Patent Publication Number: US-2021191691-A1

Title: Multiply-accumulate system and multiply-accumulate method

Description:
FIELD 
     The present disclosure relates to a multiply-accumulate system and a multiply-accumulate method. 
     BACKGROUND 
     In recent years, various neural network calculation circuits have been proposed. 
     For example, Patent Literature 1 discloses a technique for executing a calculation based on rising timing of a signal output from a comparator in a time-axis analog multiply-accumulate circuit including RC circuits and the comparator. 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1: WO 2018/034163 A 
     SUMMARY 
     Technical Problem 
     However, in the above-described conventional technique, an output from a multiplier-accumulator in a previous stage is directly output to a multiplier-accumulator in a subsequent stage. In this case, the timing of each signal output from the comparator is reduced, and it may be difficult to determine timing at which the signal is output. 
     Therefore, the present disclosure proposes a multiply-accumulate system and a multiply-accumulate method which are capable of expanding the timing of the signal output. 
     Solution to Problem 
     To solve the problem described above, a multiply-accumulate system includes: a statistic calculation unit that executes a standardization calculation for an input signal; and a multiply-accumulate device that executes multiplication-accumulation based on the standardized input signal. 
     Advantageous Effects of Invention 
     According to the present disclosure, the timing of the signal output can be expanded. Note that the effect described here is not necessarily limited and may be any effect described in the present disclosure. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic diagram illustrating a multiply-accumulate device. 
         FIG. 2  is a schematic diagram of a multiplier-accumulator of the multiply-accumulate device. 
         FIG. 3  is a diagram illustrating an example of a configuration of the multiplier-accumulator. 
         FIG. 4  is a diagram for explaining output timing of the multiplier-accumulator. 
         FIG. 5  is a diagram for explaining distributions of pieces of the output timing of the multiplier-accumulator. 
         FIG. 6  is a diagram illustrating an example of a multiply-accumulate system according to a first embodiment of the present disclosure. 
         FIG. 7  is a diagram illustrating an example of input image data and standardized input image data. 
         FIG. 8  is diagrams illustrating an example of clipped standardized input image data. 
         FIG. 9  is a diagram for explaining an output time difference between outputs from multipliers-accumulators of the multiply-accumulate system according to the first embodiment of the present disclosure. 
         FIG. 10  is a diagram illustrating an example of a processing flow of a calculation device of the multiply-accumulate system according to the first embodiment of the present disclosure. 
         FIG. 11  is a diagram illustrating an example of a multiply-accumulate system according to a second embodiment of the present disclosure. 
         FIG. 12  is diagrams illustrating an example of clipped standardized input image data. 
         FIG. 13  is a diagram for explaining an output time difference between outputs from multipliers-accumulators of the multiply-accumulate system according to the second embodiment of the present disclosure. 
         FIG. 14  is a diagram illustrating an example of a processing flow of a calculation device of the multiply-accumulate system according to the second embodiment of the present disclosure. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     A detailed description will be given below of embodiments of the present disclosure with reference to the drawings. Note that, in the following respective embodiments, the same reference numerals are given to the same portions, and a duplicate description will be omitted. 
     Further, the present disclosure will be described in the following item order. 
     1. Outline 
     1-1. Outline of multiply-accumulate device 
     1-2. Outline of multiplier-accumulator 
     1-3. Network configuration of multiply-accumulate device 
     2. First Embodiment 
     2-1. Configuration of multiply-accumulate system according to first embodiment 
     2-2. Standardized image data according to first embodiment 
     2-3. Output time difference of multiply-accumulate system according to first embodiment 
     2-4. Standardization procedure according to first embodiment 
     3. Second Embodiment 
     3-1. Configuration of multiply-accumulate system according to second embodiment 
     3-2. Standardized image data according to second embodiment 
     3-3. Output time difference of multiply-accumulate system according to second embodiment 
     3-4. Standardization procedure according to second embodiment 
     1. Outline 
     [1-1. Outline of Multiply-Accumulate Device] 
     First, a description will be given of an outline of a multiply-accumulate device  10  to which each embodiment of the present disclosure is applied. Each multiplier-accumulator  11  of the multiply-accumulate device  10  according to each embodiment of the present disclosure associates a load (weight) w i  with each of N electrical signals I i , and derives a sum of N multiplication values each obtained by multiplying each value of the electrical signal I i  and the load w i , which make a pair, by each other. Here, N is a natural number of 2 or more, and i is a natural number of N or less. 
     It is assumed that the value represented by the electrical signal I i  (hereinafter, also simply referred to as an electrical signal) is x i , and that the N electrical signals are given to one multiplier-accumulator  11  within a predetermined period T i . In this case, the sum of the N multiplication values, which is obtained by the multiplier-accumulator  11 , is represented by the following equation (1). 
     
       
         
           
             
               
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     N 
                   
                    
                   
                     
                       w 
                       i 
                     
                     · 
                     
                       x 
                       i 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     As illustrated in  FIG. 1 , the multiply-accumulate device  10  has a structure in which a plurality of the multipliers-accumulators  11  is provided in each of a plurality of layers. Each of the plurality of multipliers-accumulators  11  in a lowest layer obtains a calculation target value based on values x i  represented by the N electrical signals (for example, pulse signals) given from a plurality of external input units  12  and the load w i  applied to the respective electrical signals. Then, each of the multipliers-accumulators  11  transmits an electrical signal, which represents the calculation target value, to multipliers-accumulators  11  in an upper layer. 
     Such multipliers-accumulators  11  in the upper layer each associate the load w i  individually with the values of the electrical signals sent from the plurality of multipliers-accumulators  11  in the lower layer, and obtain a calculation target value. Then, each of the multipliers-accumulators  11  in the upper layer transmits an electrical signal, which represents the calculation target value, to multipliers-accumulators  11  in a further upper layer. The multiply-accumulate device  10  according to each embodiment of the present disclosure is designed so as to be applicable to a neural network. Such a multiply-accumulate device  10  performs, a plurality of times, processing for obtaining the calculation target values by the multipliers-accumulators  11  in the upper layer based on the calculation target values obtained by the multipliers-accumulators  11  in the lower layer. Thus, the multiply-accumulate device  10  executes image recognition processing and the like. 
     [1-2. Outline of Multiplier-Accumulator] 
     Referring to  FIG. 2 , a description will be given of a configuration and processing of a multiplier-accumulator  11   a , which are an outline of the multiplier-accumulator  11 . Here, the description will be given on the assumption that the electrical signal x i  is a variable of 0 or more and 1 or less. Note that, though there are a positive load w i   +  that is a positive value and a negative load w i   −  that is a negative value in the load w i , the description will be given here on the assumption that there is no distinction between the positive and negative of the load. 
     As illustrated in  FIG. 2 , the multiplier-accumulator  11   a  includes N input units  13 , a storage unit  14 , a comparison unit  18 , and a threshold power supply  19 . 
     The N input units  13  are connected in parallel to one another. Each of the input units  13  associates the load w i  with the electrical signal given within the predetermined period T 1 , and outputs an electric charge having a magnitude corresponding to the value obtained by multiplying the electrical signal x i  and the load w i  by each other. Further, as illustrated in  FIG. 2 , each input unit  13  includes an input terminal  15 , a resistor  16 , and a diode  17 . The input terminal  15 , the resistor  16 , and the diode  17  are connected in series to one another. In each input unit  13 , for example, each input terminal  15  is given an electrical signal of the same magnitude at different timing within the period T i . 
     The storage unit  14  is connected to each input unit  13  and stores the electric charge output from each input unit  13 . The storage unit  14  is, for example, a capacitor. 
     Outside the multiplier-accumulator  11   a , a length of the period T 1  is defined as T in , and the following equation (2) is used, whereby the value x i  represented by the electrical signal is converted into timing t i  when the electrical signal is given. That is, the electrical signal is input to the input terminal  15  at the timing t i . 
         t   i   =T   in (1− x   i )  (2)
 
     Assuming that a waveform that is generated from the timing t i  when the electrical signal is given and increases or decreases in proportion to the passage of time t is defined as a response waveform W, an electric charge amount P i (t) supplied from each input unit  13  to the storage unit  14  can be represented by a magnitude of the response waveform W. Assuming that a slope of the response waveform W with respect to the passage of time t is defined as k i , the load w i  can be converted into k i  using the following equation (3). 
         k   i   =λw   i   (3)
 
     Here, assuming that a waveform obtained by adding all the response waveforms W to one another is defined as a composite waveform TW, a magnitude of the composite waveform TW is the sum total of P 1 (t), P 2 (t), P 3 (t), . . . , and P N (t). This is equal to a voltage generated by the storage unit  14 . Here, the voltage held in the storage unit  14  is defined as V N  (t). 
     The comparison unit  18  compares a threshold and a signal input thereto with each other, and outputs a step waveform when the input signal exceeds the threshold. The comparison unit  18  is, for example, a comparator. The comparison unit  18  is connected to the storage unit  14  and the threshold power supply  19 . 
     The threshold power supply  19  gives the threshold voltage to the comparison unit  18 . Here, a magnitude of the threshold voltage is defined as θ. In this case, the comparison unit  18  outputs the step waveform at timing at which the voltage V N (t) held in the storage unit  14  exceeds the threshold θ. Assuming that the timing at which V N (t) reaches the threshold θ is defined as t v , the following equation (4) is obtained. 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                       
                         k 
                         i 
                       
                        
                       
                         ( 
                         
                           
                             t 
                             v 
                           
                           - 
                           
                             t 
                             i 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   θ 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Then, assuming that the sum total of the loads w i  is defined as β, β can be represented by the following equation (5). 
     
       
         
           
             
               
                 
                   β 
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                       w 
                       i 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Then, from the equations (2) to (5), the calculation target value of the multiplier-accumulator  11   a  can be represented by the following equation (6). 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                       
                         w 
                         i 
                       
                       · 
                       
                         x 
                         i 
                       
                     
                   
                   = 
                   
                     
                       
                         θ 
                         / 
                         λ 
                       
                       + 
                       
                         β 
                          
                         
                           ( 
                           
                             
                               T 
                               
                                 i 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                             - 
                             
                               t 
                               v 
                             
                           
                           ) 
                         
                       
                     
                     
                       T 
                       
                         i 
                          
                         
                             
                         
                          
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Here, it is assumed that all of the loads w i  are positive values. In this case, when the value x i  represented by the electrical signal given to each input terminal  15  is a minimum value 0, a left side of the equation (6) becomes 0, so that the timing of t v  becomes latest. The timing t v   min  can be represented by the following equation (7). 
     
       
         
           
             
               
                 
                   
                     t 
                     v 
                     
                       m 
                        
                       
                           
                       
                        
                       i 
                        
                       
                           
                       
                        
                       n 
                     
                   
                   = 
                   
                     
                       θ 
                       
                         λ 
                          
                         β 
                       
                     
                     + 
                     
                       T 
                       
                         i 
                          
                         
                             
                         
                          
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The fact that the left side of the equation (6) is 0 means that the timing at which the step waveform is output from the comparison unit  18  is the latest. 
     On the other hand, when the value x i  represented by the electrical signal given to each input terminal  15  is a maximum value 1, the left side of the equation (6) becomes β, so that the timing of t v  becomes earliest. The timing t v   max  is represented by the following equation (8). 
     
       
         
           
             
               
                 
                   
                     t 
                     v 
                     
                       ma 
                        
                       
                           
                       
                        
                       x 
                     
                   
                   = 
                   
                     θ 
                     
                       λ 
                        
                       β 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     The fact that the right side of the equation (6) is β means that the timing at which the step waveform is output from the comparison unit  18  is the earliest. Therefore, from the equations (7) and (8), a period T 2  during which the step waveform is output from the comparison unit  18  is [t v   max , t v   min ], and a time length T v  of the period T 2  can be given by the following equation (9) 
         T   v   =t   v   min   −t   v   max   =T   in   (9)
 
     Hence, the time length T v  of the period T 2  during which the step waveform is output from the comparison unit  18  becomes equal to the time length T in  of the period T 1  during which the electrical signal is given to each input unit  13 . 
     In order to reflect all of the electrical signals given to the respective input units  13  to the calculation target value of the multiplier-accumulator  11   a , the period T 2  needs to be present on and after the period T 1 , and θ needs to be an appropriate value. For that purpose, a condition shown in the following equation (10) is required. 
         t   v   max   &gt;T   in   (10)
 
     From the equation (8), the equation (10) can be transformed into the following equation (11). 
       θ&gt;λβ T   in   (11)
 
     Here, when ε(&gt;0) of a minute amount is defined, the threshold θ can be expressed by the following equation (12) using ε. 
       θ=(1+ε)λβ T   in   (12)
 
     From the equation (12), the threshold θ needs to be proportional to a product of the sum total β of the loads w i  and the length T in  of the period T i . 
     The following equation (13) is obtained from the equations (7) and (12), and the following equation (14) is obtained from the equations (8) and (12). 
         t   v   min =2 T   in   +εT   in   (13)
 
         t   v   max   =T   in   +εT   in   (14)
 
     Hence, a time range of the period T 2  can be represented by the equations (13) and (14). 
     Referring to  FIG. 3 , a description will be given of a multiplier-accumulator that obtains the calculation target value while distinguishing the load w i  into the positive load w i   +  and the negative load w i   − .  FIG. 3  is a view illustrating an example of a configuration of the multiplier-accumulator that obtains the calculation target value while distinguishing the load w i  into the positive load w i   +  and the negative load w i   − . 
     For the N electrical signals given in the period T 1 , a multiplier-accumulator  11 A associates w i   +  with each of N +  electrical signals (N +  is a natural number of N or less). The multiplier-accumulator  11 A associates an absolute value of w i   −  with each of (N−N + ) electrical signals. Such a multiplier-accumulator  11 A includes a first multiplier-accumulator  11 Aa, a second multiplier-accumulator  11 Ab, and a calculation unit  20 . 
     As illustrated in  FIG. 3 , the first multiplier-accumulator  11 Aa includes N +  first input units  13 A, a first storage unit  14 A, a first comparison unit  18 A, and a first threshold power supply  19 A. 
     The first input units  13 A are connected in parallel to one another. Each of the first input units  13 A associates the load w i   +  with the electrical signal given within the predetermined period T 1 , and outputs a response waveform in which a voltage changes with the passage of time. Further, as illustrated in  FIG. 3 , each first input unit  13 A includes a first input terminal  15 A, a first resistor  16 A, and a first diode  17 A. The first input terminal  15 A, the first resistor  16 A, and the first diode  17 A are connected in series to one another. In each first input unit  13 A, for example, each first input terminal  15 A is given an electrical signal of the same voltage at different timing within the period T i . 
     The first storage unit  14 A is connected to each first input unit  13 A and stores an electric charge output from each first input unit  13 A. The first storage unit  14 A is, for example, a capacitor. 
     The first comparison unit  18 A compares a first threshold and a signal input thereto with each other, and outputs a step waveform at the time (hereinafter, referred to as first timing) when the input signal exceeds the first threshold. The first comparison unit  18 A is, for example, a comparator. The first comparison unit  18 A is connected to the first storage unit  14 A and the first threshold power supply  19 A. 
     The first threshold power supply  19 A gives a first threshold voltage to the first comparison unit  18 A. Here, a magnitude of the first threshold voltage is defined as θ + . In this case, the first comparison unit  18 A outputs the step waveform at timing at which the voltage held in the first storage unit  14 A exceeds the first threshold θ + . 
     As illustrated in  FIG. 3 , the second multiplier-accumulator  11 Ab includes (N−N + )=N −  second input units  13 B, a second storage unit  14 B, a second comparison unit  18 B, and a second threshold power supply  19 B. 
     The second input units  13 B are connected in parallel to one another. Each of the second input units  13 B associates the load w i   −  with the electrical signal given within the predetermined period T 1 , and outputs a response waveform in which a voltage changes with the passage of time. Further, as illustrated in  FIG. 3 , each second input unit  13 B includes a second input terminal  15 B, a second resistor  16 B, and a second diode  17 B. The second input terminal  15 B, the second resistor  16 B, and the second diode  17 B are connected in series to one another. In each second input unit  13 B, for example, each second input terminal  15 B is given an electrical signal of the same voltage at different timing within the period T i . That is, the period during which N +  electrical signals are given to the N +  first input units  13 A coincides with the period during which N −  electrical signals are given to the N −  second input units  13 B. 
     The second storage unit  14 B is connected to each second input unit  13 B and stores an electric charge output from each second input unit  13 B. The second storage unit  14 B is, for example, a capacitor. 
     The second comparison unit  18 B compares a second threshold and a signal input thereto with each other, and outputs a step waveform at the time (hereinafter, referred to as second timing) when the input signal exceeds the second threshold. The second comparison unit  18 B is, for example, a comparator. The second comparison unit  18 B is connected to the second storage unit  14 B and the second threshold power supply  19 B. 
     The second threshold power supply  19 B gives a second threshold voltage to the second comparison unit  18 B. Here, a magnitude of the second threshold voltage is defined as θ − . In this case, the second comparison unit  18 B outputs the step waveform at timing at which the voltage held in the second storage unit  14 B exceeds the second threshold θ − . 
     Here, a magnitude of the first threshold is defined as θ + , a magnitude of the second threshold is defined as θ − , the sum total of N +  positive loads w i   +  is defined as β + , and the sum total of absolute values of N −  negative loads w i   −  is defined as β − . In this case, β +  and β −  can be represented by the following equations (15) and (16), respectively. 
     
       
         
           
             
               
                 
                   
                     β 
                     + 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         N 
                         + 
                       
                     
                      
                     
                       w 
                       i 
                       + 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     β 
                     - 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         N 
                         - 
                       
                     
                      
                     
                       
                          
                         
                           w 
                           i 
                           - 
                         
                          
                       
                        
                       
                         ( 
                         
                           &gt; 
                           0 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Here, N=N + +N −  and β=β + −β −  are established. Assuming that the first timing is defined as t v   +  and that the second timing is defined as t v   − , then from the equation (4), θ +  and θ −  can be represented by the following equations (17) and (18), respectively. 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         N 
                         + 
                       
                     
                      
                     
                       
                         w 
                         i 
                         + 
                       
                        
                       
                         ( 
                         
                           
                             t 
                             v 
                             + 
                           
                           - 
                           
                             t 
                             i 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     θ 
                     + 
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                       
                          
                         
                           w 
                           i 
                           - 
                         
                          
                       
                        
                       
                         ( 
                         
                           
                             t 
                             v 
                             - 
                           
                           - 
                           
                             t 
                             i 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       θ 
                       - 
                     
                      
                     
                       ( 
                       
                         &gt; 
                         0 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Note that λ=1 is set in the equations (17) and (18). The following equations (19) and (20) are obtained when the calculation target value (sum of N multiplication values) is divided into a calculation target value (hereinafter, a first product sum value) of the positive load w i   +  and a calculation target value (hereinafter, a second product sum value) of the negative load w i   − . 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         N 
                         + 
                       
                     
                      
                     
                       
                         w 
                         i 
                         + 
                       
                       · 
                       
                         x 
                         i 
                       
                     
                   
                   = 
                   
                     
                       
                         θ 
                         + 
                       
                       + 
                       
                         
                           β 
                           + 
                         
                          
                         
                           ( 
                           
                             
                               T 
                               
                                 i 
                                  
                                 n 
                               
                             
                             - 
                             
                               t 
                               v 
                               + 
                             
                           
                           ) 
                         
                       
                     
                     
                       T 
                       
                         i 
                          
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                       
                          
                         
                           w 
                           i 
                           - 
                         
                          
                       
                       · 
                       
                         x 
                         i 
                       
                     
                   
                   = 
                   
                     
                       
                         θ 
                         - 
                       
                       + 
                       
                         
                           β 
                           - 
                         
                          
                         
                           ( 
                           
                             
                               T 
                               
                                 i 
                                  
                                 n 
                               
                             
                             - 
                             
                               t 
                               v 
                               - 
                             
                           
                           ) 
                         
                       
                     
                     
                       T 
                       
                         i 
                          
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     The calculation unit  20  calculates the calculation target value by subtracting the second product sum value from the first product sum value. Specifically, the calculation unit  20  is connected to the first comparison unit  18 A, detects pulse signals transmitted from the first comparison unit  18 A, and calculates the first product sum value. The calculation unit  20  is connected to the second comparison unit  18 B, detects pulse signals transmitted from the second comparison unit  18 B, and calculates the second product sum value. 
     In other words, the calculation unit  20  detects that the voltage held in the first storage unit  14 A has reached the first threshold θ + , and calculates the first product sum value. The calculation unit  20  detects that the voltage held in the second storage unit  14 B has reached the second threshold θ − , and calculates the second product sum value. Then, the calculation unit  20  calculates the calculation target value by subtracting the second product sum value from the first product sum value. An equation for calculating the calculation target value can be represented by the following equation (21). 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                       
                         w 
                         i 
                       
                       · 
                       
                         x 
                         i 
                       
                     
                   
                   = 
                   
                     
                       
                         θ 
                         + 
                       
                       - 
                       
                         θ 
                         - 
                       
                       + 
                       
                         β 
                          
                         
                           T 
                           
                             i 
                              
                             
                                 
                             
                              
                             n 
                           
                         
                       
                       - 
                       
                         ( 
                         
                           
                             
                               β 
                               + 
                             
                              
                             
                               t 
                               v 
                               + 
                             
                           
                           - 
                           
                             
                               β 
                               - 
                             
                              
                             
                               t 
                               v 
                               - 
                             
                           
                         
                         ) 
                       
                     
                     
                       T 
                       
                         i 
                          
                         
                             
                         
                          
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     Here, it is assumed that the calculation unit  20  calculates the first product sum value and the second product sum value in the period T 2 . In this case, in order to reflect all of the electrical signals given to the respective first input units  13 A and all of the electrical signals given to the respective second input units  13 B to the calculation target value, the period T 2  needs to be present on and after the period T 1 . Moreover, the time length of the period T 1  and the time length of the period T 2  are both T in . Then, for that purpose, the first threshold θ +  and the second threshold θ −  need to satisfy the following equations (22) and (23), respectively. 
       θ + =(1+ε)λβ +   T   in   (22)
 
       θ − =(1+ε)λβ −   T   in   (23)
 
     As shown in the equation (22), the first threshold θ +  is proportional to a product of the sum total β +  of N +  loads w i   +  and the length T in  of the period T i . As shown in the equation (23), the second threshold θ −  is proportional to a product of the sum total β −  of the absolute values of N −  loads w i   −  and the length T in  of the period T i . The first threshold θ +  and the second threshold θ −  satisfy the above-described relationships, whereby all of the electrical signals given to the respective first input units  13 A and all of the electrical signals given to the respective second input units  13 B can be reflected to the calculation target value. In other words, values of the first threshold θ +  and the second threshold θ −  just need to be determined so as to satisfy the equations (22) and (23). 
     However, on a right side of the equation (21), a product of t v   +  and β +  and a product of t v  and β −  are present. Therefore, in order to calculate the calculation target value based on the equation (21), the calculation unit  20  requires a complicated circuit configuration. 
     Therefore, in order to simplify the circuit configuration of the calculation unit  20 , an absolute value of a dummy load w 0  that corresponds to a virtual electrical signal of a value 0 and is obtained by multiplying a difference between β +  and β −  by −1 is added to a smaller one of β +  and β − . w 0  can be represented by the following equation (24). 
         w   O =−(β + +β − )  (24)
 
     By adding the dummy load w 0 , β + =β −  is established. From the equations (22) and (23), θ + =θ −  is established. Therefore, β + =β − =β 0  is established, and the equation (21) can be transformed into the following equation (25). 
     
       
         
           
             
               
                 
                   
                     
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                         x 
                         i 
                       
                     
                   
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                         β 
                         O 
                       
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                         ( 
                         
                           
                             t 
                             v 
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                             v 
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                       T 
                       
                         i 
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                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     As shown in the equation (25), when the positive load w i   +  and the negative load w i   −  are mixed, the calculation target value can be calculated based on a difference between the first timing and the second timing. 
     Here, if “t v   − −t v   + ” that is the difference between the first timing and the second timing is input to a next layer as it is, “t v   − −t v   + ” is multiplied by a reciprocal (1/β) of the sum total of the loads. That is, for example, when simulation of a neural network is executed using this multiply-accumulate method, a distribution of the outputs from the multiplier-accumulator  11  is reduced as going deeper. 
     [1-3. Network Configuration of Multiply-Accumulate Device] 
     Referring to  FIG. 4 , a description will be given of an example of a case in which the distribution of the outputs from the multiplier-accumulator  11  is reduced.  FIG. 4  is a diagram illustrating an example of a configuration of deep neural networks (DNNs) of the multiply-accumulate device  10 . 
     As illustrated in  FIG. 4 , DNN  30  includes a Convolution layer  31 , a first ReLU layer  32 , a MaxPooling layer  33 , a first FC layer  34 , a second ReLU layer  35 , and a second FC layer  36 . Processing for causing the DNN  30  as described above to recognize a character  40  of MNIST is considered. 
       FIG. 5  is histograms illustrating distributions of the outputs from the multipliers-accumulators in the respective layers. A histogram  51  is a histogram showing a distribution of (t v   − −t v   + ) output from the Convolution layer  31 . A histogram  52  is a histogram showing a distribution of (t v   − −t v   + ) output from the first FC layer  34 . A histogram  53  is a histogram showing a distribution of (t v   − −t v   + ) output from the second FC layer  36 . As illustrated in  FIG. 5 , while the histogram  51  has a wide time distribution of pieces of output timing, the histogram  53  has output timing concentrated at one point. In this case, it may become impossible to determine the timing at which the step waveform is output. 
     Therefore, the multiply-accumulate device according to the present disclosure executes processing for expanding an interval of the timing at which the step waveform is output. Thus, the multiply-accumulate device according to the present disclosure can delay a time from the output of the step waveform to the output of the next step waveform, and accordingly, can prevent the concentration of the timing at which the step waveform is output. 
     2. First Embodiment 
     [2-1. Configuration of Multiply-Accumulate System According to First Embodiment] 
     Referring to  FIG. 6 , a description will be given of a multiply-accumulate system according to a first embodiment of the present disclosure.  FIG. 6  is a diagram illustrating an example of the multiply-accumulate system according to the first embodiment of the present disclosure. 
     As illustrated in  FIG. 6 , the multiply-accumulate system  1  includes a multiplier-accumulator  11 A and a calculation device  100 . As will be specifically described later, the calculation device  100  executes a statistical calculation for an input signal. The calculation device  100  outputs the input signal, for which the statistical calculation is executed, to the multiplier-accumulator  11 A. In this case, the multiplier-accumulator  11   a  executes multiplication-accumulation for the input signal for which the statistical calculation is executed. Note that, for the sake of simplicity,  FIG. 6  illustrates only the first multiplier-accumulator  11 Aa in the multiplier-accumulator  11 A. The calculation device  100  can be applied to the second multiplier-accumulator  11 Ab similarly to the first multiplier-accumulator  11 Aa, and accordingly, a description thereof will be omitted. 
     The calculation device  100  includes a control unit  110  and a storing unit  120 . 
     The control unit  110  controls each unit that constitutes the calculation device  100 . For example, the control unit  110  develops and executes various programs, which are stored in the storing unit  120 , thereby controlling each unit that constitutes such a calculation processing device. The control unit  110  can be achieved by, for example, an electronic circuit including a central processing unit (CPU). The control unit  110  includes a statistic calculation unit  111  and a clip calculation unit  112 . 
     The statistic calculation unit  111  executes a statistical calculation for the input signal. For example, when the input signal is an image, the statistic calculation unit  111  calculates statistics such as an average of pixel values and a standard deviation thereof for each input image. For example, when the pixel value of the image is a i , the average of the pixel values is μ, and the standard deviation of the pixel values is σ, the statistic calculation unit  111  standardizes (a i −μ)/σ=b i  and the pixel value a i  to a new pixel value b i . The statistic calculation unit  111  multiplies the standardized pixel value by a coefficient corresponding to the pixels. Here, the coefficient is, for example, a coefficient expressed by (1/α) with α as an arbitrary number. More specifically, the statistic calculation unit  111  multiplies the standardized pixel value by the coefficient so that the standardized pixel value approaches an input value range of the multiplier-accumulator  11 A. The statistic calculation unit  111  does not necessarily have to multiply the standardized pixel value by the coefficient depending on a value of the standardized pixel value. The statistic calculation unit  111  does not have to multiply the standardized pixel value by the coefficient, for example, when the value of the standardized pixel value is relatively close to the input value range of the multiplier-accumulator  11 A. A description will be given below of the case in which the statistic calculation unit  111  standardizes the pixel value, but this is an example and does not limit the present disclosure. The statistic calculation unit  111  may convert the pixel values based on the statistics by a method other than the standardization. 
     The clip calculation unit  112  clips the standardized input signal within a predetermined range. For example, the clip calculation unit  112  clips the standardized input signal in a range corresponding to the input value range of the multiplier-accumulator  11 A. When the input value range of the multiplier-accumulator  11 A is, for example, −1 or more and 1 or less, the clip calculation unit  112  clips the standardized input signal in the range of −1 or more and 1 or less. In this case, the clip calculation unit  112  clips values less than −1 to −1 and values greater than 1 to 1. 
     [2-2. Standardized Image Data According to First Embodiment] 
     Referring to  FIG. 7 , a description will be given of an example of the input image.  FIG. 7  is diagrams illustrating an example of the input image and the standardized input image. The following description will be given on the assumption that the input signal is image data, but this is an example, and does not limit the present disclosure. 
     As illustrated in  FIG. 7 , input image data  61  uses, for example, character data “7” of Modified National Institute of Standards and Technology (MNIST). A size of the character data is, for example, 28×28 pixels. In this case, a minimum value of pixel values of the input image data  61  is “0”, a maximum value of the pixel values is “255”, an average of the pixel values is about “23.54”, and a standard deviation of the pixel values is about “65.94”. In the input image data  61 , pixel values in a black region are set to “0”, and pixel values in a white region are set to “255”. A histogram  62  is a histogram showing a distribution of the pixel values of the input image data  61 . As shown in the histogram  62 , most of the pixel values of the input image data  61  are “0”, and some thereof are dispersed in “255”. 
     Standardized image data  71  is image data obtained by standardizing the input image data  61  by the statistic calculation unit  111 . In this case, a minimum value of pixel values of the standardized image data  71  is “−0.36”, a maximum value of the pixel values is “3.51”, an average of the pixel values is “0”, and a standard deviation of the pixel values is “1”. A histogram  72  is a histogram showing a distribution of the pixel values of the standardized image data  71 . As shown in the histogram  72 , the pixel values of the standardized image data  71  move to “−0.36” by standardizing the most frequent “0”, for example. 
     Referring to  FIG. 8 , a description will be given of the clipped standardized image data.  FIG. 8  is diagrams illustrating an example of the clipped standardized image data. 
     Clip image data  81  is image data obtained by multiplying the standardized image data  71  by (⅙) by the statistic calculation unit  111  and clipping the multiplied standardized image data  71  in the range of −1 or more and 1 or less by the clip calculation unit  112 . Minimum and maximum values of the clip image data  81  stay within the range of −1 or more and 1 or less at the time when the standardized image data  71  is multiplied by (⅙) by the statistic calculation unit  111 , and accordingly, a result does not change no matter whether or not the clipping is performed by the clip calculation unit  112 . The minimum value of the pixel values of the clip image data  81  is “−0.06”, the maximum value is “0.58”, an average thereof is “0”, and a standard deviation thereof is “0.17”. A histogram  82  is a histogram showing a distribution of the pixel values of the clip image data  81 . As shown in the histogram  82 , the pixel values of the clip image data  81  are not clipped to “−1” and “1”, and most thereof are “−0.06”. 
     Clip image data  83  is image data obtained by multiplying the standardized image data  71  by (⅓) by the statistic calculation unit  111  and clipping the multiplied standardized image data  71  in the range of −1 or more and 1 or less by the clip calculation unit  112 . A minimum value of the clip image data  83  stays within the range of −1 or more and 1 or less at the time when the standardized image data  71  is multiplied by (⅓) by the statistic calculation unit  111 , and accordingly, a maximum value thereof is clipped to “1”. The minimum value of the pixel values of the clip image data  83  is “−0.12”, the maximum value is “1”, an average thereof is “0.01”, and a standard deviation thereof is “0.31”. A histogram  84  is a histogram showing a distribution of the pixel values of the clip image data  83 . As shown in the histogram  84 , as for the pixel values of the clip image data  83 , values exceeding “1” are clipped to “1”, and most thereof are “−0.12”. 
     The clip image data  85  is image data clipped in the range of −1 or more and 1 or less by the clip calculation unit  112  without multiplying the standardized image data  71  by a coefficient. A minimum value of the clip image data  85  stays within the range of −1 or more and 1 or less at the time when the standardized image data  71  is standardized by the statistic calculation unit  111 , and accordingly, a maximum value thereof is clipped to “1”. A histogram  86  is a histogram showing a distribution of the pixel values of the clip image data  85 . As shown in the histogram  86 , as for the pixel values of the clip image data  85 , values exceeding “1” are clipped to “1”, and most thereof are concentrated on “−0.36”. Further, the clip image data  85  has a thicker character than the clip image data  81  and the clip image data  83 . 
       FIG. 6  will be referred to again. The calculation device  100  outputs image data such as the clip image data  81 , the clip image data  83 , and the clip image data  85  to the multiplier-accumulator  11 A. In this case, the multiplier-accumulator  11 A executes the multiplication-accumulation for the image data such as the clip image data  81 , the clip image data  83 , and the clip image data  85 . That is, the multiplier-accumulator  11 A executes the multiplication-accumulation not for the image data itself but for the image data in which the statistical calculation is executed for the image data. Thus, the difference (t v   − −t v   + ) between the first timing and the second timing is widened. 
     [2-3. Output Time Difference of Multiply-Accumulate System According to First Embodiment] 
     Referring to  FIG. 9 , a description will be given of the output time difference of the signals output from the multiplier-accumulator  11 A in the multiply-accumulate system according to the first embodiment.  FIG. 9  is a diagram for explaining the output time difference from the multiplier-accumulator  11 A.  FIG. 9  is a table illustrating, for example, the output time difference from the multiplier-accumulator  11 A of the second FC layer  36  illustrated in  FIG. 4 . Further, in  FIG. 9 , the standard deviation is taken as σ, and the evaluation is performed with the output time difference of 6σ. 
     “Original” of a standardization method illustrated in  FIG. 9  is an output time difference when the input image data  61  illustrated in  FIG. 7  that is not standardized is input. The output time difference of the input image data  61  is 5.7×10 −10  seconds. 
     “Standardization for each image” of the standardization method is an output time difference when the clip image data  81 , the clip image data  83 , and the clip image data  85 , which are illustrated in  FIG. 8 , are input to the multiply-accumulate device  10 . 1/1 of 1/α is an output time difference when the clip image data  85  is input, and the output time difference is 1.1×10 −9  seconds. ⅓ of 1/α is an output time difference when the clip image data  83  is input, and the output time difference is 9.0×10 −10  seconds. ⅙ of 1/α is an output time difference when the clip image data  81  is input, and the output time difference is 5.2×10 −10  seconds. 
     As illustrated in  FIG. 9 , when the clip image data  85  is input, the output time difference is about twice as wide as when the input image data  61  is input. When the clip image data  83  is input, the output time difference is about twice as wide as when the input image data  61  is input. The image data is input to the multiply-accumulate device  10  after being standardized in this way, whereby the output time difference is expanded. 
     [2-4. Standardization Procedure According to First Embodiment] 
     Referring to  FIG. 10 , a description will be given of processing of the control unit  110  of the calculation device  100 .  FIG. 10  is a flowchart illustrating an example of a processing flow of the control unit  110 . 
     First, the control unit  110  calculates statistics such as the average and standard deviation of the pixel values of the image data input to the multiplier-accumulator  11 A (Step S 101 ). 
     The control unit  110  standardizes the pixel values of the image data based on the calculated statistics (Step S 102 ). Next, the control unit  110  multiplies the pixel values by a coefficient corresponding to the standardized pixel value (Step S 103 ). Note that Step S 103  may be omitted depending on the standardized pixel value. 
     The control unit  110  clips the standardized data multiplied by the coefficient in a specific range (Step S 104 ). Note that Step S 104  may be omitted depending on the standard pixel value or the standardized pixel value multiplied by the coefficient. 
     Then, the control unit  110  outputs the standardized data, which is clipped in the specific range, to the multiplier-accumulator  11 A (Step S 105 ). Thus, the multiplier-accumulator  11 A executes multiplication-calculation for the standardized image data. 
     As mentioned above, in the multiply-accumulate system  1  according to the first embodiment, the statistical calculation is executed for the input image data, and the input image data is output to the multiplier-accumulator  11 A after being standardized based on the statistics. Thus, the multiplier-accumulator  11 A executes the multiplication-calculation for the input image data in which the pixel values are standardized. As a result, the difference (t v   − −t v   + ) between the first timing and the second timing can be widened. 
     3. Second Embodiment 
     [3-1. Configuration of Multiply-Accumulate System According to Second Embodiment] 
     Referring to  FIG. 11 , a description will be given of a multiply-accumulate system  1 A according to a second embodiment of the present disclosure.  FIG. 11  is a diagram illustrating an example of the multiply-accumulate system  1 A according to the second embodiment of the present disclosure. 
     As illustrated in  FIG. 11 , learning data  121  is stored in a storing unit  120 A of a calculation device  100 A. The multiply-accumulate system  1 A according to the second embodiment is different from the multiply-accumulate system  1  according to the first embodiment in that the storing unit  120 A stores learning data  121 . 
     The learning data  121  is, for example, statistics including an average, a standard deviation, and the like in the entire image data for use in the learning of the multiply-accumulate device  10 . Further, the learning data  121  may include, as a statistical value, α of a coefficient (1/α) by which the statistic calculation unit  111  multiplies the standardized pixel values. In this case, α may be learned by backpropagation and stored as the learning data  121 , for example. 
     In the multiply-accumulate system  1 A according to the second embodiment, the statistic calculation unit  111  standardizes the pixel values of the input image data based on the learning data  121 . For example, when the statistic calculation unit  111  standardizes the input image data  61 , which is illustrated in  FIG. 7 , based on the learning data  121 , a minimum value of the pixels is “−0.42”, a maximum value thereof is “2.82”, an average thereof is about “−0.13”, and a standard deviation thereof is about “0.83”. As described above, in the multiply-accumulate system  1 A according to the second embodiment, since the statistic calculation unit  111  uses the learning data  121  as the statistics, the pixel values are not completely standardized. However, even in such a case, the difference (t v   − −t v   + ) between the first timing and the second timing can be widened. 
     Further, in the multiply-accumulate system  1 A according to the second embodiment, the clip calculation unit  112  clips the input signal, which is standardized based on the learning data  121 , within a predetermined range. 
     [3-2. Standardized Image Data According to Second Embodiment] 
     Referring to  FIG. 12 , a description will be given of the clipped standardized image data.  FIG. 12  is diagrams illustrating an example of the clipped standardized input image data. 
     Clip image data  91  is image data obtained by multiplying the standardized image data, which is standardized based on the learning data  121 , by (⅙) by the statistic calculation unit  111  and clipping the multiplied standardized image data in the range of −1 or more and 1 or less by the clip calculation unit  112 . Minimum and maximum values of the clip image data  91  stay within the range of −1 or more and 1 or less at the time when the standardized image data is multiplied by (⅙) by the statistic calculation unit  111 , and accordingly, a result does not change no matter whether or not the clipping is performed by the clip calculation unit  112 . A minimum value of the pixel values of the clip image data  91  is “−0.07”, a maximum value thereof is “0.47”, an average thereof is “0.021”, and a standard deviation thereof is “0.14”. A histogram  92  is a histogram showing a distribution of the pixel values of the clip image data  91 . As shown in the histogram  92 , the pixel values of the clip image data  91  are not clipped to “−1” and “1”, and most thereof are “−0.07”. 
     Clip image data  93  is image data obtained by multiplying the standardized image data, which is standardized based on the learning data  121 , by (⅓) by the statistic calculation unit  111  and clipping the multiplied standardized image data in the range of −1 or more and 1 or less by the clip calculation unit  112 . A minimum value of the clip image data  93  stays within the range of −1 or more and 1 or less at the time when the standardized image data is multiplied by (⅙) by the statistic calculation unit  111 , and accordingly, a maximum value thereof is clipped to “1”. The minimum value of the pixel values of the clip image data  93  is “−0.14”, the maximum value is “1”, an average thereof is “0.04”, and a standard deviation thereof is “0.28”. A histogram  94  is a histogram showing a distribution of the pixel values of the clip image data  93 . As shown in the histogram  94 , as for the pixel values of the clip image data  93 , values exceeding “1” are clipped to “1”, and most thereof are “−0.14”. 
     The clip image data  95  is image data clipped in the range of −1 or more and 1 or less by the clip calculation unit  112  without multiplying the standardized image data, which is standardized based on the learning data  121 , by a coefficient. A minimum value of the clip image data  95  stays within the range of −1 or more and 1 or less at the time when the standardized image data is standardized by the statistic calculation unit  111 , and accordingly, a maximum value thereof is clipped to “1”. A histogram  96  is a histogram showing a distribution of the pixel values of the clip image data  95 . As shown in the histogram  96 , as for the pixel values of the clip image data  95 , values exceeding “1” are clipped to “1”, and most thereof are “−0.42”. Further, the clip image data  95  has a thicker character than the clip image data  91  and the clip image data  93 . 
       FIG. 11  will be referred to again. The calculation device  100 A outputs image data such as the clip image data  91 , the clip image data  93 , and the clip image data  95  to the multiplier-accumulator  11 A. In this case, the multiplier-accumulator  11 A executes the multiplication-accumulation for the image data such as the clip image data  91 , the clip image data  93 , and the clip image data  95 . Thus, the difference (t v   − −t v   + ) between the first timing and the second timing can be widened. For example, in the case of an output from the second FC layer  36  illustrated in  FIG. 4 , the difference between the first timing and the second timing (t v   − −t v   + ) is widened by standardizing the image data based on the learning data  121 . The difference is doubled approximately. That is, even in the case of the standardization based on the learning data  121 , the same effect as in the case of standardizing for each image data can be obtained. 
     [3-3. Output Time Difference of Multiply-Accumulate System According to Second Embodiment] 
     Referring to  FIG. 13 , a description will be given of the output time difference of the signals output from the multiplier-accumulator  11 A in the multiply-accumulate system according to the second embodiment.  FIG. 13  is a diagram for explaining the output time difference from the multiplier-accumulator  11 A.  FIG. 13  is a table illustrating, for example, the output time difference from the multiplier-accumulator  11 A of the second FC layer  36  illustrated in  FIG. 4 . Further, in  FIG. 9 , the standard deviation is taken as σ, and the evaluation is performed with the output time difference of 6σ. 
     As described in  FIG. 9 , “original” of a standardization method illustrated in  FIG. 13  is an output time difference of the input image data  61 , and the output time difference is 5.7×10 −10  seconds. 
     “Standardization by learning data” of the standardization method is an output time difference when the clip image data  91 , the clip image data  93 , and the clip image data  95 , which are illustrated in  FIG. 12 , are input to the multiply-accumulate device  10 . 1/1 of 1/α is an output time difference when the clip image data  95  is input, and the output time difference is 1.2×10 −9  seconds. ⅓ of 1/α is an output time difference when the clip image data  93  is input, and the output time difference is 1.1×10 −9  seconds. ⅙ of 1/α is an output time difference when the clip image data  91  is input, and the output time difference is 5.3×10 −10  seconds. 
     As illustrated in  FIG. 13 , when the clip image data  95  is input, the output time difference is about twice as wide as when the input image data  61  is input. When the clip image data  93  is input, the output time difference is about twice as wide as when the input image data  61  is input. The image data is input to the multiply-accumulate device  10  after being standardized in this way, whereby the output time difference is expanded. 
     [3-4. Standardization Procedure According to Second Embodiment] 
     Referring to  FIG. 14 , a description will be given of processing of the control unit  110 A of the calculation device  100 A.  FIG. 10  is a flowchart illustrating an example of a processing flow of the control unit  110 A. 
     First, the control unit  110 A acquires the learning data  121  for standardizing the image data input from the storing unit  120  to the multiplier-accumulator  11 A (Step S 201 ). Next, the control unit  110 A standardizes the pixel values of the image data based on the acquired learning data  121  (Step S 202 ). Since Steps S 203  to S 205  are the same as Steps S 103  to S 105  illustrated in  FIG. 9 , a description thereof will be omitted. 
     As mentioned above, in the multiply-accumulate system  1 A according to the second embodiment, the input image data is output to the multiplier-accumulator  11 A after being standardized based on the learning data  121 . Thus, the multiplier-accumulator  11 A executes the multiplication-calculation for the input image data in which the pixel values are standardized. As a result, the difference (t v   − −t v   + ) between the first timing and the second timing can be widened. 
     Although the respective embodiments of the present disclosure have been described above, the technical scope of the present disclosure is not limited to the above-mentioned respective embodiments as they are, and various modifications can be made without departing from the spirit of the present disclosure. Further, constituents which cover different embodiments and modified examples may be combined with one another as appropriate. 
     Note that the effects described in the present specification are merely examples and are not limited, and other effects may be present. 
     Note that the present technology may also adopt such configurations as follows. 
     (1) 
     A multiply-accumulate system comprising: 
     a statistic calculation unit that executes a standardization calculation for an input signal; and 
     a multiply-accumulate device that executes multiplication-accumulation based on the standardized input signal. 
     (2) 
     The multiply-accumulate system according to (1), further comprising 
     a clip calculation unit that clips the standardized input signal within a predetermined range, and outputs the clipped standardized input signal to the multiply-accumulate device. 
     (3) 
     The multiply-accumulate system according to (2), 
     wherein the statistic calculation unit multiplies the standardized input signal by a coefficient corresponding to the standardized input signal, and 
     the clip calculation unit clips, within a predetermined range, the input signal that is standardized and multiplied by the coefficient, and outputs the clipped input signal to the multiply-accumulate device. 
     (4) 
     The multiply-accumulate system according to any one of (1) to (3), 
     wherein the statistic calculation unit executes the standardization calculation based on an average and standard deviation of values of the input signal. 
     (5) 
     The multiply-accumulate system according to any one of (1) to (4), further comprising 
     a storing unit that holds learning data used for learning of the multiply-accumulate device, 
     wherein the statistic calculation unit executes the standardization calculation based on the learning data. 
     (6) 
     The multiply-accumulate system according to (2), 
     wherein the clip calculation unit clips the standardized input signal based on an input value range of the multiply-accumulate device. 
     (7) 
     The multiply-accumulate system according to (6), 
     wherein the clip calculation unit clips the standardized input signal in a range of −1 or more and 1 or less. 
     (8) 
     A multiply-accumulate method comprising: 
     executing a standardization calculation for an input signal; and 
     executing multiplication-accumulation based on the standardized input signal. 
     REFERENCE SIGNS LIST 
     
         
         
           
               1 ,  1 A MULTIPLY-ACCUMULATE SYSTEM 
               10  MULTIPLY-ACCUMULATE DEVICE 
               11 ,  11   a ,  11 A MULTIPLIER-ACCUMULATOR 
               12  EXTERNAL INPUT UNIT 
               13  INPUT UNIT 
               13 A FIRST INPUT UNIT 
               13 B SECOND INPUT UNIT 
               14  STORAGE UNIT 
               14 A FIRST STORAGE UNIT 
               14 B SECOND STORAGE UNIT 
               15  INPUT TERMINAL 
               15 A FIRST INPUT TERMINAL 
               15 B SECOND INPUT TERMINAL 
               16  RESISTOR 
               16 A FIRST RESISTOR 
               16 B SECOND RESISTOR 
               17  DIODE 
               17 A FIRST DIODE 
               17 B SECOND DIODE 
               18  COMPARISON UNIT 
               18 A FIRST COMPARISON UNIT 
               18 B SECOND COMPARISON UNIT 
               19  THRESHOLD POWER SUPPLY 
               19 A FIRST THRESHOLD POWER SUPPLY 
               19 B SECOND THRESHOLD POWER SUPPLY 
               100 ,  100 A CALCULATION DEVICE 
               110 ,  110 A CONTROL UNIT 
               111  STATISTIC CALCULATION UNIT 
               112  CLIP CALCULATION UNIT 
               120 ,  120 A STORING UNIT