Patent Publication Number: US-9418333-B2

Title: Synapse array, pulse shaper circuit and neuromorphic system

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application claims the benefit under 35 USC 119(a) of Korean Patent Application No. 10-2013-0065669 filed on Jun. 10, 2013, in the Korean Intellectual Property Office, the entire disclosure of which is incorporated herein by reference for all purposes. 
     BACKGROUND 
     1. Field 
     The following description relates to a synapse array, a pulse shaper circuit, and a neuromorphic system that includes a synapse array and/or a pulse shaper circuit. 
     2. Description of Related Art 
     A physiological brain includes hundreds of billions of neurons that are interconnected with one another in a complicated nerve network. Neurons are considered to be responsible for the intellectual capability for learning and memory. In the cellular level, neurons use their synapses to exchange signals with thousands of other neurons. Thus, the neurons may be considered the structural and functional base units for data transmission. A synapse refers to a junction between two neurons at which an axon of a first neuron and a dendrite of a second neuron are positioned next to each other for transmission of data. A single neuron is generally connected with thousands of other neurons via synapses. 
     By manufacturing an artificial nervous system that mimics a biological nervous system in a neuronal level, a data processing method of the brain may be mimicked to achieve a new data processing and storing method. 
     A neuromorphic system refers to a semiconductor circuit that is designed to mimic the operation of the biological nervous system. A neuromorphic system may be used in a variety of applications, including in the implementation of an intelligent system that is capable of adapting itself to an unspecified environment. 
     SUMMARY 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. 
     In one general aspect, there is provided a synapse array based on a static random access memory (SRAM), the synapse array including a plurality of synapse circuits, in which at least one synapse circuit among the plurality of synapse circuits includes at least one bias transistor and at least two cut-off transistors, and the at least one synapse circuit is configured to charge a membrane node of a neuron circuit connected with the at least one synapse circuit using a sub-threshold leakage current that passed through the at least one bias transistor. 
     The at least one synapse circuit may be configured to change a value of the SRAM using a leakage current that passed through the at least two cut-off transistors. 
     The neuron circuit may be configured to fire a spike based on a result of comparing a number of occurrences of oscillation pulses generated based on a voltage of the membrane node to a predetermined reference number. 
     The neuron circuit may include: a pulse generator configured to generate an oscillation pulse based on a voltage of the membrane node; a counter configured to count a number of occurrences of the oscillation pulse; and a comparator configured to compare the number of occurrences to a predetermined reference number. 
     The comparator may be configured to compare the reference number with the number of occurrences, in synchronization with a clock signal periodically input. 
     The neuron circuit may further include a transistor connected to a ground. The oscillation pulse may be used to reset the membrane node by activating the transistor. 
     The at least two cut-off transistors may include a first cut-off transistor and a second cut-off transistor. The first cut-off transistor may be connected to a power voltage for pull-up. The second cut-off transistor may be connected to a ground for pull-down. The at least one bias transistor may be connected to the membrane node of the neuron circuit connected with the at least one synapse circuit. 
     In another general aspect, there is provided a pulse shaper circuit that is configured to generate a digital pulse indicating whether pulses corresponding to spikes fired by a neuron circuit potentiate or depress a synaptic weight of a synapse circuit. 
     The general aspect of the pulse shaper circuit may further include: a finite impulse response (FIR) filter comprising a 1-bit D flip flop chain configured to store the pulses; a first OR calculator configured to generate the digital pulse by performing OR calculation with respect to at least one pulse corresponding to potentiation of the synaptic weight among the stored pulses; and a second OR calculator is configured to generate the digital pulse by performing OR calculation with respect to at least one pulse corresponding to depression of the synaptic weight among the stored pulses. 
     The pulse shaper circuit may be configured to generate the digital pulse for maintaining the synaptic weight based on a value of the first OR calculator and a value of the second OR calculator. 
     In another general aspect, there is provided a neuromorphic system including: a synapse array based on a SRAM, the synapse array including at least one synapse circuit; a neuron circuit connected with the synapse circuit, the synapse circuit being configured to charge a membrane node of the neuron circuit using a sub-threshold leakage current that passed through at least one bias transistor of the synapse array, and the neuron circuit being configured to fire spikes based on a voltage of the membrane node; and a pulse shaper circuit configured to generate a digital pulse corresponding to the fired spikes. 
     The synapse array may include a plurality of synapse circuits, the plurality of synapse circuits including the at least one synapse circuit. The neuromorphic system may include a plurality of neuron circuits and a plurality of pulse shaper circuits. The neuromorphic system may further include a spike-timing dependent plasticity (STDP) logic circuit configured to determine an update state of a synapse circuit among the plurality of synapse circuits and an updated value for the synapse circuit based on the digital pulse, and an encoder configured to access a synapse circuit to be updated according to the digital pulse. 
     The neuron circuit may be configured to fire spikes based on a result of comparing a number of occurrences of oscillation pulses generated based on the voltage of the membrane node to a predetermined reference number. 
     The synapse array may further include at least two cut-off transistors, and may be configured to change a value of the SRAM using a leakage current that passed through the at least two cut-off transistors. 
     The neuron circuit may include: a pulse generation unit configured to generate an oscillation pulse based on a voltage of the membrane node; a counter configured to count a number of occurrences of the oscillation pulse; and a comparator configured to compare the number of occurrences to a predetermined reference number. 
     The neuron circuit may further include a transistor connected to a ground. The oscillation pulse may be used to reset the membrane node by activating the transistor. 
     The at least two cut-off transistors may include a first cut-off transistor and a second cut-off transistor. The first cut-off transistor may be connected to a power voltage for pull-up. The second cut-off transistor may be connected to a ground for pull-down. The at least one bias transistor may be connected to the membrane node of the neuron circuit connected with the synapse circuit. 
     The pulse shaper circuits may be configured to generate a digital pulse indicating whether pulses corresponding to spikes fired by a neuron circuit potentiate or depress a synaptic weight of the synapse circuit. 
     The STDP logic circuit may be configured to determine an update state of the plurality of synapse circuits and an updated value for the synapse circuits based on whether the digital pulse potentiates or depresses the synaptic weight. 
     The STDP logic circuit may be configured to determine the update state and the updated value of the synapse circuits, depending on a spike time between digital pulses corresponding to the spikes fired by the plurality of neuron circuits. 
     The neuromorphic system may be configured to enable a write line (WL) of a synapse circuit corresponding to a first neuron circuit at a falling edge of a first digital pulse corresponding to a spike fired by the first neuron circuit in response to the first neuron circuit among the plurality of neuron circuits firing the spike. 
     The STDP logic circuit may be configured to determine the updated value of the synapse circuit corresponding to the first neuron circuit based on a value of a second digital pulse of a second neuron seen from the falling edge of the first digital pulse. 
     The STDP logic circuit may be configured to update a value for potentiating the synaptic weight as the updated value in response to the first digital pulse preceding the second digital pulse. 
     The STDP logic circuit may be configured to update a value for depressing the synaptic weight as the updated value in response to the second digital pulse preceding the first digital pulse. 
     The STDP logic circuit may be configured to determine to maintain the value of the synapse circuit corresponding to the first neuron circuit in response to ‘0’ being detected at the falling edge of the first digital pulse. 
     The encoder may be configured to transmit the updated value to the synapse circuits according to the digital pulse. 
     Other features and aspects will be apparent from the following detailed description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating an overall structure of an example of a neuromorphic to system. 
         FIG. 2  is a diagram illustrating an example of a synapse circuit included in a neuromorphic system. 
         FIG. 3  is a diagram illustrating an example of a neuron circuit included in a neuromorphic system. 
         FIG. 4  is a diagram illustrating an example of a pulse shaper circuit included in a neuromorphic system. 
         FIG. 5  is a diagram illustrating an example of a spike-timing dependent plasticity (STDP) operation method of a neuromorphic system. 
     
    
    
     Throughout the drawings and the detailed description, unless otherwise described or provided, the same drawing reference numerals will be understood to refer to the same elements, features, and structures. The drawings may not be to scale, and the relative size, proportions, and depiction of elements in the drawings may be exaggerated for clarity, illustration, and convenience. 
     DETAILED DESCRIPTION 
     The following detailed description is provided to assist the reader in gaining a comprehensive understanding of the methods, apparatuses, and/or systems described herein. However, various changes, modifications, and equivalents of the systems, apparatuses, and/or methods described herein will be apparent to one of ordinary skill in the art. The progression of processing steps and/or operations described is an example; however, the sequence of steps and/or operations is not limited to that set forth herein and may be changed as is known in the art, with the exception of steps and/or operations necessarily occurring in a certain order. Also, description of well-known functions and constructions may be omitted to for increased clarity and conciseness. 
     The features described herein may be embodied in different forms, and are not to be construed as being limited to the examples described herein. Rather, the examples described herein have been provided so that this disclosure will be thorough and complete, and will convey the full scope of the disclosure to one of ordinary skill in the art. 
       FIG. 1  illustrates an overall structure of an example of a neuromorphic system  100 . 
     Referring to  FIG. 1 , the neuromorphic system  100  includes a static random access memory (SRAM)-based synapse array  110 , a plurality of neuron circuits  130 , a plurality of pulse shaper circuits  150 , a spike-timing dependent plasticity (STDP) logic circuit  170 , and an encoder  190 . However, in other examples, a neuromorphic system may include one or more of the SRAM-based synapse array, neurons circuits, pulse shaper circuits, STDP logic circuit and encoder, without including all of these structures. 
     Referring to  FIG. 1 , the SRAM-based synapse array  110  includes a plurality of synapse circuits based on an SRAM structure. Each of the synapse circuits may include at least one bias transistor and at least two cut-off transistors. 
     The synapse circuit may charge membrane nodes of the neuron circuits  130  that is connected with the synapse circuit, using a sub-threshold leakage current that passed through the at least one bias transistor. In addition, the synapse circuit may change a value of the SRAM by using a leakage current that passes through the at least two cut-off transistors. 
     The synapse circuit may include the at least two cut-off transistors, for example, a first cut-off transistor and a second cut-off transistor. The first cut-off transistor may be connected to a voltage drain drain (VDD) for pull-up. The second cut-off transistor may be connected to a ground (GND) for pull-down. The at least one bias transistor may be connected to the membrane nodes of the neuron circuits  130  that is connected to the synapse circuit. 
     WLx/WLxB indicated at the synapse array  110  refers to a word line, that is, a line for selecting an address of an axon. In WLx/WLxB, x refers to an order of each line. In this example, x may be a natural number ranging from 0 to 3. A logic value of WLx of the synapse array  110  is 1. When a corresponding line is selected, an STDP result may be used for the SRAM through C 1 C 0 x, that is, STDP information of each neuron transmitted through an STDP logic circuit. STDP refers to a learning mechanism postulated to exist in synapses of biological nerve networks. Based on STDP, synaptic efficacy or weight is slightly altered between two neurons based on information such as the timing of a pre-synaptic spike in a pre-synaptic neuron and a post-synaptic spike in a post-synaptic neuron. That is, a synaptic circuit may be potentiated or depressed to change the efficacy of data transmission between two neurons. The operation and configuration of an example of the synapse circuit are further described below with reference to  FIG. 2 . 
     The plurality of neuron circuits  130  may fire spikes based on a result of comparing a number of occurrences of oscillation pulses generated on the basis of an input voltage input from the membrane nodes, to a predetermined reference number. An example of the neuron circuit  130  is further described below with reference to  FIG. 3 . 
     The plurality of pulse shaper circuits  150  may receive a signal transmitted from the neuron circuit  130 , and may generate a pulse for the STDP operation based on the signal. The pulse shaper circuits  150  may generate digital pulses corresponding to the spikes fired at the neuron circuits  130 . The pulse shaper circuits  150  may generate the digital pulses that indicate whether pulses corresponding to the fired spikes potentiate (strengthen) or depress (weaken) a synaptic weight of the synapse circuit. An example of the pulse shaper circuit  150  is further described below with reference to  FIG. 4 . 
     The STDP logic circuit  170  may receive the signal generated by the pulse shaper circuits  150 , and may perform the STDP operation based on the signal. That is, the STDP logic circuit  170  may determine an update state of the plurality of synapse circuits and updated values for the synapse circuits, based on the digital pulses generated by the pulse shaper circuits  150 . In addition, the STDP logic circuit  170  may include an address event representation (AER) function, by which the STDP logic circuit  170  may transmit a test result related to the neuron circuits  130  and information regarding firing generated in a random neuron circuit  130  to other neuron circuits  130 . The updated value determined by the STDP logic circuit  170  may be transmitted to the synapse array  110  through the WBLx line. 
     The STDP logic circuit  170  may determine the presence of absence of an updating event (update state) and the updated values of the synapse circuits, based on a spike time between the digital pulses corresponding to the spikes fired by the plurality of neuron circuits  130 . 
     The operation of the STDP logic circuit  170  is further described below with reference to  FIG. 5 . 
     The encoder  190  may access the synapse array  110  according to the digital pulses generated by the pulse shapers  150 . The encoder  190  may access the synapse arrays to be updated according to the digital pulses, or transmit the updated values to the synapse circuits according to the digital pulses. For example, in the event that a firing occurred in a neuron circuit  130 , the pulse generated at a pulse shaper circuit  150 , for example ‘1’, may be transmitted to the encoder  190 . In response, the encoder  190  may transmit a logic value ‘1’ to WL0 to update the synaptic weight of the synapse circuit corresponding to the neuron circuit  130 . In this example, the WL0 line (or other WLx line) refers to a line for selecting the address of a word line. That is, the WL0 line (or other WLx line) may correspond to a Write Enable state. In the event that WL0 is equal to ‘1’, states of the synapse circuits corresponding to a first word line, for example, corresponding to an axon of neuron circuit A in  FIG. 5  may be the Write Enable state. However, in the event that the neuron circuit  130  did not fire, the encoder  190  does not transmit the pulse and, in this state, the logic value ‘0’ may be applied to WL2. Therefore, synapse circuits corresponding to a third word line may be in a Write Disable state and data may not be written. 
     For example, in the event that a first neuron circuit among the plurality of neuron circuits  130  fired the spike, the neuromorphic system may enable a write line, for example the WLX line, of the synapse circuit corresponding to the first neuron circuit in a falling edge of a first digital pulse corresponding to the fired spike. 
     Generally, the neuromorphic system may be greatly affected by a leakage current of devices, a mismatch between devices, and a process voltage temperature (PVT) variation. Further, with an increase in the number of neuron circuits and synapse circuits included in a neuromorphic system, more scale-down complementary metal oxide semiconductor (CMOS) process may be used for high integration. However, as the process becomes more scale-down, the leakage current from semiconductor components may further increase. The increase in leakage current may potentially cause continuous firings inside a neuron circuit even when no external stimulation is applied to the neuron circuit. 
     In general, leakage current has been considered an adverse side effect in designing a neuromorphic system. However, according to one example, the neuromorphic system may be implemented in such a way that it meets the demand for high integration and low power, by using a small amount of current equivalent to the amount of leakage current. 
       FIG. 2  illustrates an example of a synapse circuit  200  included in a neuromorphic system. The neuromorphic system may correspond to the neuromorphic system illustrated in  FIG. 1 . Further, according to another example, a synapse circuit may include only a portion of the structures illustrated in  FIG. 2 . 
     Referring to  FIG. 2 , the synapse circuit  200  includes at least two cut-off transistors  210  and  230 , and at least one bias transistor  260 . 
     The synapse circuit  200  is configured to charge a membrane node of a neuron circuit connected with the synapse circuit  200 , using a sub-threshold leakage current that passed through the at least one bias transistor  260 . 
     The at least two cut-off transistors  210  and  230  include a first cut-off transistor  210  and a second cut-off transistor  230 . 
     In this example, the first cut-off transistor  210  is a P-metal oxide semiconductor (P-MOS) transistor. The first cut-off transistor  210  is connected to a power voltage VDD for pull-up. The second cut-off transistor  230  is an N-MOS transistor and is connected to a ground GND for pull-down. 
     The bias transistor  260  is a transistor located at a last position of a third device  250  in which three P-MOS transistors are serially connected. The bias transistor  260  may be connected to the membrane node of the neuron circuit connected to the synapse circuit  200 . The third device  250  in which the three P-MOS transistors are serially connected may be connected to an RWLBx line and a Cmemx line. The third device  250  may be used in performing a read operation. In the event that firing occurs at a neuron circuit corresponding to the RWLBx line, all neuron circuits that are connected to the neuron circuit may have a logic value ‘1.’ 
     While a write line WLx of the synapse circuit  200  is enabled, in this example, the synapse circuit  200  may change a value of the cross-coupled inverter  240  to a value provided by a writing circuit  220 . At most time, the write line WLx is in a disabled state. 
     A neuromorphic system using a general SRAM structure may be implemented only with a cross-coupled inverter  240  configuration. In such a case, because a leakage current between the power voltage VDD and the ground GND, flowing through the cross-coupled inverter  240 , may be great in amount, the leakage power consumption may increase. 
     However, the neuromorphic system according to the present disclosure may considerably reduce the leakage power consumption caused by the first cut-off transistor  210  and the second cut-off transistor  230 . For example, when the first cut-off transistor  210  and the second cut-off transistor  230  are in an off state, the leakage current between the power voltage VDD and the ground GND may be substantially suppressed, thereby reducing the leakage power consumption. 
     In the event that a value of a node n1 is ‘0’ in the cross-coupled inverter  240 , the SRAM may have a value of approximately ‘0.’ In the event that the value of the node n1 is ‘1,’ the SRAM may have a value that is approximately ‘1’ and a value of a node n2 may be approximately ‘0.’ Therefore, the node n2 may allow the current that is necessary for operation to flow toward the membrane node. Here, a voltage slightly lower than the power voltage VDD may be applied to the bias transistor  260  located at the third position of the third device  250  through an external bias circuit. Accordingly, only a minor amount of current equivalent to the sub-threshold leakage current may flow inside the bias transistor  260 . 
     In the event that firing occurs at the neuron circuit during a writing operation, it is possible for the current to flow among the neuron circuits in different directions according to whether the synaptic weight of the synapse circuit corresponds to potentiation or depression. 
     In the event that the synaptic weight is ‘1,’ the current may flow from a pre-synaptic neuron circuit to a post-synaptic neuron circuit. Conversely, in the event that the synaptic weight is ‘−1,’ the current may flow from a post-synaptic neuron circuit to a pre-synaptic neuron circuit. 
     In addition, a first device, that is, the writing circuit  220  including two serially connected N-MOS transistors and two serially connected P-MOS transistors may be connected to the WLx word line as a result of the STDP and therefore may perform the writing operation. 
     Referring back to the synapse circuit of  FIG. 2 , in the event that the transistor is turned on, a current of several nano amperes (1×10 −9  A) may flow through the transistor. In the event that the transistor is in an OFF state, a current of several pico amperes (1×10 −12  A) may flow through the transistor. The magnitudes of currents may be considered as a leakage current level of a general synapse circuit. According to one example, it is possible to operate the neuron circuit with such a small amount of current, thereby achieving a high level of integration and a reduction of power consumption in the neuromorphic system. 
     Because the synapse circuit according to the embodiment uses a synapse circuit based on the SRAM structure, the synapse circuit takes up a relatively small area and is efficient in achieving high integration. Moreover, the synapse circuit may charge the membrane node of the neuron with a small amount of current using the cut-off transistors. Therefore, even with a highly integrated circuit, a firing rate of the neuron circuit may be maintained at a level similar to an actual biological neuron. 
     Furthermore, due to the cut-off transistors that is connected to the power voltage VDD and the ground GND through pull-up and pull-down, a leakage current may not be generated even in a static state remembering the synaptic weight. Therefore, a neuromorphic system that operates with low power consumption may be achieved. 
       FIG. 3  illustrates an example of a neuron circuit  300  included in a neuromorphic system. The neuromorphic system may correspond to the neuromorphic system illustrated in  FIG. 1 . Further, according to another example, a neuron circuit may include only a portion of the structures illustrated in  FIG. 3 . 
     Referring to  FIG. 3 , the neuron circuit  300  according to one example includes a pulse generator  310 , a counter  330 , and a comparator  350 . 
     In the event that a voltage is applied through a membrane node, the pulse generator  310  may generate an oscillation pulse based on the voltage. For example, the voltage applied to the pulse generator  310  may have a wave form similar to a wave form  301  illustrated in  FIG. 3 . The oscillation pulse generated by the pulse generator  310  may be a digital pulse similar to a wave form  303  illustrated in  FIG. 3 . 
     The pulse generator  310  includes a transistor  320 . The transistor  320  connects to a ground GND through a source terminal thereof, and connects to the membrane node through a drain terminal thereof. The oscillation pulse generated by the pulse generator  310  may activate the transistor  320 , thereby resetting the membrane node. By resetting the membrane node, the transistor  320  may participate in the generation of the oscillation pulse. 
     The counter  330  may count a number of occurrences of the oscillation pulses or a number of the oscillation pulses generated in the pulse generator  350 . 
     The comparator  350  may compare a predetermined reference number with the number of occurrences of the oscillation pulses counted by the counter  330 . The comparator  350  may compare the reference number with the number of occurrences, in synchronization with a clock signal that is periodically input. 
     The comparator  350  may fire a spike based on a result of the comparison. The pulse generated in the comparator  350  may be connected to a reset terminal of the counter  330  and be transmitted to a pulse shaper circuit. Here, the transmitted pulse may pass through a finite impulse response (FIR) filter and be overwritten to a synaptic weight of the synapse circuit by an STDP logic circuit. 
       FIG. 4  is a diagram illustrating an example of a pulse shaper circuit included in a neuromorphic system. The neuromorphic system may correspond to the neuromorphic system illustrated in  FIG. 1 . Further, according to another example, a pulse shaper circuit may include only a portion of the structures illustrated in  FIG. 4 . 
     Referring to  FIG. 4 , the pulse shaper circuit according to one example may form the shape of a neuron spike that is necessary for the STDP operation. That is, the pulse shaper circuit may generate a digital pulse indicating whether pulses corresponding to the spike fired to by the neuron circuit are to potentiate or depress the synaptic weight of the synapse circuit. 
     The pulse shaper circuit  400  includes a FIR filter  410 , a first OR calculator  430 , and a second OR calculator  450 . 
     The FIR filter  410  may be in the form of a 1-bit D flip-flop chain and be configured to store pulses transmitted from the neuron circuit. 
     The first OR calculator  430  may generate the digital pulse by performing an OR calculation with respect to at least one pulse corresponding to potentiation of the synaptic weight among the pulses stored in the FIR filter  410 . 
     The second OR calculator  450  may generate the digital pulse by performing OR calculation with respect to at least one pulse that corresponds to depression of the synaptic weight among the pulses stored in the FIR filter  410 . 
     Output values of the first OR calculator  430  and the second OR calculator may express the synaptic weights of +1, 0, and −1 through simple calculation. For example, the output value ‘1(+1)’ of the first OR calculator  430  may refer to potentiation of the synaptic weight, and the output value ‘1(−1)’ of the second OR calculator  450  may refer to depression of the synaptic weight. Further, in the event that the output value of the first OR calculator  430  and the second OR calculator  450  is ‘0,’ it may indicate no change to the synaptic network. 
       FIG. 5  illustrates an example of a spike-timing dependent plasticity (STDP) operation method of a neuromorphic system. The neuromorphic system may correspond to the neuromorphic system illustrated in  FIG. 1 . 
     Referring to  FIG. 5 , the STDP operation of the neuromorphic system is described. 
     Presuming that a firing has occurred in a neuron circuit A  509  among a plurality of neuron circuits, a WLx word line that corresponds to an axon of the neuron circuit A  509  is enabled at a falling edge of a pulse shaper signal. Further, pulse values of other neurons may be updated to the synapse circuit through the pulse shaper circuit. 
     For example, when IF denotes a signal informing of firing of the neuron has and PS denotes a digital pulse shape generated by the pulse shaper circuit, the IF may have ‘1’ or ‘0’ as a pulse value generated in the pulse generator  330  of  FIG. 3 . The PS may have a value of 1, −1, or 0. All neurons may each have its IF value and its PS value. 
     Presuming that a firing has occurred in the neuron circuit A  509 , simple logic calculation may be performed with respect to the PS values of other neurons and the IF value of the neuron circuit A  509  when the falling edge of the pulse shaper signal starts. Based on a result of the logic calculation, the synapse circuit may be updated. 
     The foregoing operation may be performed in the STDP logic circuit  507 . Whether an update has occurred among a plurality of synapse circuits and updated values of the synapse circuits may be determined based on whether the digital pulses generated in the pulse shaper circuit potentiate or depress the synaptic weight. 
     In addition, the STDP logic circuit  507  may determine update of the synapse circuits and the updated values, depending on a spike time between digital pulses corresponding to spikes fired by the plurality of neuron circuits. 
     The STDP logic circuit  507  may determine an updated value of a synapse circuit that corresponds to a first neuron circuit, based on a second digital pulse value of a second neuron seen from the falling edge of a first digital pulse. 
     In the event that the first digital pulse precedes the second digital pulse, the STDP logic circuit  507  may determine the updated value as a value for potentiating the synaptic weight. In the event that the second digital pulse precedes the first digital pulse, the STDP logic circuit  507  may determine the updated value as a value for depressing the synaptic weight. 
     In the event that a value ‘0’ is detected at the falling edge of the first digital pulse, the STDP logic circuit  507  may determine to maintain the value of the synapse circuit corresponding to the first neuron circuit. 
     Hereinafter, relationships between the neuron circuit A  509  and ‘other’ neuron circuits is further described to explain the operation of the STDP logic circuit  507  based on an order between the first digital pulse and the second digital pulse. 
     For example, presuming that a firing has occurred in the neuron circuit A  509  of  FIG. 5 , the value of the second digital pulse of ‘other’ neuron circuits seen from the falling edge of the first digital pulse corresponding to the spike of the neuron circuit A  509  may occur later than that of the neuron circuit A  509 . In Case 1 illustrated in  FIG. 5 , in the case of potentiation  510 , the value ‘+1’ may be obtained when ‘other’ neuron circuits are seen from the falling edge of the first digital pulse. The value ‘+1’ refers to potentiation of the synaptic weight. The STDP logic circuit  507  may generate a pulse (C 1 C 0 =00) for potentiation update of the synaptic weight. In this example, neurons corresponding to  501  among axon lines of the neuron circuit A may be updated to a pulse value ‘+1’ of ‘other’ neuron circuits. That is, C 1 C 0 =00, at the falling edge of the neuron circuit A  509 . 
     The value of the second digital pulse of ‘other’ neuron circuits seen from the falling edge of the first neuron corresponding to the spike of the neuron circuit A  509  may be earlier than the neuron circuit A  509 , as in Case 2 shown by depression  530 . In Case 2 illustrated in  FIG. 5 , the value ‘−1’ may be obtained when ‘other’ neuron circuits are seen from the falling edge of the first digital pulse. The value ‘−1’ refers to depression of the synaptic weight. The STDP logic circuit  507  may generate a pulse (C 1 C 0 =11) for depression update of the synaptic weight. In this example, neurons corresponding to  503  among the axon lines of the neuron circuit A  509  may be updated to a pulse value ‘−1’ of ‘other’ neuron circuits. That is, C 1 C 0 =11, at the falling edge of the neuron circuit A  509 . 
     In addition, ‘0’ may be obtained as the value of the second digital pulse of ‘other’ neuron circuits seen from the falling edge of the first neuron corresponding to the spike of the neuron circuit A  509 , as illustrated in Case 3 of no change  550 . In this case, a time difference between the first digital pulse and the second digital pulse is so great that the synaptic weight is not influenced at all. That is, in this case, a previous value of the synaptic weight may be maintained. Therefore, since the STDP logic circuit  507  needs to not update the synaptic weight, the value is controlled to meet C 1 C 0 =01 so that the transistors are in its OFF state. Accordingly, an SRAM value is not changed. Here, neurons corresponding to  505  among the axon lines of the neuron circuit A  509  are not changed at the falling edge of the neuron circuit A  509 . 
     When a spike is fired at the first neuron circuit among the plurality of neuron circuits, the neuromorphic system may access the WLx line (refer to the WLx word line of  FIG. 1 ) of the synapse circuit corresponding to the first neuron circuit at the falling edge of the first digital pulse corresponding to the fired spike, thereby enabling the WLx line. 
     As described above, the STDP logic circuit  507  may determine whether an update of the synapse array occurred and the updated value, and access the WLx line (refer to the WLx word line of  FIG. 1 ) of the synapse circuit to be updated through an encoder. Here, the updated value of the corresponding synapse may be determined by C 1 C 0  output from the STDP logic circuit. 
     With the various examples described above, a high integration and low-power neuromorphic system may be implemented, by flowing only a minor current equivalent to a leakage current to a neuron circuit and a synapse circuit constituting the neuromorphic system. 
     While this disclosure includes specific examples, it will be apparent to one of ordinary skill in the art that various changes in form and details may be made in these examples without departing from the spirit and scope of the claims and their equivalents. The examples described herein are to be considered in a descriptive sense only, and not for purposes of limitation. Descriptions of features or aspects in each example are to be considered as being applicable to similar features or aspects in other examples. Suitable results may be achieved if the described techniques are performed in a different order, and/or if components in a described system, architecture, device, or circuit are combined in a different manner and/or replaced or supplemented by other components or their equivalents. Therefore, the scope of the disclosure is defined not by the detailed description, but by the claims and their equivalents, and all variations within the scope of the claims and their equivalents are to be construed as being included in the disclosure.