Patent Publication Number: US-11663457-B2

Title: Neural network circuits having non-volatile synapse arrays

Description:
CROSS-REFERENCE TO PRIOR APPLICATIONS 
     This is a Divisional application of U.S. patent application Ser. No. 16/196,617, filed on Nov. 20, 2018, titled “Neural Network Circuits Having Non-Volatile Synapse Arrays,” which claims priority of U.S. Patent Application Nos. 62/592,300, 62/620,947 and 62/655,074, filed on Nov. 29, 2017, Jan. 23, 2018, and Apr. 9, 2018, respectively, which are all hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND 
     A. Technical Field 
     The present invention relates to neural network circuits, and more particularly, to neural network circuits having non-volatile synapse arrays using analog values. 
     B. Background of the Invention 
     An Artificial Neural Network (ANN) is a neural network that mimics a computational model of the human brain. A neural network can be described as many neurons connected with each other through synapses between them. The strengths of the connections, or the weight parameter of each synapse, can be adjusted through a learning process as a trainable parameter. In recent years, artificial intelligence (AI) using ANNs have been applied to various fields, such as visual and audio detection/recognition, language translation, gaming, medical decision-making, financial or weather forecasting, drones, autonomous driving cars, and etc. 
     Traditionally, computation of neural networks requires high performance cloud servers having multiple central processing units (CPUs) and/or graphics processing units (GPUs), since the complexity of computation prohibits mobile devices from running AI program locally due to the limited power and computation resource of the mobile devices. Other existing application-specific integrated circuit (ASIC) or field-programmable gate array (FPGA) approaches that accelerate computation of neural network with dedicated complementary metal-oxide-semiconductor CMOS) logic can be power efficient compared to such generic CPU and GPU based approaches, but still wastes unnecessary power and latency to move data to and from the separate off-chip non-volatile memory (NVM) where the trained weight parameters are stored. As such, there is a need for neural network circuits that consume significantly less computational resources. 
     SUMMARY OF THE DISCLOSURE 
     In one aspect of the present invention, a non-volatile synapse circuit, includes: a first input signal line for providing a first input signal, a reference signal line for providing a reference signal, first and second output lines for carrying first and second output signals, and first and second cells for generating the first and second output signals, respectively. Each of the first and second cells includes a first upper select transistor, having a gate that is electrically coupled to the first input signal line, and a first resistive changing element with one end connected to the first upper select transistor in series and an other end electrically coupled to the reference signal line, with a value of the first resistive changing element being programmable to change a magnitude of an output signal. A drain of the first upper select transistor of the first cell is electrically coupled to the first output line and a drain of the first upper select transistor of the second cell is electrically coupled to the second output line. 
     A method for programming a threshold voltage (VTH) of a floating gate in a non-volatile synapse that includes a pair of transistors arranged to have a floating gate node, includes: applying a first electrical pulse across the pair of transistors, the first electrical signal having a first height and a first width; and then applying a first sequence of pulses across the pair of transistors while increasing a height of each pulse from a previous pulse by a preset value, with each pulse of the first sequence of pulses having a second width that is narrower than the first width. This results in programming a voltage on the floating gate node. 
     In another aspect of the present invention, a non-volatile neural network includes: a first neural array layer including a first plurality of neurons; a second neural array layer including a second plurality of neurons; and a synapse array layer disposed between the first and second neural array layers and including a plurality of non-volatile synapses. Each non-volatile synapse in the synapse array layer is electrically coupled to a neuron of the first plurality of first neurons and to one or more neurons of the second plurality of neurons, and includes: a first input signal line for receiving a first input signal from a neuron in the first plurality of neurons; a reference signal line for providing a reference signal; first and second output lines for carrying first and second output signals therethrough, the first and second output signals being processed and transmitted to one or more neurons of the second plurality of neurons; and first and second cells for generating the first and second output signals, respectively. Each of the first and second cells includes a first upper select transistor, having a gate that is electrically coupled to the first input signal line, and a first resistive changing element with one end connected to the first upper select transistor in series and an other end electrically coupled to the reference signal line, with a value of the first resistive changing element being programmable to change a magnitude of an output signal. A drain of the first upper select transistor of the first cell is electrically coupled to the first output line and a drain of the first upper select transistor of the second cell is electrically coupled to the second output line. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       References will be made to embodiments of the invention, examples of which may be illustrated in the accompanying figures. These figures are intended to be illustrative, not limiting. Although the invention is generally described in the context of these embodiments, it should be understood that it is not intended to limit the scope of the invention to these particular embodiments. 
         FIG.  1    shows a schematic diagram of a neural network according to embodiments of the present disclosure. 
         FIG.  2    shows a schematic diagram of an array of synapses according to embodiments of the present disclosure. 
         FIG.  3    shows a schematic diagram of a synapse according to embodiments of the present disclosure. 
         FIG.  4    shows a schematic diagram of another synapse according to embodiments of the present disclosure. 
         FIG.  5    shows a schematic diagram of another synapse according to embodiments of the present disclosure. 
         FIG.  6    shows a schematic diagram of another synapse according to embodiments of the present disclosure. 
         FIG.  7    shows a schematic diagram of another synapse according to embodiments of the present disclosure. 
         FIG.  8    shows a schematic diagram of another synapse according to embodiments of the present disclosure. 
         FIG.  9 A- 9 B  show comparison of conventional methods for programming the threshold voltage (VTH) to a method according to embodiments of the present disclosure. 
         FIG.  10 A- 10 B  show another method for programming a threshold voltage (VTH) of a floating gate node according to embodiments of the present disclosure. 
         FIG.  11    shows a flow chart of an illustrative process for programming a threshold voltage (VTH) of a floating gate node according to embodiments of the present disclosure. 
         FIG.  12 A- 12 C  illustrates differential signaling according to embodiments of the present disclosure. 
         FIG.  13    shows a schematic diagram of a chip that includes a neural network according to embodiments of the present disclosure. 
         FIG.  14    shows a schematic diagram of a neural network that includes a non-volatile synapse array according to embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following description, for the purposes of explanation, specific details are set forth in order to provide an understanding of the disclosure. It will be apparent, however, to one skilled in the art that the disclosure can be practiced without these details. One skilled in the art will recognize that embodiments of the present disclosure, described below, may be performed in a variety of ways and using a variety of means. Those skilled in the art will also recognize additional modifications, applications, and embodiments are within the scope thereof, as are additional fields in which the disclosure may provide utility. Accordingly, the embodiments described below are illustrative of specific embodiments of the disclosure and are meant to avoid obscuring the disclosure. 
     A reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, characteristic, or function described in connection with the embodiment is included in at least one embodiment of the disclosure. The appearance of the phrase “in one embodiment,” “in an embodiment,” or the like in various places in the specification are not necessarily all referring to the same embodiment. 
       FIG.  1    shows a schematic diagram of a neural network  100  according to embodiments of the present disclosure (like reference numerals denote like elements throughout the specification). As depicted, the neural network  100  may include five neuron array layers (or shortly, neuron layers)  110 ,  130 ,  150 ,  170  and  190 , and synapse array layers (or shortly, synapse layers)  120 ,  140 ,  160  and  180 . Each of the neuron layers (e.g.,  110 ) may include a suitable number of neurons. In  FIG.  1   , only five neuron layers and four synapse layers are shown. However, it should be apparent to those of ordinary skill in the art that the neural network  100  may include other suitable numbers of neuron layers and a synapse layer may be disposed between two adjacent neuron layers. 
     It is noted that each neuron (e.g.,  112   a ) in a neuron layer (e.g.,  110 ) may be connected to one or more of the neurons (e.g.,  132   a - 132   m ) in the next neuron array layer (e.g.,  130 ) through m synapses in a synapse layer (e.g.,  120 ). For instance, if each of the neuron in the neuron layer  110  is electrically coupled to all the neurons in the neuron layer  130 , synapse layer  120  may include n×m synapses. In embodiments, each synapse may have a trainable weight parameter (w) that describes the connection strength between two neurons. 
     In embodiments, the relationship between input neuron signals (Ain) and output neuron signals (Aout) may be described by an activation function with the following equation: 
                   Aout   =       f   ⁡   (       W   ×   Ain     +   Bias     )     .             (   1   )               
where, Ain and Aout are matrices representing input signals to a synapse layer and output signals from the synapse layer, respectively, W is a matrix representing the weights of synapse layer, and Bias is a matrix representing the bias signals for Aout. In embodiments, W and Bias may be trainable parameters and stored in a logic friendly non-volatile memory (NVM). For instance, a training/machine leaning process may be used with known data to determine W and Bias. In embodiments, the function f may be a non-linear function, such as sigmoid, tan h, ReLU, leaky ReLU, etc. In embodiments, Aout may be activated when (W×Ain+Bias) is greater than a certain threshold.
 
     By way of example, the relationship described in equation (1) may be illustrated for neuron layer  110  having two neurons, synapse layer  120 , and neuron layer  130  having three neurons. In this example, Ain representing output signals from the neuron array layer  110  may be expressed as a matrix of 2 rows by 1 column; Aout representing output signals from the synapse layer  120  may be expressed as a matrix of 3 rows by 1 column; W representing the weights of the synapse layer  120  may be expressed as a matrix of 3 rows by 2 columns, having six weight values; and Bias representing bias values added to the neuron layer  130  may be expressed as a 3 rows by 1 column matrix. A non-linear function f applied to each element of (W×Ain+Bias) in equation (1) may determine the final values of each element of Aout. By way of another example, the neuron array layer  110  may receive input signals from sensors and the neuron array layer  190  may represent response signals. 
     In embodiments, there may be numerous neurons and synapses in the neural network  100 , and matrix multiplication and summation in equation (1) may be a process that may consume a large amount of computing resources. In conventional processing-in-memory computing approaches, a computing device performs the matrix multiplication within an NVM cell array using analog electrical values rather than using the digital logic and arithmetic components. These conventional designs aim to reduce the computational load and reduce power requirements by reducing the communication between CMOS logic and NVM components. These conventional approaches, however, are prone to have large variations on current input signals to each synapse because of large parasitic resistance on the current input signal path in a large scale NVM cell array. Also, sneak currents through half-selected cells in a large array change the programmed resistance values, resulting in unwanted program disturbance and degradation of neural network computation accuracy. 
     Unlike the conventional approaches, in embodiments, a power efficient neural network may be based on logic friendly non-volatile synapses with a differential architecture, where the differential architecture may include a select transistor and a logic friendly NVM. In embodiments, a fully differential synapse architecture may widen the operational range of the synapse circuit as a multiplier. Compared to conventional architectures, in embodiments, the slight multiplication error may be beneficial for compensating certain levels of quantization noise of the trained weight parameters. 
     As discussed below in detail, in embodiments, input signal to each synapse in the synapse layers  120 ,  140 ,  160 , and  180  may be directed to the gate terminal of the select transistor of the synapse, suppressing multiplication noise. In embodiments, the multiplier current may be approximately the gate terminal voltage times the resistance level of variable resistor or NVM. 
       FIG.  2    shows a schematic diagram of an array of synapses  200  according to embodiments of the present disclosure. As depicted, the array of synapses  200  may include: non-volatile synapses  210  arranged into rows and columns; positive output current lines (Bit Lines)  266  that are electrically coupled to column selection transistors  263 , respectively; negative output current lines (Bit Line Bar lines)  267  that are electrically coupled to column selection transistors  268 , respectively. In embodiments, the drain terminals of the column selection transistors  263  may be electrically coupled to the positive current port  241  of sensing circuit  250 , and the drain terminals of the column selection transistors  268  may be electrically coupled to the negative current port  242  of the sensing circuit  250 . 
     In embodiments, each non-volatile synapse  210  may store one positive weight value and one negative weight value. In embodiments, each non-volatile synapse  210  may be electrically coupled to: a signal line (or, equivalently reference signal line) (e.g., SL 1 )  264  to receive a reference voltage input  201 ; a word line (or, equivalently, input signal line) (e.g., WL 1 )  265  to receive a signal voltage input  202 ; a positive output line (e.g., BL 1 )  266  to output a positive current output  203 ; and a negative output line (e.g., BLB 1 )  267  to output a negative current output  204 . 
     In embodiments, each of the signal voltage input  202  and reference voltage input  201  may be associated with both the positive and the negative weight values, respectively, and the positive current output  203  may be associated with the positive weight value, and the negative current output  204  may be associated with the negative weight value. 
     In embodiments, the positive (or negative) weight value that is stored in each non-volatile synapse  210  may be represented as a reciprocal of variable resistance value, and the signal voltage input  202  and the reference voltage input values  201  may be electrical voltage values. In embodiments, the value of the positive current output  203  may be the result of a multiplication of the positive weight value times the signal voltage input  202 , and the value of the negative current output  204  may be the result of a multiplication of the negative weight value times the signal voltage input  202 . 
     As depicted in  FIG.  2   , each row of the non-volatile synapses array  200  may share a reference voltage line, SL,  264  and a signal voltage line, WL,  265 , where each SL may provide reference voltage inputs  201  to the non-volatile synapses in the corresponding row, and each WL may provide signal voltage inputs  202  to the non-volatile synapses in the corresponding row, such that the non-volatile synapses in a row may receive substantially the same signal voltage input and the same reference voltage input. 
     As discussed above, each column of the non-volatile synapses array  200  may share a positive output current line (BL)  266  and a negative output current line (BL-Bar)  267 , i.e., each positive current output  203  of the synapses of the column may be collected by a corresponding BL  266  and each negative current output  204  of the synapses of the column may be collected by a corresponding BL-bar lines  267 . As such, the electrical current on the BL line  266  may be the summation of the positive electrical output currents  203  from the synapses of the column. Similarly, in embodiments, the electrical current value on the BL-bar lines  267  may be the summation of the negative electrical output currents  204  from the synapses of the column. 
     In embodiments, each positive output current line (BL)  266  may be electrically coupled to the source terminal of a corresponding column selection transistor  263 , and each negative output current line (BL-Bar)  267  may be electrically coupled to the source terminal of a corresponding column selection transistor  268 . In embodiments, the column selection transistors of a pair of BL and BL-Bar lines  263  and  268  may receive the same column selection signal at the gate terminals from an external column selection circuit (not shown in  FIG.  2   ). In embodiments, the lines from the drain terminals of the column selection transistors  263  may be electrically coupled to the positive current input  241  of the sensing circuit  250 . In embodiments, the lines from the drain terminals of the column selection transistors  268  may be electrically coupled to the negative current input  242 . 
     In embodiments, the electrical current value (IBL)  261  of the positive current port  241  may be the value on the positive output current BL  266  that receives a column selection signal on its respective column selection transistor  263 . Likewise, the electrical current value (IBL-bar)  262  of the negative current input  242  may be the negative output current line BL-Bar  267  that receives a column selection signal on its respective column selection transistor  268 . 
     In embodiments, one or more of the rows of the synapses  210  may have a fixed input signal voltage on the WLs  265  and the synapses on such rows may store bias values for their columns. In embodiments, the array of synapses may implement the matrix multiplication in equation (1) 
               W   ×   Ain     +   Bias         
where, W may be the synapse array, and Ain the matrix representing the WL inputs.
 
     In embodiments, each non-volatile synapse  210  may have two circuits (or equivalently cells) that store negative and positive weights. In embodiments, as discussed above, the weight values may be represented by the reciprocal value of a variable resistance, 1/Rn=W_neg, and 1/Rp=W_pos, respectively. Each row of synapses in the array  200  may receive an input signal as an electrical voltage, Ain. In response to the input signal, each synapse in the array  200  may produce a positive output current through BL (e.g., BL 0   266 ) and a negative output current through BLB (e.g.,  267 ), where the value of the positive output current BLc may be expressed as: BLc=Ain×W_pos and the negative output current BLBc may be expressed as: BLBc=Ain×W_neg. 
     In embodiments, the weight values, W, for each synapse layer of the neural network  100  may be determined (calculated and adjusted) in a separate training phase. Then, input signals, Ain, may be applied to the neural network  100  during the inference phase, where the pre-determined weights may be used to produce output values. In embodiments, the weight values that may be determined during the training phase may not change during the inference stage. 
     In embodiments, as discussed above, a BL (e.g., BL 1 ) may be electrically coupled to all of the output lines of the synapses in a column of the synapse array  200 , and the BL-bar line (e.g., BLB 1 ) may be electrically coupled to all of the output lines of the synapses of the synapse array  200 . Such configuration may make the current value on each BL  266  (or BLB  267 ) be the summation of the individually calculated current values of the corresponding column of synapses in the array  200 . In embodiments, the output current on a line, BLn, and a line, BLBn, may be expressed as: 
     
       
         
           
             
               
                 
                   
                     BLn 
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     In embodiments, one or more of the rows of the array  200  may have a fixed input signal voltage and the synapses on such rows may store bias values for their columns. In such a case, the total electric current on BLn and BLBn may be expressed as: 
     
       
         
           
             
               
                 
                   BLn 
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     In embodiments, in the sensing circuit  250 , the current input signal (I sig =IBL  261  or IBLB  262 ) from the synapse array may be converted to a voltage signal (V sig ) using a Capacitive Trans Impedance Amplifier (CTIA) and further processed to produce a digital signal using an Analog Digital Converter (ADC). In embodiments, the ADC may have a single-slope column ADC architecture using an offset canceling column comparator and a counter. Such design may use minimal area and power dissipation compared to other ADC architectures, such as pipelined or successive approximation ADCs. 
     In embodiments, each synapse layer (e.g.,  120 ) in the neural network  100  may have electrical components (not shown in  FIG.  2   ) that may be electrically coupled to BL  266  and BLB  267  and electrically process the output currents on the BL and BLB lines. For instance, the electrical components may provide differential sensing, convert the output current signals to voltage signals, further convert to digital signals and summate the digital signals in an accumulator. In another example, the electrical components may perform other various processing operations, such as normalization and activation, to the accumulated value, to thereby implement the activation function for Aout of equation (1). In embodiments, the final Aout may be stored in a data buffer and used to generate the input signals for the next neural array layer in the neural network  100 . 
     It is noted that, in embodiments, separate circuits (not shown in  FIG.  2   ) may be included in the neural network  100  to perform auxiliary functions such as: (1) a router/controller that maps the logical neuron-synapse structure of the neural network  100  to the physical address mapping of the synapse array  200 , (2) a driving circuit that drives the input signals to the appropriate rows of synapses of a configuration, (3) a selection circuit that provides column selection for the sensing circuits that are shared by more than one column of synapses, (4) a voltage generator that generates reference voltages used to select synapses, and (5) a storage that stores the configurations for the router controller and sensing circuits  250 . 
       FIG.  3    shows a schematic diagram of a synapse  300  according to embodiments of the present disclosure. In embodiments, the synapse  300  may be used as the synapse  210  in  FIG.  2   . As depicted, the synapse  300  may include: a pair of input transistors  311  and  312 ; and a pair of non-volatile resistive changing elements, R_p  313  and R_n  314  (hereinafter, the term “non-volatile resistive changing element” and “resistor” are used interchangeably). Stated differently, the synapse  300  may have a pair of 1T-1R (one-transistor one-resistor) structure. In embodiments, the resistors R_p  313  and R_n  314  may be logic friendly non-volatile resistive changing elements. In embodiments, the synapse  300  may be considered to have two cells  332  and  334 , where each cell may have one input transistor  311  (or  312 ) and a resistor R_p  312  (or R_n  314 ). 
     In embodiments, the logic friendly non-volatile resistive changing element, R_p  313  (or R_n  314 ) may be associated with the positive (or negative) weight parameter that the synapse  300  may remember/store. In embodiments, each resistor may be electrically coupled to the source terminal of the input transistor (e.g.,  311 ) and the reference signal line  264  may apply a reference signal to the resistor. In embodiments, the word line (WL)  265  may apply an input signal voltage to the gate terminal of the input transistor (e.g.,  311 ). 
     In embodiments, the resistance value R (=R_p or R_n) may be programmed into the resistive changing element in a training phase. When the synapse input signal is applied on WL  265 , the synapse output current may approximate the multiplication of the weight (represented by 1/R) by input value Ain from the previous neuron, where Ain may be represented by a voltage on WL  265 . 
     In embodiments, the neural network parameters that are stored in the synapse array  200  may have about similar number of positive and negative weight parameters. Unused resistive elements in the array  200  may be programmed to have a resistance value higher than a preset value. The electrical current through each unused resistive element should substantially be zero, so that the output current of the cell substantially does not add to the output current on the BL (or BLB) of the cell. Therefore, the effect of the unused resistive elements on the computation is minimized, and power consumption is reduced. Trained weight parameters may be quantized and programmed into the resistive changing elements without much accuracy degradation of neural network computation. When the resistance value, R, of the resistor R_p  313  (or R_n  314 ) is programmed in the training phase and a scaled synapse input signal WLs is applied through WL  265 , the synapse output current, IC, on BL  266  (or BLB  267 ) may be described by equations (4) and (5): 
                     dIC   /   dWL     =       ∼     gm   /     (     1   +     gm   *   R       )         =     ∼       1   /   R     ⁢           (     when   ⁢         R   ⁢         is   ⁢         greater   ⁢         enough   ⁢         than   ⁢         1   /   gm     )                   (   4   )               
where, gm is the conductance of the input transistor, and
 
                   IC   =       ∼     W   ⁢     L   /   R         =     ∼     w   ⁢         Ain   ⁢           (         where   ⁢         w     =     1   /   R       ,     Ain   =   WL                       (   5   )               
where w and Ain may produce their multiplication result IC approximately.
 
     As indicated in equation (5), the output current IC may approximate the multiplication of the input signal (input voltage Ain) times the weight (w). Unlike the conventional systems, this analog multiplication operation of equation (5), which occurs in the synapse  300 , does not require the use of complex digital logic gates, significantly reducing the complexity of synapse structure and usage of computational resources. 
     In embodiments, the input signal Ain may be an output signal from a previous neuron (as shown in  FIG.  1   ) and driven to the gate of the input transistor  311  (or  312 ). Driving the input signal Ain to the gate may minimize the noise generated by parasitic resistance in a large array of synapse since there is no static on-current into the gate of the select transistor. In contrast, in conventional systems, input signals are driven to the selector or resistive changing element of the synapse, which is prone to have large variations on current input signals to each synapse because of large parasitic resistance in a large array and static current flow during operation. 
     In conventional systems, when programming resistive changing elements, sneak currents through half-selected cells in a large array can change previously programmed resistance values, resulting in unwanted program disturbances. In contrast, in embodiments, the input transistor  311  (or  312 ) may be enabled for a program pulse to be driven only to the selected resistor  313  (or  314 ) in a large array. Therefore, in embodiments, unselected synapses may not disturb the programming of selected synapses, where selected synapses may be programmed by applying suitable bias conditions to the BL (or BLB) and SL nodes. 
     By way of an example and not limitation, the array of synapse  200  may be located in a synapse layer  120 , where the output signals from a previous neuron (e.g.,  112   a ) in the neuron array layer  110  may be input to a synapse  300  of the synapse array  200  and the output signals from BL  266  and BLB  267  of the synapse  300  may be input to one or more of the next neurons (e.g.,  132   a - 132   m ) in the neuron array layer  130 . 
     In embodiments, the resistor  313  (or  314 ) may be implemented with various circuits (or memories), such as non-volatile MRAM, RRAM, or PRAM or single-poly embedded flash memory, where the circuit may be programmed to remember (store) an associate parameter that may be represented by a reciprocal of resistance. It is noted that, in embodiments, the multiplication operation may be completed within the synapse with analog values, without the use of digital logic and arithmetic circuits. 
       FIG.  4    shows a schematic diagram of another synapse  400  according to embodiments of the present disclosure. In embodiments, the synapse  400  may show an exemplary implementation of the resistors  313  and  314  in  FIG.  3   . Stated differently, in embodiments, the resistor  313  may be implemented by the components in the box  452  in  FIG.  4   . 
     As depicted in  FIG.  4   , the synapse  400  includes a pair of a logic compatible embedded flash memory cells  432  and  434 , where the floating gate nodes, FG_p and FG_n, in the flash memory cells may be associated with the positive and negative weight parameters respectively that this synapse  400  remembers/stores. 
     In embodiments, the synapse input signal on WL  420  may be shared between the two branches that may draw differential synapse output currents (IBL and IBLB) on BL  406  and BLB  407 . In embodiments, the program word line (or, shortly program line, PWL)  418 , write word line (or, shortly write line, WWL)  416 , and erase word line (or, shortly erase line, EWL)  414  may be used to provide additional control signals for program, write and erase operations of the logic compatible embedded flash memory cells  432  and  434 . 
     In embodiments, the memory cells  432  and  434  may include logic transistors, obviating any additional process overhead beyond standard logic process. In embodiments, the coupling transistor  422  (and  423 ) directly connected to PWL  418  may be upsized for higher coupling of the floating gate nodes (FG_p and FG_n) to the control signal provided through PWL  418 . In embodiments, the coupling transistor  422  (or  423 ) directly coupled to PWL  418  may be relatively larger than the write transistor  424  (or  425 ). With high program voltages driven to PWL  418  and WWL  416 , the memory cell  432  (or  434 ) may be selected and programmed by injecting electrons into FG_p while applying 0 volt to BL  406  (or BLB  407 ), whereas the unselected cell  434  (or  432 ) may be program-inhibited by applying VDD to BLB  407  (or BL  406 ) and applying VDD to WL  420  to thereby turn off the select transistor of the unselected cell  434  (or  432 ). Hereinafter, the term select transistor refers to a transistor having a gate that is electrically coupled to the BL  406  or BLB  407 . 
     In embodiments, with high erase voltage driven only to WWL  416 , the selected WL may be erased by ejecting electrons from FG. Unselected WLs may not be driven to any higher voltage than VDD during program and erase operation; therefore, there is no disturbance in the unselected WLs. In embodiments, FG node voltage may be a function of signals on PWL  418 , WWL  416  and stored number of electrons in the FG node. Conductance of the read transistors (e.g.,  462 ) electrically coupled to the FG may be programmable by controlling voltages at PWL  418  and WWL  416  and the electrical charge stored at the FG node. 
     In embodiments, when the threshold voltage of the embedded flash cell  432  (or  434 ) is programmed, and when a scaled synapse input signal is provided through WL  420 , there may be a certain range of the threshold voltage such that the equation (5) may be approximately met where cell output currents (=IBL and IBLB) are proportional to the programmed weight parameter as well as the input signal. 
     In embodiments, neural network  100  may be robust to the random errors or small variation of weight parameters. In embodiments, when the pre-trained weight parameters, W, are quantized during computation of the neural network  100 , neural network performance or inference accuracy may be optimized with the slight multiplication error from equation (5) as long as the multiplication error is within a certain range. Furthermore, the slight multiplication error from the proposed approximate multiplier may compensate quantization noise of the trained weight parameters of the neural network  100 . Nevertheless, to avoid severe cell retention error caused by large cell threshold voltage shift after repetitive training of the neural network, an intentional self-healing current may be applied through WWL  416 , as the intentional self-healing current may cure the damaged gate oxide of the device electrically coupled to WWL  416  of embedded flash memory cells  432  and  434 . In embodiments, applying the self-healing current may not be required with every training or inference, and therefore has minimal effect on performance or power consumption. 
     In embodiments, each cell (e.g.,  432 ) may include coupling transistor  422 , write transistor  424  and upper (or first) select transistor  460 , read transistor  462 , and lower select transistor  464 . It is noted that the single-poly embedded flash memory in the synapse  400  may be used as the resistive changing element, and the conductance of the read transistors (e.g.,  462 ) that are electrically coupled to the floating gate (FG) of the flash, may serve as the resistive changing element. In embodiments, the conductance of the read transistors (e.g.,  462 ) may be determined by the threshold voltage VTH of their respective FG nodes, FG_p or FG_n. The VTH of the FG nodes FG_p or FG_n may be first coarsely programmed using a balanced step pulse programming method, then subsequent constant pulse programming steps with reduced voltages can fine tune the VTH value to accurately program the weight value to be stored in the synapse  400 . The programming steps are described in conjunction with  FIGS.  10 A- 10 B . 
       FIG.  5    shows a schematic diagram of a synapse  500  according to embodiments of the present disclosure. In embodiments, the synapse  500  may be used as the synapse  210  in  FIG.  2   . As depicted, the synapse  500  may have three pairs of IT-IRs, where the three word lines, WLa, WLb, and WLc, may be electrically coupled to the gates of the six transistors. It is noted that the synapse  500  may have other suitable number of input transistors and resistors as well as word lines that are electrically coupled to the input transistors. For instance, in embodiments, the synapse  500  may be modified so that the word line WLa and the components in the 1T-1R units  550  and  551  may be deleted, i.e., each cell may have two pairs of 1T-1Rs. In another example, in embodiments, the synapse  500  may be modifies so that each cell may have four pairs of 1T-1Rs and four word lines (input signal lines) WLs. 
     In embodiments, the SL, BL and BLB of the synapse  500  may have similar functions as the SL, BL and BLB in the synapse  300  of the synapse  300 . The difference between the synapse  300  and synapse  500  is that the synapse  500  may receive input signals from the previous neuron through the three word lines, WLa, WLb and WLc. More specifically, the signal from each WL may be driven to a gate terminal of a corresponding input transistor. 
     It is noted that each synapse  500  may be electrically coupled to three word lines WLa, WLb and WLc, while each synapse  210  in  FIG.  2    is shown to be coupled to one word line  265 . Thus, it is noted that each word line  265  in  FIG.  2    collectively refers to one or more word lines that are electrically coupled to a synapse that includes one or more input transistors. 
     In embodiment, the synapse  500  may be considered to have two cells  532  and  534 , where each cell may have three pairs of 1T-1R (one transistor-one resistor and each 1T-1R pair may be electrically coupled to WL and SL. 
     It is noted that each resistor in the synapse  500  may be implemented by various circuits (or memories), such as non-volatile MRAM, RRAM, or PRAM or single-poly embedded flash memory, where the circuit may be programmed to remember (store) an associated parameter that may be represented by a resistance. In embodiments, each resistor in the synapse  500  may be implemented by the components in the box  452  in  FIG.  4   , where each synapse  500  may be electrically connected to PWL, WWL and EWL in the manner similar to the synapse  400 . 
       FIG.  6    shows a schematic diagram of another synapse  600  according to embodiments of the present disclosure. In embodiments, the synapse  600  may be used as the synapse  210  in  FIG.  2   . As depicted, each of the cells  632  and  634  may include two transistors (e.g.,  602  and  606 ) and one resistor (e.g.,  613 ) and electrically coupled to two input signal (or word) lines, word line (WL) and word line bar (WLB), and one reference signal line, SL. It is noted that each synapse  600  may be electrically coupled to the two word lines, while each synapse  210  in  FIG.  2    is shown to be coupled to one word line  265 . Thus, as discussed above, each word line  265  in  FIG.  2    collectively refers to one or more word lines that are electrically coupled to a synapse that includes one or more input transistors. 
     In embodiments, the synapse resistors R_p  613  and R_n  614 , the reference signal line SL, output current lines BL and BLB may have similar functions as the corresponding components of the synapse  230  in  FIG.  3   . For instance, the input selection transistors  602  and  604 , which are electrically coupled to WL and the respective resistors R_p  613  and R_n  614 , may correspond to input selection transistors  211  and  212  respectively. 
     Compared with the synapse  300  in  FIG.  3   , the synapse  600  may be electrically coupled to another input signal line, WLB, where WLB may provide a differential input signal voltage relative to WL. In embodiments, additional input selection transistors  606  and  608  may be electrically coupled to WLB through their gate terminals. In embodiments, the source terminals of input selection transistors  606  and  608  may be electrically coupled to the resistors R_p  613  and R_n  614  respectively. In embodiments, the drain terminal of the transistor  602  may be electrically coupled to BL and the drain terminal of the transistor  606  may be electrically coupled to BLB. Likewise, the drain terminals of the transistor  604  may be electrically coupled to BLB and the drain terminal of the transistor  608  may be electrically coupled to BL. 
     In embodiments, the synapse  600  may receive differential input signals, where WL provides a positive input signal voltage (to the common mode reference), a_pos, and WLB provides a negative input signal voltage (to the common mode reference), a_neg. In embodiments, R_p  613  may store a positive weight w_pos and R_n  614  may store a negative weight w_neg. Thus, in embodiments, the output signal currents (BLo) on BL may be the sum of two output signals from the two cells  532  and  534 : 
     
       
         
           
             
               
                 
                   BLo 
                   = 
                   
                     
                       a_pos 
                           
                       × 
                       w_pos 
                     
                     + 
                     
                       a_neg 
                       × 
                       w_neg 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Likewise, the output signal current (BLBo) on BLB may be the sum of two output signals from the two cells  532  and  534 : 
     
       
         
           
             
               
                 
                   BLBo 
                   = 
                   
                     
                       a_pos 
                       × 
                       w_neg 
                     
                     + 
                     
                       a_neg 
                       × 
                       
                         w_pos 
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Thus, some embodiments with differential signaling on WL and WLB as depicted, may have a greater range of output currents on BL and BLB compared to the other embodiments with single-ended signaling on the WL of synapse  300  depicted in  FIG.  3   . In addition, embodiments with differential input signaling as depicted may suppress transistor offset noise as well as common mode noise from variations in supply voltage or temperature. 
     It is noted that each resistor in the synapse  600  may be implemented by various circuits (or memories), such as non-volatile MRAM, RRAM, or PRAM or single-poly embedded flash memory, where the circuit may be programmed to remember (store) an associated parameter.  FIG.  7    shows a schematic diagram of another synapse  700  according to embodiments of the present disclosure. In embodiments, the synapse  700  may show an exemplary implementation of the resistors  613  and  614  in  FIG.  6   . Stated differently, the components in the box  752  may correspond to the resistor  613  in  FIG.  6   . 
     As depicted in  FIG.  7   , the synapse  700  may include two cells  732  and  734 . In embodiments, the cell  732  (or  734 ) may be similar to the cell  432  (or  434 ) of the synapse  400 , with the difference that the cell  732  (or  734 ) may include an additional upper select transistor  720  (or  722 ) and an additional input signal line WLB. In embodiments, the gate of the transistor  720  (or  722 ) may be electrically coupled to the input signal line WLB and the drain of the transistor  720  (or  722 ) may be electrically coupled to the output signal line BLB. 
       FIG.  8    shows a schematic diagram of another synapse  800  according to embodiments of the present disclosure. In embodiments, the synapse  800  may be used as the synapse  210  in  FIG.  2   . As depicted, the synapse  800  may include two cells  832  and  834 , where each cell may include three resistors and six transistors. The synapse  800  may have the 2T-1R structure, i.e., each cell may include three sets of 2T-1R unit  802 . The synapse  800  may be electrically coupled to six input signal lines: three word lines, WLa, WLb, and WLc; and three word Line Bars, WLaB, WLbB, and WLcB. It is noted that each cell of the synapse  800  may include other suitable number of 2T-1R units  802 . In embodiments, each pair of WL and WLB (e.g., WLa and WLaB) may provide differential input signals to the cells  832  and  834 . 
     In embodiments, the reference signal lines, SL, may provide a reference signal to the cells  832  and  834 . In embodiments, each of the output signal lines, BL and BLB, may collect the output signals from the drain terminals of three transistors in the cell  832  and the drain terminals of three transistors in the cell  834 . In embodiments, the synapse  800  may receive differential input signals, where each WLi provides a positive input signal voltage, a_pos_i, and each WLBj provides a negative input signal voltage, a_neg_j. In embodiments, each R_p may store a positive weight w_pos_i and each R_n may store a negative weight w_neg_j. In embodiments, the output signal currents (BLo) on BL may be the sum of six output signals from the two cells  832  and  834 : 
                   BLo   =       ∑     (     a_pos   ⁢   _i         ×         w_neg   ⁢   _i     )       +     ∑     (     a_neg   ⁢   _j         ×         w_pos   ⁢   _i     )                 (   8   )               
Likewise, the output signal current (BLBo) on BLB may be the sum of six output signals from the two cells  832  and  834 :
 
     
       
         
           
             
               
                 
                   BLBo 
                   = 
                   
                     ∑ 
                     
                       ( 
                       
                         
                           a_pos 
                           ⁢ 
                           _i 
                               
                           × 
                               
                           w_neg 
                           ⁢ 
                           _j 
                         
                         + 
                         
                           ∑ 
                           
                             
                               ( 
                               
                                 a_neg 
                                 ⁢ 
                                 _j 
                                     
                                 × 
                                     
                                 w_pos 
                                 ⁢ 
                                 _i 
                               
                               ) 
                             
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     It is noted that each resistor in the synapse  800  may be implemented by various circuits (or memories), such as non-volatile MRAM, RRAM, or PRAM or single-poly embedded flash memory, where the circuit may be programmed to remember (store) an associated parameter. In embodiments, each resistor in the synapse  800  may be implemented by the components in the box  752  in  FIG.  7   , where each synapse  800  may be electrically connected to PWL, WWL and EWL in the manner similar to the synapse  700 . 
     In general, the conductance of a read transistor (e.g.,  462 ) may be changed by injecting electrons into the floating gate.  FIG.  9 A- 9 B  show a comparison of two conventional methods for programming the threshold voltage (VTH) of a floating gate node (column  910  and  914 ) to the method according to the embodiments (column  912 ).  FIG.  9 A  shows a table  900  that includes the voltage heights and widths of signals applied to the terminals PWL and WWL during program operation of the floating gate cell ( 432 ), thus injecting electrons into the floating gate. As depicted, the table  900  includes three columns  910 ,  912  and  914  that correspond to three approaches for applying voltage signals, respectively. 
     The column  910  shows a conventional incremental step pulse programming method where each subsequent program step increases program voltage from the previous step by an amount delta with a constant pulse width (T_pulse). The column  912  shows a balanced step pulse programming method according to the embodiments where the first step has a longer programming pulse width by certain design parameter (m) compared to the programming method in column  910 . The column  914  shows a conventional constant pulse programming method where every step has the same program voltage and program pulse width. 
       FIG.  9 B  shows the plots of VTH  950  of the floating gate cell ( 432  or  434 ) according to the three methods in  FIG.  9 A . In  FIG.  9 B , the three plots  960 ,  962 , and  964  correspond to the three methods  910 ,  912 , and  914 , respectively, and each plot in  FIG.  9 B  shows the VTH of the floating gate cell ( 432  or  434 ) after each step of the corresponding method in  FIG.  9 A . 
     Based on the plots  950 , the balanced step pulse programming method according to embodiments of the present disclosure may be preferred among these three methods. Each step increases the VTH by approximately the same amount, delta, thus the VTH may be programmed accurately, resulting in a narrower VTH variation than the other methods. 
       FIG.  10 A- 10 B  show another method for programming the threshold voltage (VTH) of a floating gate cell ( 432  or  434 ) according to embodiments of the present disclosure.  FIG.  10 A  shows a table  1000  that includes the voltage heights and widths of signals applied to the terminals PWL and WWL during program operation of the floating gate cell ( 432  or  434 ), thus injecting electrons into the floating gate.  FIG.  10 B  shows a plot  1050  of the VTH stored in the floating gate cell ( 432  or  434 ) at each step in  FIG.  10 B . 
     As depicted, for several initial steps (here, up to step  4 ), the balanced step pulse programming method (also mentioned in conjunction with  FIGS.  9 A and  9 B ) may be used to coarsely program the cell VTH to a value that does not exceed the target VTH. In some embodiments, the target VTH may be achieved up to these initial steps (up to steps  4 ) with acceptable margin. In some other embodiments, more precise programming to the target VTH may be necessary. In these embodiments, the difference between the current VTH and target VTH may be less than the available increasement of the VTH at each step (delta in  FIG.  10 B ). Then, subsequent constant pulse programming steps are applied further to accurately program the VTH. 
     In embodiments, the subsequent constant pulse programming steps use a reduced programming pulse height (by alpha in  FIG.  10 A ) but an increased pulse width (T_pulse*n, n is not less than 1.0), to set the VTH at the target. As a result, the programming scheme in  FIGS.  10 A- 10 B  can control the final programmed cell threshold voltage below available voltage step (=delta) generated from on-chip voltage references from the target VTH. 
       FIG.  11    shows a flow chart  1100  of an illustrative process for programming threshold voltage (VTH) of a floating gate node according to embodiments of the present disclosure. At step  1102 , a voltage pulse (e.g., step  1  in  FIG.  10 A ) having a first height (e.g., VPGM) and the first width (T_pulse*m, m is not less than 1.0) may be applied to the PWL and WWL terminals of a floating gate cell ( 432  or  434 ), thus injecting electrons into the floating gate. At step  1104 , a first sequence of voltage pulses (such as steps  2 - 4  in  FIG.  10 A ) may be applied to the PWL and WWL terminals while increasing the height of each pulse from the previous pulse by a preset value (e.g., delta). 
     At step  1106 , it may be determined whether the target VTH was reached after applying the first sequence of pulses. If the answer to the determination is positive, the process proceeds to step  1108 . At step  1108 , the process stops. Otherwise, at step  1110 , a second sequence of voltage pulses (such as steps  5 - 19  in  FIG.  10 A ) may be applied to the PWL and WWL terminals. In embodiments, each pulse of the second sequence of pulses may have a width (T_pulse*n, n is not less than 1.0) that is not narrower than the pulse in the previous steps (T_pulse). In embodiments, the second sequence of pulses have a height that is lower than the first height (VPGM−alpha), and the second sequence of pulses have a width (T_pulse*n) that is not narrower than the second width (T_pulse). In embodiments, by way of example, the values may be m=9.0, n=5.0, alpha=0.8V, delta=0.1V, and VPGM=7.2V. 
     It is noted that the methods for programming VTH of the floating gate node in  FIGS.  9 A- 11    may be applied to the cells  732  and  734 . More specifically, the method associated with column  912  in  FIG.  9 A  and/or the method described in conjunction with  FIGS.  10 A- 10 B  may be used to program VTH of the cells  732  and  734 . 
     Each synapse in  FIGS.  3 - 8    may generate two output signals through two output signal lines BL and BLB, where the differential signaling technique may be applied to generate the two output signals. The differential signaling may reduce the sensitivity to transistor offsets and common mode noise from supply voltage and temperature variations that can introduce serious errors to the output current in prior art designs of synapses or devices for weighted sum computations. 
       FIG.  12 A- 12 C  illustrates differential signaling according to embodiments of the present disclosure. As depicted in  FIG.  12 A , the I BL  line  1212  and I BL-Bar  line  1214  may be the output currents through the output signal lines BL (e.g.,  106 ) and BLB (e.g.,  107 ) of a synapse, respectively. By way of example, each output current may range from a minimum of 0.5 (A.U.) to a maximum of 1.5 (A.U.), depending on the resistance values of R_p and R_n. In the embodiments, I BL  line  1212  may be a sum of a first current signal  1224  and an offset current signal  1220 , while the I BL  line  1214  may be a sum of the offset current  1220  and the second current signal  1226 . As depicted, the offset current  1220  may include transistor offsets and common mode noise. 
     As depicted in  FIG.  12 B , by applying the differential signaling technique on the two output signal lines  1212  and  1214 , the offset current  1220  may be canceled, and the values of output current signals  1224  and  1226  may be obtained. By way of example, the output current signals  1224  and  1226  may range from 0.0 (A.U.) to 1.0 (A.U.). 
     Furthermore, in embodiments, the first current signal  1224  may have an opposite polarity to the second current signal  1226 . By using differential signaling on the two output currents, as depicted in  FIG.  12 C , the difference between the two signals, I BL −I BL-Bar    1216 , may range from the minimum of −1.0 to a maximum of +1.0, i.e., the range of the combined signal may be twice as large as the range of a single output. 
       FIG.  13    shows a schematic diagram of a chip  1300  that includes a neural network according to embodiments of the present disclosure. As depicted, the chip  1300  may have a system-on-chip structure and include: non-volatile neural network  1316 ; a CPU  1312  for controlling the elements on the chip  1300 ; a sensor  1314  for providing input signals to the non-volatile neural network  1316 ; and a memory  1318 . In embodiments, the neural network  1316  may be similar to the neural network  100  in  FIG.  1   . In embodiments, the chip  1300  may be a silicon chip and the components  1312 - 1318  may be integrated on the chip  1300 . 
       FIG.  14    shows a schematic diagram of a system  1400  for operating a non-volatile synapse array according to embodiments of the present disclosure. As depicted, the system  1400  may include: a non-volatile synapse array  1410 ; a reference generator  1402 ; a configuration storage  1404 ; a row driver  1406  for selecting a row of synapses among the non-volatile synapse array  1410 ; a router/controller  1408 ; a column selector  1412  for selecting a column of synapses among the non-volatile synapse array  1410 ; a sensing circuit  1414 ; an accumulator  1416  for collecting output values from the non-volatile synapse array  1410 ; normalization/activation/pooling function block  1418 ; and a data buffer  1420  for buffering data from the non-volatile synapse array  1410 . In embodiments, the non-volatile synapse array  1410  may be similar to the non-volatile synapse array  200 , and the sensing circuit  1414  may be similar to the sensing circuit  250  in  FIG.  2   . 
     The reference generator  1402  provides the voltage levels required by reference signals (e.g., SL in  FIGS.  2 - 8   ) and input signal lines (e.g., WL in  FIGS.  2 - 8   ) used by the row driver  1406 . The configuration storage  1404  stores data for a finite state machine used by router/controller  1408 , the physical mapping of weight parameters to synapse location within synapse array  200 , as well as other configuration parameters for sensing circuits. In the embodiments, the configuration storage may be implemented as an on-chip non-volatile memory. The router/controller  1408  implements a finite state machine to control the row selection sequences by the row driver  1406 . Sensing circuits  1414  include voltage regulators and analog-digital converters to convert the output current signals from the selected columns into voltage signals and further into digital values. The result from a sensing circuit is summated in an accumulator  1416 . Normalization/activation/pooling function blocks  1418  perform required signal processing operation on the accumulator value. Multiple dedicated DSPs or embedded CPU cores can be included to perform such numerical operations in parallel. 
     While the invention is susceptible to various modifications and alternative forms, specific examples thereof have been shown in the drawings and are herein described in detail. It should be understood, however, that the invention is not to be limited to the particular forms disclosed, but to the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the scope of the appended claims.