiliary storage device 730 in the form of a program.
  • the CPU 710 reads out the program from the auxiliary storage device 730, develops it in the main storage device 720, and executes the above processing according to the program.
  • the CPU 710 reserves a storage area for the processing of FIG. 5 in the main storage device 720 according to the program.
  • step S611 is stored in the auxiliary storage device 730 in the form of a program.
  • the CPU 710 reads out the program from the auxiliary storage device 730, develops it in the main storage device 720, and executes the above processing according to the program.
  • the CPU 710 reserves a storage area for the processing of FIG. 6 in the main storage device 720 according to the program.
  • a program for executing all or part of the processing in FIG. 5 and the processing in FIG. , the processing of each unit may be performed.
  • the "computer system” referred to here includes hardware such as an OS (Operating System) and peripheral devices.
  • “computer-readable recording medium” refers to portable media such as flexible discs, magneto-optical discs, ROM (Read Only Memory), CD-ROM (Compact Disc Read Only Memory), hard disks built into computer systems It refers to a storage device such as
  • the program may be for realizing part of the functions described above, or may be capable of realizing the functions described above in combination with a program already recorded in the computer system.
  • the present invention may be applied to design methods and recording media.

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2013119867A1 (en) * 2012-02-08 2013-08-15 Qualcomm Incorporated Methods and apparatus for spiking neural computation
WO2019125419A1 (en) * 2017-12-19 2019-06-27 Intel Corporation Device, system and method for varying a synaptic weight with a phase differential of a spiking neural network
WO2020241356A1 (ja) * 2019-05-30 2020-12-03 日本電気株式会社 スパイキングニューラルネットワークシステム、学習処理装置、学習処理方法および記録媒体

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2013119867A1 (en) * 2012-02-08 2013-08-15 Qualcomm Incorporated Methods and apparatus for spiking neural computation
WO2019125419A1 (en) * 2017-12-19 2019-06-27 Intel Corporation Device, system and method for varying a synaptic weight with a phase differential of a spiking neural network
WO2020241356A1 (ja) * 2019-05-30 2020-12-03 日本電気株式会社 スパイキングニューラルネットワークシステム、学習処理装置、学習処理方法および記録媒体

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