JP2010123072A - Back propagation learning method for pulse neuron model - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a back propagation learning method applicable to a hierarchal pulse neural network. <P>SOLUTION: In this back propagation learning method for pulse neuron model, a teacher signal is generated using the duality of the pulse neuron model, and learning is performed using the teacher signal. By generating the teacher signal using the duality of the pulse neuron model, calculation of differentiating an error function is not required, and the method becomes applicable to the hierarchal pulse neural network. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a back-propagation learning method for a neural network, and more particularly, to a back-propagation learning method suitable for a neural network constructed by a pulse neuron model (hereinafter referred to as “pulse neural network”).

  In order to solve a general non-linear problem with a neural network, it is necessary to use a hierarchical neural network with three or more layers having an intermediate layer between an input layer and an output layer. A back propagation method (error back propagation method) is known.

  As a supervised learning method for a pulse neural network, there is a method described in Non-Patent Document 1 below.

  Furthermore, as a back-propagation method using duality for a digital perceptron, there is a method described in Non-Patent Document 2 below.

The following Non-Patent Document 3 describes a hardware method for a pulse neuron model.
Kuroyanagi Shu, Akira Iwata, “Supervised Learning Rules for Pulsed Neuron Model”, IEICE Technical Report, IEICE, March 1998, NC97-151, p. 95-102 K. Yamada, S. Kuroyanagi, Akira Iwata, "Supervised learning method for neural network using duality existing in neuron model", IEICE Transactions (D-II), February 2004, No. J87-D-II, No. 2, p. 399-406 Noriyoshi Futaki, Susumu Kuroyanagi, Akira Iwata, “Implementation Method of Pulsed Neuron Model for FPGA”, IEICE NC Research Technical Report, The Institute of Electronics, Information and Communication Engineers, March 2002, NC2001-211, p . 121-128

  However, the commonly used back-propagation method aims to minimize the error, and therefore performs a calculation that differentiates the error function. However, since the output function cannot be differentiated in the pulse neuron model, there is a problem that this calculation cannot be performed and a general back propagation method cannot be applied.

  Further, the method of Non-Patent Document 1 considers only a two-layer structure of an input layer and an output layer, and has a problem that it cannot be applied to a hierarchical pulse neural network (a pulse neural network having three or more layers). .

  Further, the technique of Non-Patent Document 2 is a technique for a digital perceptron and has not been applied to a hierarchical pulse neural network in which input / output is a pulse.

  An object of the present invention is to solve the above-described problem and to provide a back-propagation learning method applicable to a hierarchical pulse neural network.

  The back-propagation learning method for the pulse neuron model of the present invention is characterized in that a teacher signal is generated using the duality of the pulse neuron model and learning is performed using the teacher signal.

  According to this, a back-propagation learning method applicable to a hierarchical pulse neural network can be provided.

Here, as described in claim 2, the teacher signal given to the j-th pulse neuron model of the intermediate layer is T _j , and the latter layer when the intermediate layer is the previous stage (hereinafter referred to as “output layer”). ), The output potential of the kth pulse neuron model of the output layer is p ^O _k (t) (where t is time), the teacher potential of the kth pulse neuron model of the output layer is p ^T _k (t), and the intermediate layer H _j (t) is the output of the jth pulse neuron model of the first layer, and w ^O _kj (t) is the connection weight between the jth pulse neuron model of the intermediate layer and the kth pulse neuron model of the output layer. , The learning coefficient is α ^O , the number of pulse neuron models in the output layer is K, the elapsed time is A, the membrane potential decay constant is β≡exp (−1 / τ) (where τ is the time constant of the input potential) When the following [Equation 12] Ri j th pulse neuron model of the intermediate layer by calculated the teacher signal T _j can and to perform learning.

また、請求項３記載のように、中間層のｊ番目のパルスニューロンモデルに与えられる教師信号をＴ_ｊ、出力層のｋ番目のパルスニューロンモデルの出力電位をｐ^Ｏ _ｋ（ｔ）（但し、ｔは時間）、前記出力層のｋ番目のパルスニューロンモデルの教師電位をｐ^Ｔ _ｋ（ｔ）、前記中間層のｊ番目のパルスニューロンモデルの出力をＨ_ｊ（ｔ）、前記中間層のｊ番目のパルスニューロンモデルと前記出力層のｋ番目のパルスニューロンモデルとの間の結合重みをｗ^Ｏ _ｋｊ（ｔ）、学習係数をα^Ｏ、前記出力層のパルスニューロンモデルの数をＫ、学習のための閾値をθ_learnとしたとき、下記［数１３］のように定義された誤差ΔＴ_ｊを計算し、下記（１）〜（３）に従って教師信号Ｔ_ｊを決定し、該教師信号Ｔ_ｊにより前記中間層のｊ番目のパルスニューロンモデルを学習させることとしてもよい。

Further, as described in claim 3, the teacher signal given to the j-th pulse neuron model in the intermediate layer is T _j , and the output potential of the k-th pulse neuron model in the output layer is p ^O _k (t) (where t is time), the teacher potential of the k-th pulse neuron model of the output layer is p ^T _k (t), the output of the j-th pulse neuron model of the intermediate layer is H _j (t), j of the intermediate layer The connection weight between the kth pulse neuron model of the output layer and the kth pulse neuron model of the output layer is w ^O _kj (t), the learning coefficient is α ^O , the number of pulse neuron models of the output layer is K, When the threshold value for the _learning is θ _learn , an error ΔT _j defined as in the following [Equation 13] is calculated, the teacher signal T _j is determined according to the following (1) to (3), and the teacher signal T _j J of the intermediate layer It may be learned eye pulse neuron model.

（１）｜ΔＴ_ｊ｜≦θ_learnの場合、Ｔ_ｊ＝Ｈ_ｊ（ｔ）とする。

(1) When | ΔT _j | ≦ θ _learn , T _j = H _j (t).

(2) When ΔT _j <−θ _learn , T _j = 0.

(3) When ΔT _j > θ _learn , T _j = 1.

In addition, as described in claim 4, the teacher signal given to the jth pulse neuron model of the intermediate layer is T _j , the output signal at time t of the kth pulse neuron model of the output layer is O _k , and the output layer the k-th T ^{O k} teacher signal at time t to the pulse neuron _model, the output H _j of the j-th pulse neuron model of the intermediate layer _(t), the a j-th pulse neuron model of the intermediate layer The connection weight with the k-th pulse neuron model in the output layer is w ^O _kj (t), the learning coefficient is α ^O , the number of pulse neuron models in the output layer is K, and the learning threshold is θ _learn when, to calculate the defined error [Delta] T _j as follows Equation 15], the following (1) to determine the teacher signal T _j in accordance with ~ (3), j th of said intermediate layer by該教teacher signal T _j It may be learned pulsed neuron model.

（１）｜ΔＴ_ｊ｜≦θ_learnの場合、Ｔ_ｊ＝Ｈ_ｊ（ｔ）とする。

(1) When | ΔT _j | ≦ θ _learn , T _j = H _j (t).

(2) When ΔT _j <−θ _learn , T _j = 0.

(3) When ΔT _j > θ _learn , T _j = 1.

  The learning / identification apparatus of the present invention is characterized in that learning is performed by the back-propagation learning method for any one of the above-described pulse neuron models, and input data is identified.

The arithmetic circuit according to the present invention is characterized by generating a teacher signal T _j of a back-propagation learning method for a pulse neuron model according to claim 4.

For example, in the arithmetic circuit, when k is a neuron number (k = 1 to K) of the output layer, the arithmetic signal T ^O _k , the output signal O _k, and the connection weight w ^O _kj (t) are used. , T ^O _k = 0 and O _k = 0, 0 when T ^O _k = 0 and O _k = 1, -w ^O _kj (t), w when T ^O _k = 1 and O _k = 0 ^O _kj (t) is K logic circuits that output 0 when T ^O _k = 1 and O _k = 1, an adder that adds outputs from the respective logic circuits, and an output from the adder performs multiplication of the learning coefficient alpha ^O performing a bit shift with respect to the error [Delta] t and a shift computing unit for calculating a _j, output H _{j (t} from the error [Delta] t _j and the intermediate layer output from the shift calculator ) by comparing the, a comparator for outputting a teacher signal T _j according to the above rule (1) to (3), It can be made with.

  According to the back-propagation learning method of the present invention, calculation for differentiating the error function is not required, and the method can be applied to a hierarchical pulse neural network.

[First Embodiment]
First, the proposed method 1, which is a back-propagation learning method according to the first embodiment, will be described. In the proposed method 1, as shown in FIG. 2, a part for calculating and holding the output potential p ^O (t) as compared with the conventional pulse neuron model (see Non-Patent Document 1) as shown in FIG. A new pulse neuron model in which a part for calculating and holding the teacher potential p ^T (t) and a part for calculating and holding the input potential (input potential) Inp _k (t) rising at a fixed value are added as components. Use.

In the pulse neuron model shown in FIG. 2, as in the pulse neuron model shown in FIG. 1, when the input pulse IN _k (t) arrives at the k-th synapse, the local membrane potential p _k (t) becomes the connection weight w _k. Increase by the value of. The local membrane potential p _k (t) decreases according to the following equation [Equation 1] with the passage of time. The internal potential I (t) of the pulse neuron model is calculated by the following equation [Equation 2], and the output o (t) is calculated by the following equation [Equation 3]. Note that τ is a time constant, n is the total number of inputs, θ is a threshold value, H is a unit step function, t is time, and Δt = 1.

また、図２に示すパルスニューロンモデルにおいては、入力パルス「１」がk番目のシナプスに到達すると、入力ポテンシャルInp_ｋ（ｔ）は固定重み１だけ増加し、時定数τで減衰する（下記［数９］参照）。出力電位ｐ^Ｏ（ｔ）は、パルスニューロンモデルが発火したとき固定重み１だけ増加し、時定数τ^Ｏで上記［数１］と同様に減衰する。教師電位ｐ^Ｔ（ｔ）は、教師信号「１」を受け取ったとき固定重みｗ^Ｔだけ増加し、時定数τ^Ｔで上記［数１］と同様に減衰する。

In the pulse neuron model shown in FIG. 2, when the input pulse “1” reaches the k-th synapse, the input potential Inp _k (t) increases by a fixed weight 1 and attenuates with a time constant τ (see below [ (See Equation 9]). The output potential p ^O (t) increases by a fixed weight 1 when the pulse neuron model is ignited, and attenuates in the same manner as in [Equation 1] with the time constant τ ^O. When the teacher signal “1” is received, the teacher potential p ^T (t) increases by a fixed weight w ^T and is attenuated by the time constant τ ^T in the same manner as in the above [Equation 1].

  In Proposed Method 1, the duality of the pulse neuron model configured as described above is used. The duality of the neuron model is described in Non-Patent Document 2 described above. To explain briefly, the output of a general neuron model is calculated by the following equation [Equation 4].

なお、上記[数４]及び以下の[数５]〜[数７]において、ｗは結合重みベクトル、ｉは入力ベクトル、θは結合重み以外のパラメタのベクトル、ｆは出力関数である。出力が結合重みベクトルと入力ベクトルの内積で決まるニューロンモデルは双対性を有しており、その出力は、次式[数５]に示すように、結合重みベクトルｗと入力ベクトルｉの値を入れ替えた双対ニューロンモデルの出力と同じである。

In the above [Equation 4] and the following [Equation 5] to [Equation 7], w is a coupling weight vector, i is an input vector, θ is a vector of parameters other than the coupling weight, and f is an output function. The neuron model whose output is determined by the inner product of the connection weight vector and the input vector has duality, and the output replaces the values of the connection weight vector w and the input vector i as shown in the following formula [5]. This is the same as the output of the dual neuron model.

パルスニューロンモデルも、上記式[数１]〜[数３]から分かるように、双対性を有し、結合重みｗ_ｋと入力ＩＮ_ｋとは交換可能である。

The pulse neuron model also has duality as can be seen from the above equations [Expression 1] to [Expression 3], and the connection weight w _k and the input IN _k can be exchanged.

The following equation [Equation 6] is a function used for updating the connection weight vector, but as shown in the following equation [Equation 7], the same function can also be used for updating the input vector due to the duality of the neuron model. Note that w ^new is the updated connection weight vector, and i ^new is the updated input vector.

双対性を有するニューロンモデルに対して、ある学習則に基づく関数ｇによって、望ましい結合重みが求められるとき、関数ｇの引数の結合重みベクトルと入力ベクトルとを入れ替えることで、望ましい入力を求めることができる。ニューロンモデルに対する望ましい入力は、その前段のニューロンモデルの望ましい出力、すなわち、教師信号となる。

When a desired connection weight is obtained for a neuron model having duality by a function g based on a certain learning rule, a desired input can be obtained by replacing the connection weight vector of the argument of the function g and the input vector. it can. A desirable input to the neuron model is a desirable output of the preceding neuron model, that is, a teacher signal.

Based on the above, the proposed method 1 will be described. In the following description, H _j (t) is the output of the _jth pulse neuron model of the intermediate layer, Inp _j (t) is the input potential from the jth pulse neuron model of the intermediate layer, and p ^O _k (t ) Is the output potential of the kth pulse neuron model of the output layer (that is, the subsequent layer when the intermediate layer is the previous stage), and p ^T _k (t) is the teacher potential of the kth pulse neuron model of the output layer. , W ^O _kj (t) is a connection weight between the j-th pulse neuron model in the intermediate layer and the k-th pulse neuron model in the output layer, and α ^O is a learning coefficient.

  The update of the weight of the pulse neuron model can be expressed by the following equation [Equation 8], as can be seen from the description of Non-Patent Document 1.

Inp_ｊ（ｔ）は、次式[数９]で更新される。

Inp _j (t) is updated by the following equation [Equation 9].

τを定数とすると、βも定数となる。また、Ａは経過時間である。[数９]により、[数８]は次式[数１０]のように書き換えられる。

If τ is a constant, β is also a constant. A is the elapsed time. From [Equation 9], [Equation 8] can be rewritten as the following equation [Equation 10].

ここで、Ｈ_ｊは中間層のｊ番目のパルスニューロンモデルから出力層のｋ番目のパルスニューロンモデルへの入力に相当するので、パルスニューロンモデルの双対性から、ｗ^Ｏ _ｋｊとＨ_ｊとを入れ替えることにより、中間層のｊ番目のパルスニューロンモデルから出力層のｋ番目のパルスニューロンモデルへの望ましい入力Ｔ_ｋｊが次式[数１１]で求められることとなる。

Here, since H _j corresponds to an input from the j-th pulse neuron model in the intermediate layer to the k-th pulse neuron model in the output layer, w ^O _kj and H _j are switched from the duality of the pulse neuron model. Thus, a desirable input T _kj from the j-th pulse neuron model of the intermediate layer to the k-th pulse neuron model of the output layer is obtained by the following equation [Equation 11].

そして、望ましい入力Ｔ_ｋｊをｋ＝１〜Ｋ（Ｋ：出力層のパルスニューロンモデルの総数）について集めたものが、中間層のｊ番目のパルスニューロンモデルの望ましい出力、すなわち、中間層のｊ番目のパルスニューロンモデルに対する教師信号Ｔ_ｊとなることから、中間層のｊ番目のパルスニューロンモデルに対する教師信号Ｔ_ｊは次式[数１２]で計算できる。

A collection of desirable inputs T _kj for k = 1 to K (K: the total number of pulse neuron models in the output layer) is the desired output of the j th pulse neuron model in the intermediate layer, that is, the j th in the intermediate layer. since the teacher signal T _j of relative pulse neuron model, the teacher signal T _j for the j-th pulse neuron model of the intermediate layer can be calculated by the following formula [formula 12].

提案手法１は、上記[数１２]により計算される教師信号Ｔ_ｊにより、中間層のｊ番目のパルスニューロンモデルを学習させる。すなわち、提案手法１では、前段の層の出力（すなわち、後段の層の入力）Ｈ_ｊ、後段の層の出力電位ｐ^Ｏ _ｋ、後段の層の教師電位ｐ^Ｔ _ｋ、及び、前段の層と後段の層との間の結合重みｗ^Ｏ _ｋｊから、前段の層の教師信号を算出して、その教師信号により前段の層を学習させる。

In Proposed Method 1, the j-th pulse neuron model of the intermediate layer is learned by the teacher signal T _j calculated by the above [Equation 12]. That is, in the proposed method 1, the output of the preceding layer (that is, the input of the succeeding layer) H _j , the output potential p ^O _{k of} the succeeding layer, the teacher potential p ^T _k of the succeeding layer, and the preceding layer A teacher signal of the preceding layer is calculated from the connection weight w ^O _kj with the succeeding layer, and the preceding layer is learned by the teacher signal.

FIG. 3 shows a configuration example of a learning / identification device that performs learning using the proposed method 1 and identifies input data. FIG. 3 shows an example of a three-layer pulse neural network having an input layer 1, an intermediate layer 2, and an output layer 3. The number of teacher signal generation elements is the same as the number J of pulse neuron models in the intermediate layer 2. A teacher signal generation element layer 4 having 5 is provided. The number of pulse neuron models in the output layer 3 is K. The output H _j from the intermediate layer 2, the output O _k from the output layer 3, and the teacher signal T _k given to the output layer 3 are also given to each teacher signal generation element 5. A bias input is given to the intermediate layer 2. Further, the weight (connection weight) of each pulse neuron model in the output layer is copied to the corresponding teacher signal generation element 5. Each pulse neuron model of the input layer 1 is a pulse neuron model shown in FIG. 1, and each pulse neuron model of the intermediate layer 2 and the output layer 3 is a pulse neuron model shown in FIG. The input layer 1 is configured to give the input pulse to the intermediate layer 2 in the same pattern.

The operation of the learning / identification device at the time of learning will be described with reference to FIG. 4. After the processing starts, the learning / identification device starts with each of the input layer 1, the intermediate layer 2, and the output layer 3. The pulse neuron model is initialized (step S101). Next, each weight w ^O _kj (t) (k = 1 to K) of the output layer 3 is copied to the j-th teacher signal generation element 5 (S102). Note that j = 1 to J.

Then, learning is started (S103), and each element (pulse neuron model) in the input layer 1, the intermediate layer 2, and the output layer 3 performs a forward-looking calculation as usual (S104). Each element of the output layer 3 updates the weight w ^O _kj (t) based on the teacher signal T ^O _k (t) given from the outside (S105). On the other hand, each teacher signal generation element 5 calculates the above [number] from the copied weight w ^O _kj (t), the output O _k (t) from the output layer 3, and the teacher signal T ^O _k (t). 12], the teacher signal T _j (t) is calculated and output (S106). It is assumed that the learning coefficient α ^O is previously given to each teacher signal generation element 5. The teacher signal T _j (t) obtained in step S106 is given to the j-th element of the intermediate layer 2, and each element of the intermediate layer 2 updates the weight based on the teacher signal T _j (t) ( S107). When steps S105 to 107 are completed, the process returns to step S102, and thereafter, steps S102 to 107 are repeated for a predetermined number of times of learning.

The configuration example shown in FIG. 3 and the operation flow shown in FIG. 4 are also applicable to the proposed method 2 and the proposed method 3, which will be described later. In the proposed method 3, the error ΔT _j is calculated according to the following [Equation 15], and the teacher signal T _j (t) is output according to the following rules (1) to (3).

  According to the proposed method 1, the hierarchical pulse neural network can be learned by a method completely different from a general back-propagation method for differentiating an error function.

[Second Embodiment]
Next, a proposed method 2 according to the second embodiment obtained by improving the proposed method 1 will be described. In the above [Equation 12], the teacher signal T _j becomes a real value, and as it is, it cannot be easily handled by the pulse neuron model. Therefore, assuming that β≡exp (−1 / τ) <1, β ^a is sufficiently small, and β ^a w ^O _kj (ta) is negligible except for a = 0, [Equation 12] It converts like following Formula [Formula 13].

そして、ΔＴ_ｊと学習のための閾値θ_learn（≧０）を用いて、次の（１）〜（３）のように教師信号Ｔ_ｊを出力する。

Then, using ΔT _j and the learning threshold θ _learn (≧ 0), the teacher signal T _j is output as in the following (1) to (3).

(1) When | ΔT _j | ≦ θ _learn , it is assumed that H _j (t) matches the desired output T _j , T _j = H _j (t), and learning is continued.

(2) When ΔT _j <−θ _learn , H _j is an undesirable output 1, so T _j = 0 and the connection weight is updated so that the jth pulse neuron model in the intermediate layer does not output 1 To do.

(3) When ΔT _j > θ _learn , H _j should be output 1, so T _j = 1, and the connection weight is updated so that the j-th pulse neuron model in the intermediate layer outputs 1.

As described above, in the proposed method 2, ΔT _j is calculated according to the above [Equation 13], and learning is performed by determining T _j according to the rules (1) to (3). According to the above rules (1) to (3), the teacher signal T _j is a pulse (0 or 1), so that the handling by the pulse neuron model is facilitated and the hardware is also facilitated. An experimental example of the proposed method 2 is shown below.

<Experiment 1>
In Experiment 1, a learning / identification device having a three-layer pulse neural network as shown in FIG. 3 was configured on a computer by software, and XOR (exclusive OR) was learned and identified as a simple nonlinear problem. . Table 1 shows the number of elements in each layer and various parameters used in the experiment. One element of the input layer is an element for bias input in which 1 is always input to the element of the intermediate layer.

そして、図５の下段に示すように入力層に入力パルスを入力するとともに、図５の上段に示すように出力層に教師パルスＴ_ｋを与えて、提案手法２により学習を行った。図５において、Ｘ軸（横軸）は時間であり、Ｙ軸（縦軸）はパルスニューロンモデルの番号（ニューロン番号）である。色の濃淡はパルス頻度を表し、白い部分は０（パルスが無い状態）を表し、色が濃いほどパルス頻度が高く、黒い部分は１（常にパルスがある状態）を表す。実験１では、ＸＯＲ問題を学習するので、（ニューロン番号１の素子に与えられる信号，ニューロン番号２の素子に与えられる信号）と表記したとき、図５に示すように、入力が（０，０）の場合は教師信号（０，１）、入力が（１，０）の場合は教師信号（１，０）、入力が（０，１）の場合は教師信号（１，０）、入力が（１，１）の場合は教師信号（０，１）を与える。

Then, an input pulse was input to the input layer as shown in the lower part of FIG. 5, and a teacher pulse T _k was given to the output layer as shown in the upper part of FIG. In FIG. 5, the X-axis (horizontal axis) is time, and the Y-axis (vertical axis) is the pulse neuron model number (neuron number). The shade of the color represents the pulse frequency, the white part represents 0 (no pulse), the darker the color, the higher the pulse frequency, and the black part 1 (always with a pulse). In Experiment 1, since the XOR problem is learned, when expressed as (signal given to the element of neuron number 1, signal given to the element of neuron number 2), the input is (0, 0) as shown in FIG. ) Is the teacher signal (0, 1), the input is (1, 0), the teacher signal (1, 0), the input is (0, 1), the teacher signal (1, 0), and the input is In the case of (1, 1), a teacher signal (0, 1) is given.

  FIG. 6 shows the result when the same input pulse as that in FIG. 5 is input and discriminated after learning using the input and the teacher signal. FIG. 6 shows, in order from the top, an intermediate layer teacher pulse train, an intermediate layer output pulse train, an output layer teacher pulse train, and an output layer output pulse train. In FIG. 6, as in FIG. 3, the X axis is time, and the Y axis is a neuron number. In FIG. 6, the neuron number is omitted, but the output pulse train and teacher pulse train of the output layer are numbers 1 and 2 in order from the bottom, and the output pulse train and teacher pulse train of the intermediate layer are number 1 in order from the bottom. 2, 3, 4 The color shading represents the pulse frequency as in FIG. FIG. 6 shows that although the output pulse train of the output layer has a low pulse frequency as a whole, the pattern coincides with the teacher pulse train for the output layer, and correct identification is performed as a result of learning.

<Experiment 2>
In Experiment 2, a learning / identification device having a three-layered pulse neural network as shown in FIG. 3 is configured on a computer by software, and an alarm clock alarm sound (hereinafter referred to as “alarm”) and interphone call are configured. Sound (hereinafter referred to as “interphone”), boiling sound of whistling kettle (hereinafter referred to as “kettle”), telephone bell sound (hereinafter referred to as “telephone”), human voice, and white noise. Sound data obtained by converting six kinds of sounds into a pulse train for each frequency band was input and learned by Proposed Method 2. Table 2 shows the number of elements in each layer and various parameters used in the experiment. One element of the input layer is an element for bias input. The output layer has six elements for learning the six types of sounds.

  Table 3 shows the results of inputting and recognizing the six types of sound data used for learning after learning.

表３の数字は、左から順に、アラーム、インターフォン、ケトル、電話、人の声、ホワイトノイズを学習した素子の認識率（＝出力層における全発火数に対する当該素子の発火数）を表す。例えば、入力信号がアラームであるとき、アラームを学習した素子の認識率は１００％であり、他の素子の認識率は０％である。表３から、学習の結果、６種の音を略誤り無く認識できていることが分かる。

The numbers in Table 3 represent, from the left, the recognition rate (= number of firings of the element relative to the number of all firings in the output layer) of learning an alarm, interphone, kettle, telephone, human voice, and white noise. For example, when the input signal is an alarm, the recognition rate of the element that has learned the alarm is 100%, and the recognition rate of the other elements is 0%. From Table 3, it can be seen that, as a result of learning, six types of sounds can be recognized without substantial error.

According to the proposed method 2, with perform substantially correct recognition result of learning, so the teacher signal T _j may be a pulse, is easy to handle by the pulse neuron model is suitable for a hierarchical pulse neural network.

[Third Embodiment]
Next, the proposed method 3 according to the third embodiment in which the proposed method 2 is suitable for hardware implementation of a hierarchical pulse neural network will be described.

In the proposed method 2, the calculation of ΔT _j is not suitable for realization with a digital circuit. Therefore, the output potential p ^O _k (t) and the teacher potential p ^T _k (t) of [Equation 13] are output as the output signal O _k of the k-th pulse neuron model of the output layer at time t and the output at time t, respectively. Substituting the teacher signal T ^O _k (also expressed as T _k ) for the k-th pulse neuron model of the layer, [Equation 13] is transformed into the following equation [Equation 14]. Both O _k and T ^O _k are pulses (0 or 1).

そして、次式[数１５]のようにΔＴ_ｊを定義し、学習のための閾値θ_learnを用いて、上記（１）〜（３）のルールに従って教師信号Ｔ_ｊを出力する。

Then, ΔT _j is defined as in the following equation [Formula 15], and the teacher signal T _j is output according to the rules (1) to (3) using the threshold θ _learn for learning.

提案手法３は、上記[数１５]を用いてΔＴ_ｊを計算し、閾値θ_learnを用いて上記（１）〜（３）のように教師信号Ｔ_ｊを中間層のｊ番目のパルスニューロンモデルに与えることを特徴とする。提案手法３を用いた実験例を以下に示す。

The proposed method 3 calculates ΔT _j using the above [Equation 15], and uses the threshold θ _learn to _{convert the} teacher signal T _j into the j-th pulse neuron model of the intermediate layer as in the above (1) to (3). It is characterized by giving to. An experiment example using the proposed method 3 is shown below.

<Experiment 3>
A learning / identification apparatus having a three-layer pulse neural network as shown in FIG. 3 was configured on a computer by software, and an experiment similar to Experiment 1 was performed. That is, the number of elements in each layer and various parameters used in the experiment are as shown in Table 1. As shown in the lower part of FIG. 5, an input pulse is input to the input layer, and as shown in the upper part of FIG. The teaching pulse T _k was given to the output layer, and learning was performed by the proposed method 3.

  FIG. 7 shows the result of inputting and identifying the same input pulse as in FIG. 5 after learning. FIG. 7 shows the intermediate layer teacher pulse train, the intermediate layer output pulse train, the output layer teacher pulse train, and the output layer output pulse train in order from the top, as in FIG. 6, where the X axis is time, and the Y axis is the neuron number. However, the neuron number is omitted. The color shading represents the pulse frequency as in FIG. FIG. 7 shows that although the output pulse train of the output layer has a low pulse frequency as a whole, the pattern coincides with the teacher pulse train for the output layer, and correct identification is performed as a result of learning.

<Experiment 4>
A learning / identification device having a three-layer pulse neural network as shown in FIG. 3 was configured on a computer by software, and an experiment similar to Experiment 2 was performed. In other words, the number of elements in each layer and various parameters used in the experiment are as shown in Table 2, and the six types of sounds of alarm, intercom, kettle, telephone, human voice, and white noise used in Experiment 2 were used. The sound data generated from the above is input and learning is performed by the proposed method 3.

  Table 4 shows the results of inputting and recognizing the six types of sound data used for learning after learning.

表４の数字は、左から順に、アラーム、インターフォン、ケトル、電話、人の声、ホワイトノイズを学習した素子の認識率を表す。表４から、学習の結果、６種の音を略誤り無く認識できていることが分かる。

The numbers in Table 4 represent the recognition rate of elements that have learned alarms, intercoms, kettles, telephones, human voices, and white noise in order from the left. From Table 4, it can be seen that, as a result of learning, six types of sounds can be recognized without substantial error.

According to the proposed method 3, the learning signal can be recognized substantially correctly, the teacher signal T _j can be converted into a pulse, and ΔT _j can be easily calculated by a digital circuit. Therefore, the hardware of the hierarchical pulse neural network can be realized. Suitable for wear.

For example, the teacher signal generation element 5 can be realized by a digital circuit as shown in FIG. 8, reference numeral 10, as shown in Table 5, the teacher pulse ^T _{O k} and the output pulse _{O k} and a weight ^w _O kj (t) from the _{^0, w O} kj (t) or ^-w _O kj (t ) Is an adder for adding outputs from the respective logic circuits 10, and reference numeral 12 is a bit shift for realizing α ^O multiplication on the output from the adder 11. The reference numeral 13 compares the output from the shift calculator 12, that is, ΔT _j with the output H _j from the intermediate layer, and in accordance with the rules (1) to (3), the teacher signal T _j Is a comparator that outputs The comparator 13 holds or receives the learning threshold value θ _learn as an input.

また、図１、２に示すようなパルスニューロンモデルも、上記非特許文献３に記載されているように、デジタル回路で実現可能である。したがって、提案手法３によって学習し入力データを識別する学習・識別装置は、デジタル回路で実現可能である。

The pulse neuron model as shown in FIGS. 1 and 2 can also be realized by a digital circuit as described in Non-Patent Document 3 above. Therefore, the learning / identification device that learns by the proposed method 3 and identifies input data can be realized by a digital circuit.

  As described above, the proposed method 3 can be easily realized in a digital circuit, and can also be implemented on FPGA (Field Programmable Gate Arrays). That is, all of the proposed methods 1 to 3 can be realized by software on a general computer, but hardware is desirable for speeding up the processing, and the proposed method 3 is particularly suitable for hardware.

  The proposed methods 1 to 3 can of course be applied to a hierarchical pulse neural network having four or more layers having a plurality of intermediate layers, in which the output layer is an intermediate layer.

It is a block diagram of the conventional pulse neuron model. It is a block diagram of the pulse neuron model which concerns on embodiment of this invention. It is a block diagram of the learning and identification apparatus which concerns on the same embodiment. It is a flowchart which shows the operation | movement at the time of learning of the learning / identification apparatus based on the embodiment. It is a figure which shows the input pulse train of the input layer in Experiment 1 and Experiment 3, and the teacher pulse train of an output layer. It is a figure which shows the output pulse train and teacher pulse train of the intermediate | middle layer in Experiment 1, and the output pulse train and teacher pulse train of an output layer. It is a figure which shows the output pulse train and teacher pulse train of the intermediate | middle layer in Experiment 3, and the output pulse train and teacher pulse train of an output layer. This is an example in which a teacher signal generation element is formed into a digital circuit.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Input layer 2 ... Intermediate layer 3 ... Output layer 4 ... Teacher potential generation element layer 5 ... Teacher potential generation element 10 ... Logic circuit 11 ... Adder 12 ... Shift computing unit 13 ... Comparator

Claims (7)

  A back-propagation learning method for a pulse neuron model, characterized in that a teacher signal is generated using the duality of a pulse neuron model and learning is performed using the teacher signal. The teacher signal given to the jth pulse neuron model of the intermediate layer is T _j , and the output potential of the kth pulse neuron model of the subsequent layer (hereinafter referred to as “output layer”) when the intermediate layer is the previous stage. P ^O _k (t) (where t is time), the teacher potential of the k-th pulse neuron model of the output layer is p ^T _k (t), and the output of the j-th pulse neuron model of the intermediate layer is H _j (t), the connection weight between the j-th pulse neuron model of the intermediate layer and the k-th pulse neuron model of the output layer is w ^O _kj (t), the learning coefficient is α ^O , and the output layer When the number of pulse neuron models is K, the elapsed time is A, and the membrane potential decay constant is β≡exp (−1 / τ) (where τ is the time constant of the input potential), wherein in the signal _{T j} Back propagation learning method for pulsed neuron model according to claim 1, wherein the j-th pulse neuron model layers and performs the learning.

The teacher signal given to the jth pulse neuron model of the intermediate layer is T _j , and the output potential of the kth pulse neuron model of the subsequent layer (hereinafter referred to as “output layer”) when the intermediate layer is the previous stage. P ^O _k (t) (where t is time), the teacher potential of the k-th pulse neuron model of the output layer is p ^T _k (t), and the output of the j-th pulse neuron model of the intermediate layer is H _j (t), the connection weight between the j-th pulse neuron model of the intermediate layer and the k-th pulse neuron model of the output layer is w ^O _kj (t), the learning coefficient is α ^O , and the output layer When the number of pulse neuron models is K and the learning threshold is θ _learn , an error ΔT _j defined as the following equation is calculated, and the teacher signal T _j is determined according to the following (1) to (3). and,該教teacher signal T Back propagation learning method for pulsed neuron model according to claim 1, wherein the train the j-th pulse neuron model of the intermediate layer by.

(1) When | ΔT _j | ≦ θ _learn , T _j = H _j (t).
(2) When ΔT _j <−θ _learn , T _j = 0.
(3) When ΔT _j > θ _learn , T _j = 1. The teacher signal given to the j-th pulse neuron model of the intermediate layer is T _j , and the time t of the k-th pulse neuron model of the subsequent layer (hereinafter referred to as “output layer”) when the intermediate layer is the previous stage. Is the output signal at O _k , the teacher signal at time t to the k-th pulse neuron model of the output layer is T ^O _k , the output of the j-th pulse neuron model of the intermediate layer is H _j (t), and the intermediate The connection weight between the j-th pulse neuron model of the layer and the k-th pulse neuron model of the output layer is w ^O _kj (t), the learning coefficient is α ^O , and the number of pulse neuron models of the output layer is K , when the threshold value for the learning and theta _learn, to calculate a defined error [Delta] T _j by the following equation to determine the teacher signal T _j according to the following (1) to (3),該教teacher signal T _j More backpropagation learning method for pulsed neuron model according to claim 1, wherein the train the j-th pulse neuron model of the intermediate layer.

(1) When | ΔT _j | ≦ θ _learn , T _j = H _j (t).
(2) When ΔT _j <−θ _learn , T _j = 0.
(3) When ΔT _j > θ _learn , T _j = 1.   5. A learning / identification apparatus, wherein learning is performed by the back-propagation learning method for the pulse neuron model according to claim 1 to identify input data. An arithmetic circuit that generates a teacher signal T _j of a back-propagation learning method for the pulse neuron model according to claim 4. When k is the neuron number of the output layer (k = 1 to K), T ^O _k = 0 and T _k from the teacher signal T ^O _k , the output signal O _k and the connection weight w ^O _kj (t) 0 when O _k = ^0, the ^-w _O kj (t) when _{T O} k = 0 and _O k = ^1, when _{T O} k = 1 and _O k = 0 ^w _O kj a (t), K logic circuits that output 0 when T ^O _k = 1 and O _k = 1,
An adder for adding outputs from the logic circuits;
A shift computing unit that performs bit shift on the output from the adder and multiplies the learning coefficient α ^O to calculate an error ΔT _j ;
A comparator that compares the error ΔT _j output from the shift calculator with the output H _j (t) from the intermediate layer and outputs the teacher signal T _j according to the rules (1) to (3);
The arithmetic circuit according to claim 6, further comprising:

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