Patent Publication Number: US-11646075-B2

Title: Neural network classifier using array of three-gate non-volatile memory cells

Description:
RELATED APPLICATIONS 
     This application is a divisional of U.S. application Ser. No. 16/382,045, filed on Apr. 11, 2019, which claims the benefit of U.S. Provisional Application Nos. 62/794,492, filed Jan. 18, 2019 and 62/798,417, filed Jan. 29, 2019. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to neural networks. 
     BACKGROUND OF THE INVENTION 
     Artificial neural networks mimic biological neural networks (the central nervous systems of animals, in particular the brain) which are used to estimate or approximate functions that can depend on a large number of inputs and are generally known. Artificial neural networks generally include layers of interconnected “neurons” which exchange messages between each other.  FIG.  1    illustrates an artificial neural network, where the circles represent the inputs or layers of neurons. The connections (called synapses) are represented by arrows, and have numeric weights that can be tuned based on experience. This makes neural nets adaptive to inputs and capable of learning. Typically, neural networks include a layer of multiple inputs. There are typically one or more intermediate layers of neurons, and an output layer of neurons that provide the output of the neural network. The neurons at each level individually or collectively make a decision based on the received data from the synapses. 
     One of the major challenges in the development of artificial neural networks for high-performance information processing is a lack of adequate hardware technology. Indeed, practical neural networks rely on a very large number of synapses, enabling high connectivity between neurons, i.e. a very high computational parallelism. In principle, such complexity can be achieved with digital supercomputers or specialized graphics processing unit clusters. However, in addition to high cost, these approaches also suffer from mediocre energy efficiency as compared to biological networks, which consume much less energy primarily because they perform low-precision analog computation. CMOS analog circuits have been used for artificial neural networks, but most CMOS-implemented synapses have been too bulky given the high number of neurons and synapses. 
     BRIEF SUMMARY OF THE INVENTION 
     The aforementioned problems and needs are addressed by a neural network device that includes a first plurality of synapses configured to receive a first plurality of inputs and to generate therefrom a first plurality of outputs. The first plurality of synapses includes a plurality of memory cells, wherein each of the memory cells includes spaced apart source and drain regions formed in a semiconductor substrate with a channel region extending there between, a floating gate disposed over and insulated from a first portion of the channel region, a first gate disposed over and insulated from a second portion of the channel region, and a second gate disposed over and insulated from the floating gate or disposed over and insulated from the source region. Each of the plurality of memory cells is configured to store a weight value corresponding to a number of electrons on the floating gate. The plurality of memory cells are configured to generate the first plurality of outputs based upon the first plurality of inputs and the stored weight values. The memory cells of the first plurality of synapses are arranged in rows and columns. The first plurality of synapses includes a plurality of first lines each electrically connecting together the first gates in one of the rows of the memory cells, a plurality of second lines each electrically connecting together the second gates in one of the rows of the memory cells, a plurality of third lines each electrically connecting together the source regions in one of the rows of the memory cells, and a plurality of fourth lines each electrically connecting together the drain regions in one of the columns of the memory cells. The first plurality of synapses is configured to receive the first plurality of inputs as electrical voltages on the plurality of first lines or on the plurality of second lines or on the plurality of third lines, and to provide the first plurality of outputs as electrical currents on the plurality of fourth lines. 
     A neural network device can include a first plurality of synapses configured to receive a first plurality of inputs and to generate therefrom a first plurality of outputs. The first plurality of synapses includes a plurality of memory cells, wherein each of the memory cells includes spaced apart source and drain regions formed in a semiconductor substrate with a channel region extending there between, a floating gate disposed over and insulated from a first portion of the channel region, a first gate disposed over and insulated from a second portion of the channel region, and a second gate disposed over and insulated from the floating gate or disposed over and insulated from the source region. Each of the plurality of memory cells is configured to store a weight value corresponding to a number of electrons on the floating gate. The plurality of memory cells are configured to generate the first plurality of outputs based upon the first plurality of inputs and the stored weight values. The memory cells of the first plurality of synapses are arranged in rows and columns. The first plurality of synapses includes a plurality of first lines each electrically connecting together the first gates in one of the rows of the memory cells, a plurality of second lines each electrically connecting together the second gates in one of the rows of the memory cells, a plurality of third lines each electrically connecting together the source regions in one of the rows of the memory cells, and a plurality of fourth lines each electrically connecting together the drain regions in one of the columns of the memory cells. The first plurality of synapses is configured to receive the first plurality of inputs as electrical voltages on the plurality of fourth lines, and to provide the first plurality of outputs as electrical currents on the plurality of third lines. 
     A neural network device can include a first plurality of synapses configured to receive a first plurality of inputs and to generate therefrom a first plurality of outputs. The first plurality of synapses includes a plurality of memory cells, wherein each of the memory cells includes spaced apart source and drain regions formed in a semiconductor substrate with a channel region extending there between, a floating gate disposed over and insulated from a first portion of the channel region, a first gate disposed over and insulated from a second portion of the channel region, and a second gate disposed over and insulated from the floating gate or disposed over and insulated from the source region. Each of the plurality of memory cells is configured to store a weight value corresponding to a number of electrons on the floating gate. The plurality of memory cells are configured to generate the first plurality of outputs based upon the first plurality of inputs and the stored weight values. The memory cells of the first plurality of synapses are arranged in rows and columns, and wherein the first plurality of synapses includes a plurality of first lines each electrically connecting together the first gates in one of the rows of the memory cells, a plurality of second lines each electrically connecting together the second gates in one of the rows of the memory cells, a plurality of third lines each electrically connecting together the source regions in one of the rows of the memory cells, a plurality of fourth lines each electrically connecting together the drain regions in one of the columns of the memory cells, and a plurality of transistors each electrically connected in series with one of the fourth lines. The first plurality of synapses is configured to receive the first plurality of inputs as electrical voltages on gates of the plurality of transistors, and to provide the first plurality of outputs as electrical currents on the plurality of third lines. 
     A neural network device can include a first plurality of synapses configured to receive a first plurality of inputs and to generate therefrom a first plurality of outputs. The first plurality of synapses includes a plurality of memory cells, wherein each of the memory cells includes spaced apart source and drain regions formed in a semiconductor substrate with a channel region extending there between, a floating gate disposed over and insulated from a first portion of the channel region, a first gate disposed over and insulated from a second portion of the channel region, and a second gate disposed over and insulated from the floating gate or disposed over and insulated from the source region. Each of the plurality of memory cells is configured to store a weight value corresponding to a number of electrons on the floating gate. The plurality of memory cells are configured to generate the first plurality of outputs based upon the first plurality of inputs and the stored weight values. The memory cells of the first plurality of synapses are arranged in rows and columns, and wherein the first plurality of synapses includes a plurality of first lines each electrically connecting together the first gates in one of the rows of the memory cells, a plurality of second lines each electrically connecting together the second gates in one of the columns of the memory cells, a plurality of third lines each electrically connecting together the source regions in one of the rows of the memory cells, and a plurality of fourth lines each electrically connecting together the drain regions in one of the columns of the memory cells. The first plurality of synapses is configured to receive the first plurality of inputs as electrical voltages on the plurality of second lines or on the plurality of fourth lines, and to provide the first plurality of outputs as electrical currents on the plurality of third lines. 
     A neural network device can include a first plurality of synapses configured to receive a first plurality of inputs and to generate therefrom a first plurality of outputs. The first plurality of synapses includes a plurality of memory cells, wherein each of the memory cells includes spaced apart source and drain regions formed in a semiconductor substrate with a channel region extending there between, a floating gate disposed over and insulated from a first portion of the channel region, a first gate disposed over and insulated from a second portion of the channel region, and a second gate disposed over and insulated from the floating gate or disposed over and insulated from the source region. Each of the plurality of memory cells is configured to store a weight value corresponding to a number of electrons on the floating gate. The plurality of memory cells are configured to generate the first plurality of outputs based upon the first plurality of inputs and the stored weight values. The memory cells of the first plurality of synapses are arranged in rows and columns. The first plurality of synapses includes a plurality of first lines each electrically connecting together the first gates in one of the columns of the memory cells, a plurality of second lines each electrically connecting together the second gates in one of the rows of the memory cells, a plurality of third lines each electrically connecting together the source regions in one of the rows of the memory cells, and a plurality of fourth lines each electrically connecting together the drain regions in one of the columns of the memory cells. The first plurality of synapses is configured to receive the first plurality of inputs as electrical voltages on the plurality of first lines or on the plurality of fourth lines, and to provide the first plurality of outputs as electrical currents on the plurality of third lines. 
     Other objects and features of the present invention will become apparent by a review of the specification, claims and appended figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram that illustrates an artificial neural network. 
         FIG.  2    is a side cross sectional view of a conventional 2-gate non-volatile memory cell. 
         FIG.  3    is a diagram illustrating a conventional array architecture for the memory cell of  FIG.  2   . 
         FIG.  4    is a side cross sectional view of a conventional 2-gate non-volatile memory cell. 
         FIG.  5    is a diagram illustrating a conventional array architecture for the memory cell of  FIG.  4   . 
         FIG.  6    is a side cross sectional view of a conventional 4-gate non-volatile memory cell. 
         FIG.  7    is a diagram illustrating a conventional array architecture for the memory cell of  FIG.  6   . 
         FIG.  8 A  is a diagram illustrating neural network weight level assignments that are evenly spaced. 
         FIG.  8 B  is a diagram illustrating neural network weight level assignments that are unevenly spaced. 
         FIG.  9    is a flow diagram illustrating a bidirectional tuning algorithm. 
         FIG.  10    is a block diagram illustrating weight mapping using current comparison. 
         FIG.  11    is a block diagram illustrating weight mapping using voltage comparison. 
         FIG.  12    is a diagram illustrating the different levels of an exemplary neural network utilizing a non-volatile memory array. 
         FIG.  13    is a block diagram illustrating a vector multiplier matrix. 
         FIG.  14    is a block diagram illustrating various levels of a vector multiplier matrix. 
         FIG.  15    is a side cross sectional view of a 3-gate non-volatile memory cell. 
         FIG.  16    is a schematic diagram illustrating an architecture of an array of the three-gate memory cells of  FIG.  15    arranged as a source summing matrix multiplier. 
         FIG.  17    is a schematic diagram illustrating a current-to-voltage converter using three-gate memory cells. 
         FIGS.  18 - 29    are schematic diagrams illustrating architectures of arrays of the three-gate memory cell of  FIG.  15    arranged as a source or drain summing matrix multipliers. 
         FIG.  30    is a side cross sectional view of a 3-gate non-volatile memory cell. 
         FIGS.  31 - 39    are schematic diagrams illustrating architectures of arrays of the three-gate memory cell of  FIG.  30    arranged as a drain or source summing matrix multipliers. 
         FIG.  40    is a diagram illustrating a controller on the same chip as the memory array(s) for implementing the operation of the memory array(s). 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The artificial neural networks of the present invention utilize a combination of CMOS technology and non-volatile memory arrays. Digital non-volatile memories are well known. For example, U.S. Pat. No. 5,029,130 (“the &#39;130 patent”) discloses an array of split gate non-volatile memory cells, and is incorporated herein by reference for all purposes. The memory cell disclosed in the &#39;130 patent is shown in  FIG.  2    as memory cell  10 . Each memory cell  10  includes source and drain regions  14 / 16  formed in a semiconductor substrate  12 , with a channel region  18  there between. A floating gate  20  is formed over and insulated from (and controls the conductivity of) a first portion of the channel region  18 , and over a portion of the drain region  16 . A control gate  22  (i.e., a second, channel controlling gate) has a first portion  22   b  that is disposed over and insulated from (and controls the conductivity of) a second portion of the channel region  18 , and a second portion  22   c  that extends up and over the floating gate  20 . The floating gate  20  and control gate  22  are insulated from the substrate  12  by a gate oxide  26 . 
     The memory cell  10  is erased (where electrons are removed from the floating gate  20 ) by placing a high positive voltage on the control gate  22 , which causes electrons on the floating gate  20  to tunnel through an intermediate insulation  24  from the floating gate  20  to the control gate  22  via Fowler-Nordheim tunneling. 
     The memory cell  10  is programmed (where electrons are placed on the floating gate  20 ) by placing a positive voltage on the control gate  22 , and a positive voltage on the drain  16 . Electron current will flow from the source  14  towards the drain  16 . The electrons will accelerate and become heated when they reach the gap between the control gate  22  and the floating gate  20 . Some of the heated electrons will be injected through the gate oxide  26  onto the floating gate  20  due to the attractive electrostatic force from the floating gate  20 . 
     The memory cell  10  is read by placing positive read voltages on the drain  16  and control gate  22  (which turns on the portion of the channel region under the control gate). If the floating gate  20  is positively charged (i.e. erased of electrons and capacitively coupled to a positive voltage on the drain  16 ), then the portion of the channel region  18  under the floating gate  20  is turned on as well, and current will flow across the channel region  18 , which is sensed as the erased or “1” state. If the floating gate  20  is negatively charged (i.e. programmed with electrons), then the portion of the channel region  18  under the floating gate  20  is mostly or entirely turned off, and current will not flow (or there will be little flow) across the channel region  18 , which is sensed as the programmed or “0” state. 
     The architecture of a conventional array architecture for the memory cell  10  is shown in  FIG.  3   . The memory cells  10  are arranged in rows and columns. In each column, the memory cells are arranged end to end in mirror fashion, so that they are formed as pairs of memory cells each sharing a common source region  14 (S), and each adjacent set of memory cell pairs sharing a common drain region  16 (D). All the source regions  14  for any given row of memory cells are electrically connected together by a source line  14   a . All the drain regions  16  for any given column of memory cells are electrically connected together by a bit line  16   a . All the control gates  22  for any given row of memory cells are electrically connected together by a control gate line  22   a . Therefore, while the memory cells can be individually programmed and read, memory cell erasure is performed row by row (each row of memory cells is erased together, by the application of a high voltage on the control gate line  22   a ). If a particular memory cell is to be erased, all the memory cells in the same row are also erased. 
     Those skilled in the art understand that the source and drain can be interchangeable, where the floating gate  20  can extend partially over the source  14  instead of the drain  16 , as shown in  FIG.  4   .  FIG.  5    best illustrates the corresponding memory cell architecture, including the memory cells  10 , the source lines  14   a , the bit lines  16   a , and the control gate lines  22   a . As is evident from the figures, memory cells  10  of the same row share the same source line  14   a  and the same control gate line  22   a , while the drain regions of all cells of the same column are electrically connected to the same bit line  16   a . The array design is optimized for digital applications, and permits individual programming of the selected cells, e.g., by applying 1.6 V and 7.6 V to the selected control gate line  22   a  and source line  14   a , respectively, and grounding the selected bit line  16   a . Disturbing the non-selected memory cell in the same pair is avoided by applying a voltage greater than 2 volts on the unselected bit lines  16   a  and grounding the remaining lines. The memory cells  10  cannot be erased individually because the process responsible for erasure (the Fowler-Nordheim tunneling of electrons from the floating gate  20  to the control gate  22 ) is only weakly affected by the drain voltage (i.e., the only voltage which may be different for two adjacent cells in the row direction sharing the same source line  14   a ). A non-limiting example of operational voltages can include: 
                                     TABLE 1                       CG 22a   BL 16a   SL 14a                                                                    Read 1   0.5-3    V   0.1-2    V   0    V           Read 2   0.5-3    V   0-2    V   2-0.1    V           Erase   ~11-13    V   0    V   0    V           Program   1-2    V   1-3    uA   9-10    V                    
Read 1 is a read mode in which the cell current comes out on the bit line. Read 2 is a read mode in which the cell current comes out on the source line.
 
     Split gate memory cells having more than two gates are also known. For example, memory cells having source region  14 , drain region  16 , floating gate  20  over a first portion of channel region  18 , a select gate  28  (i.e., a second, channel controlling gate) over a second portion of the channel region  18 , a control gate  22  over the floating gate  20 , and an erase gate  30  over the source region  14  are known, as shown in  FIG.  6    (see for example U.S. Pat. No. 6,747,310, which is incorporated herein by reference for all purposes). Here, all gates are non-floating gates except floating gate  20 , meaning that they are electrically connected or connectable to a voltage or current source. Programming is shown by heated electrons from the channel region  18  injecting themselves onto the floating gate  20 . Erasing is shown by electrons tunneling from the floating gate  20  to the erase gate  30 . 
     The architecture for a four-gate memory cell array can be configured as shown in  FIG.  7   . In this embodiment, each horizontal select gate line  28   a  electrically connects together all the select gates  28  for that row of memory cells. Each horizontal control gate line  22   a  electrically connects together all the control gates  22  for that row of memory cells. Each horizontal source line  14   a  electrically connects together all the source regions  14  for two rows of memory cells that share the source regions  14 . Each bit line  16   a  electrically connects together all the drain regions  16  for that column of memory cells. Each erase gate line  30   a  electrically connects together all the erase gates  30  for two rows of memory cells that share the erase gate  30 . As with the previous architecture, individual memory cells can be independently programmed and read. However, there is no way to erase memory cells individually. Erasing is performed by placing a high positive voltage on the erase gate line  30   a , which results in the simultaneous erasing of both rows of the memory cells that share the same erase gate line  30   a . Exemplary, non-limiting operating voltages can include those in Table 2 below (in this embodiment, select gate lines  28   a  can be referred to as word lines WL): 
                                         TABLE 2                   SG 28a   BL 16a   CG 22a   EG 30a   SL 14a                                                                            Read 1   0.5-2   V   0.1-2   V   0-2.6   V   0-2.6   V   0   V       Read 2   0.5-2   V   0-2   V   0-2.6   V   0-2.6   V   2-0.1   V                                                 Erase   −0.5 V/0 V   0   V   0 V/−8 V   8-12   V   0   V                                                         Program   1   V   1   uA   8-11   V   4.5-5   V   4.5-5   V                    
Read 1 is a read mode in which the cell current comes out on the bit line. Read 2 is a read mode in which the cell current comes out on the source line.
 
     In order to utilize the above described non-volatile memory arrays in neural networks, two modifications may be made. First, the lines may be reconfigured so that each memory cell can be individually programmed, erased and read without adversely affecting the memory state of other memory cells in the array, as further explained below. Second, continuous (analog) programming of the memory cells may be provided. Specifically, the memory or program state (i.e. charge on the floating gate as reflected by the number of electrons on the floating gate) of each memory cells in the array can be continuously changed from a fully erased state to a fully programmed state, and vice versa, independently and with minimal disturbance of other memory cells. This means the cell storage is analog or at the very least can store one of many discrete values, which allows for very precise and individual tuning of all the cells in the memory array, and which makes the memory array ideal for storing and making fine tuning adjustments to the synapsis weights of the neural network. 
     Memory Cell Programming and Storage 
     The neural network weight level assignments as stored in the memory cells can be evenly spaced as shown in  FIG.  8 A , or unevenly spaced as shown in  FIG.  8 B . Programming of the non-volatile memory cells can be implemented using a bidirectional tuning algorithm such as that shown in  FIG.  9   . Icell is the read current of the target cell being programmed, and Itarget is the desired read current when the cell is ideally programmed. The target cell read current Icell is read (step  1 ) and compared to the target read current Itarget (step  2 ). If the target cell read current Icell is greater than the target read current Itarget, a programming tuning process is performed (step  3 ) to increase the number of electrons on the floating gate  20  (in which a look up table or a silicon based approximate function may be used to determine the desired initial and increment programming voltage VCG on the control gate  22 ) (steps  3   a - 3   b ), which can be repeated as necessary (step  3   c ). If the target cell read current Icell is less than the target read current Itarget, an erase tuning process is performed (step  4 ) to decrease the number of electrons on the floating gate  20  (in which a look up table or a silicon based approximate function may be used to determine the desired initial and increment erase voltage VEG on the erase gate  30 ) (steps  4   a - 4   b ), which can be repeated as necessary (step  4   c ). If a programming tuning process overshoots the target read current, then an erase tuning process is performed (step  3   d  and starting with step  4   a ), and vice versa (step  4   d  and starting with step  3   a ), until the target read current is achieved (within an acceptable delta value). 
     Programming of the non-volatile memory cells can instead be implemented using a unidirectional tuning algorithm using programming tuning. With this algorithm, the memory cell  10  is initially fully erased, and then the programming tuning steps  3   a - 3   c  in  FIG.  9    are performed until the read current of the target memory cell  10  reaches the target threshold value. Alternately, the tuning of the non-volatile memory cells can be implemented using the unidirectional tuning algorithm using erasing tuning. In this approach, the memory cell is initially fully programmed, and then the erasing tuning steps  4   a - 4   c  in  FIG.  9    are performed until the read current of the target memory cell reaches the target threshold value. 
       FIG.  10    is a diagram illustrating weight mapping using current comparison. The weight digital bits (e.g., 5-bit weight for each synapsis, representing the target digital weight for the memory cell) are input to a digital-to-analog converter (DAC)  40 , which converts the bits to voltage Vout (e.g., 64 voltage levels-5 bits). Vout is converted to a current Iout (e.g. 64 current levels-5 bits) by voltage-to-current converter V/I Conv  42 . The current Iout is supplied to a current comparator IComp  44 . Program or erase algorithm enabling are input to the memory cell  10  (for example, erase: incrementing EG voltage; or program: increment CG voltage). The output memory cell current Icellout (i.e. from a read operation) is supplied to the current comparator IComp  44 . The current comparator IComp  44  compares the memory cell current Icellout with the current Iout derived from the weight digital bits to produce a signal indicative of the weight stored in the memory cell  10 . 
       FIG.  11    is a diagram illustrating weight mapping using voltage comparison. The weight digital bits (e.g., 5-bit weight for each synapsis) are input to a digital-to-analog converter (DAC)  40 , which converts the bits to voltage Vout (e.g., 64 voltage levels-5 bits). Vout is supplied to a voltage comparator VComp  46 . Program or erase algorithm enabling are input to the memory cell  10  (for example, erase: incrementing EG voltage; or program: increment CG voltage). The output memory cell current Icellout is supplied to current-to-voltage converter UV Conv  48  for conversion to a voltage V 2 out (e.g. 64 voltage levels-5 bits). Voltage V 2 out is supplied to voltage comparator VComp  46 . The voltage comparator VComp  46  compares the voltages Vout and V 2  out to produce a signal indicative of the weight stored in the memory cell  10 . 
     Another embodiment for weight mapping comparison uses variable pulse widths (i.e., pulse width is proportional or inversely proportional to the value of weight) for the input weight and/or the output of the memory cell. In yet another embodiment for weight mapping comparison, digital pulses (e.g., pulses generated from clocks, where the number of pulses are proportional or inversely proportional to the value of weight) are used for the input weight and/or the output of the memory cell. 
     Neural Networks Employing Non-Volatile Memory Cell Array 
       FIG.  12    conceptually illustrates a non-limiting example of a neural network utilizing a non-volatile memory array. This example uses the non-volatile memory array neural net for a facial recognition application, but any other appropriate application could be implemented using a non-volatile memory array based neural network. S 0  is the input layer, which for this example is a 32×32 pixel RGB image with 5 bit precision (i.e. three 32×32 pixel arrays, one for each color R, G and B, each pixel being 5 bit precision). The synapses CB 1  going from S 0  to C 1  have both different sets of weights and shared weights, and scan the input image with 3×3 pixel overlapping filters (kernel), shifting the filter by 1 pixel (or more than 1 pixel as dictated by the model). Specifically, values for 9 pixels in a 3×3 portion of the image (i.e., referred to as a filter or kernel) are provided to the synapses CB 1 , whereby these 9 input values are multiplied by the appropriate weights and, after summing the outputs of that multiplication, a single output value is determined and provided by a first synapse of CB 1  for generating a pixel of one of the layers of feature map C 1 . The 3×3 filter is then shifted one pixel to the right (i.e., adding the column of three pixels on the right, and dropping the column of three pixels on the left), whereby the 9 pixel values in this newly positioned filter are provided to the synapses CB 1 , whereby they are multiplied by the same weights and a second single output value is determined by the associated synapse. This process is continued until the 3×3 filter scans across the entire 32×32 pixel image, for all three colors and for all bits (precision values). The process is then repeated using different sets of weights to generate a different feature map of C 1 , until all the features maps of layer C 1  have been calculated. 
     In layer C 1 , in the present example, there are 16 feature maps, with 30×30 pixels each. Each pixel is a new feature pixel extracted from multiplying the inputs and kernel, and therefore each feature map is a two dimensional array, and thus in this example the synapses CB 1  constitutes 16 layers of two dimensional arrays (keeping in mind that the neuron layers and arrays referenced herein are logical relationships, not necessarily physical relationships—i.e., the arrays are not necessarily oriented in physical two dimensional arrays). Each of the 16 feature maps is generated by one of sixteen different sets of synapse weights applied to the filter scans. The C 1  feature maps could all be directed to different aspects of the same image feature, such as boundary identification. For example, the first map (generated using a first weight set, shared for all scans used to generate this first map) could identify circular edges, the second map (generated using a second weight set different from the first weight set) could identify rectangular edges, or the aspect ratio of certain features, and so on. 
     An activation function P 1  (pooling) is applied before going from layer C 1  to layer S 1 , which pools values from consecutive, non-overlapping 2×2 regions in each feature map. The purpose of the pooling stage is to average out the nearby location (or a max function can also be used), to reduce the dependence of the edge location for example and to reduce the data size before going to the next stage. At layer S 1 , there are 16 15×15 feature maps (i.e., sixteen different arrays of 15×15 pixels each). The synapses and associated neurons in CB 2  going from layer S 1  to layer C 2  scan maps in S 1  with 4×4 filters, with a filter shift of 1 pixel. At layer C 2 , there are 22 12×12 feature maps. An activation function P 2  (pooling) is applied before going from layer C 2  to layer S 2 , which pools values from consecutive non-overlapping 2×2 regions in each feature map. At layer S 2 , there are 22 6×6 feature maps. An activation function is applied at the synapses CB 3  going from layer S 2  to layer C 3 , where every neuron in layer C 3  connects to every map in layer S 2 . At layer C 3 , there are 64 neurons. The synapses CB 4  going from layer C 3  to the output layer S 3  fully connects S 3  to C 3 . The output at layer S 3  includes 10 neurons, where the highest output neuron determines the class. This output could, for example, be indicative of an identification or classification of the contents of the original image. 
     Each level of synapses is implemented using an array, or a portion of an array, of non-volatile memory cells.  FIG.  13    is a block diagram of the vector-by-matrix multiplication (VMM) array that includes the non-volatile memory cells, and is utilized as the synapses between an input layer and the next layer. Specifically, the VMM array  32  includes an array of non-volatile memory cells  33 , erase gate and word line gate decoder  34 , control gate decoder  35 , bit line decoder  36  and source line decoder  37 , which decode the inputs for the memory cell array  33 . Source line decoder  37  in this example also decodes the output of the memory cell array  33 . Alternatively, bit line decoder  36  can decode the output of the non-volatile memory cell array  33 . The memory array serves two purposes. First, it stores the weights that will be used by the VMM array  32 . Second, the memory cell array effectively multiplies the inputs by the weights stored in the memory cell array and adds together the results along each output line to produce the output, which will be the input to the next layer or input to the final layer. By performing the multiplication and addition function, the memory array negates the need for separate multiplication and addition logic circuits and is also power efficient due to its in-situ memory computation. 
     The output of the memory cell array is supplied to a single or differential summing circuit  38 , which sums up the outputs of the memory cell array to create a single value for that convolution. The summed up output values are then supplied to the activation function circuit  39 , which rectifies the output. The activation function can be sigmoid, tanh, or ReLu function. The rectified output values from circuit  39  become an element of a feature map as the next layer (C 1  in the description above for example), and are then applied to the next synapse to produce next feature map layer or final layer. Therefore, in this example, the memory cell array  33  constitutes a plurality of synapses (which receive their inputs from the prior layer of neurons or from an input layer such as an image database), and summing circuit  38  and activation function circuit  39  constitute a plurality of neurons. 
       FIG.  14    is a block diagram depicting the usage of numerous layers of VMM arrays  32 , here labeled as VMM arrays  32   a ,  32   b ,  32   c ,  32   d , and  32   e . As shown in  FIG.  14   , the input, denoted Inputx, is converted from digital to analog by a digital-to-analog converter  31 , and provided to input VMM array  32   a . The output generated by the input VMM array  32   a  is provided as an input to the next VMM array (hidden level 1)  32   b , which in turn generates an output that is provided as an input to the next VMM array (hidden level 2)  32   c , and so on. The various layers of VMM array  32  function as different layers of synapses and neurons of a convolutional neural network (CNN). Each VMM array  32   a ,  32   b ,  32   c ,  32   d , and  32   e  can be a stand-alone, physical non-volatile memory array, or multiple VMM arrays could utilize different portions of the same physical non-volatile memory array, or multiple VMM arrays could utilize overlapping portions of the same physical non-volatile memory array. The example shown in  FIG.  14    contains five layers ( 32   a ,  32   b ,  32   c ,  32   d ,  32   e ): one input layer ( 32   a ), two hidden layers ( 32   b ,  32   c ), and two fully connected layers ( 32   d ,  32   e ). One of ordinary skill in the art will appreciate that this is merely exemplary and that a system instead could comprise more than two hidden layers and more than two fully connected layers. 
       FIGS.  15 - 16    illustrate a configuration of an array of three-gate memory cells arranged as a source summing matrix multiplier. The three-gate memory cell is shown in  FIG.  15   , and is the same as that of  FIG.  6   , except there is no erase gate. In one embodiment, cell erasing is performed by applying a positive voltage to the select gate  28 , where electrons tunnel from the floating gate  20  to the select gate  28 . Below is a table of exemplary and non-limiting operational voltages for the three-gate memory cell of  FIG.  15   . 
                                     TABLE 3                   SG 28a   BL 16a   CG 22a   SL 14a                                                                    Read 1   0.5.0-2   V   0.1-2   V   0-2.6   V   0.1-2   V       Read 2   0.5-2   V   0-2   V   0-2.6   V   2-0.1   V                                             Erase   3-12   V   0   V   0 V to −13 V   0   V                                                 Program   1   V   1   uA   8-11   V   4.5-8   V                    
Read 1 is a read mode in which the cell current comes out on the bit line. Read 2 is a read mode in which the cell current comes out on the source line. An alternative erase operation for the three-gate memory cell of  FIG.  15    can have the p-type substrate  12  at a high voltage, e.g., 10V to 20V, and the control gate  22  at a low or negative voltage, e.g. −10V to 0V, whereby electrons will tunnel from the floating gate  20  to the substrate  12 .
 
     The lines for the array of the three-gate memory cells of  FIG.  15    are shown in  FIG.  16   , and are the same as that in the array of  FIG.  7   , except that there is no erase gate line  30   a  (because there are no erase gates), and the source lines  14   a  run vertically instead of horizontally, so that each memory cell can be independently programmed, erased and read. Specifically, each column of memory cells includes a source line  14   a  connecting together all the source regions  14  for the memory cells in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vin 3  and are placed on the control gate lines  22   a . The matrix current outputs Iout 0  . . . Ioutn are produced on the source lines  14   a . Each output Iout is a sum of the input current I times the weight W stored in the cell, for all the cells in the column:
 
 I out=Σ( Ii*Wij )
 
where “i” represents the row and “j” represents the column in which the memory cell resides. In the case where a input voltage is applied instead of input current, as indicated in  FIG.  16    as Vin 0 -Vin 3 , then each output Iout is proportional to the sum of the input voltage times the weight W stored in the cell, for all the cells in the column:
 
 I out αΣ( Vi*Wij )
 
     Each memory cell column acts as a single neuron having a summed weight value expressed as output current Iout dictated by the sum of the weight values stored in the memory cells in that column. The output of any given neuron is in the form of current, which can then be used as an input current Iin after adjustment by an activation function circuit for the next subsequent VMM array stage. 
     Given that the inputs are voltages, and the outputs are currents, in  FIG.  16   , each subsequent VMM stage after the first stage preferably includes circuitry for converting incoming currents from the previous VMM stage into voltages to be used as the input voltages Vin.  FIG.  17    illustrates an example of such current-to-voltage conversion circuitry, which is a modified row of memory cells that log converts the incoming currents Iin 0  . . . Iin 1  into the input voltages Vin 0  . . . Vin 1  for application to the subsequent stage. The memory cells described herein are biased in weak inversion,
 
 Ids=Io*e   (Vg−Vth)/kVt   =w*Io*e   (Vg)/kVt  
         where w=e (−Vth)/kVt  
 
For the I-to-V log converter using a memory cell to convert input current into an input voltage:
 
 Vg=k*Vt* log[ Ids/wp*Io ]
 
Here, wp is w of a reference or peripheral memory cell. For a memory array used as a vector matrix multiplier VMM, the output current is:
 
 I out= wa*Io*e   (Vg)kVt ,namely
 
 I out=( wa/wp )* I in= W*I in
 
 W=e   (Vthp−Vtha)/kVt  
 
Here, wa=w of each memory cell in the memory array. A select gate line  28   a  can be used as the input for the memory cell for the input voltage, which is connected to the bit lines  16   a  by switches BLR that are closed during current to voltage conversion.
       

     Alternatively, the non-volatile memory cells of VMM arrays described herein can be configured to operate in the linear region:
 
 Ids =beta*( Vgs−Vth )* Vds ;beta= u*Cox*Wt/L,  
 
     where Wt and L are the width and length respectively of the transistor 
     Wα (Vgs−Vth), meaning weight W is proportional to (Vgs−Vth) 
     A select gate line or control gate line or bit line or source line can be used as the input for the memory cell operated in the linear region. The bit line or source line can be used as the output for the output neuron. 
     For an I-to-V linear converter, a memory cell (such as a reference memory cell or a peripheral memory cell) or a transistor operating in the linear region or a resistor can be used to linearly convert an input/output current into an input/output voltage. Alternatively, the non-volatile memory cells of VMM arrays described herein can be configured to operate in the saturation region:
 
 Ids=α ½*beta*( Vgs−Vth ) 2 ;beta= u*Cox*Wt/L  
 
     Wα (Vgs−Vth) 2 , meaning weight W is proportional to (Vgs−Vth) 2    
     A select gate line or control gate can be used as the input for the memory cell operated in the saturation region. The bit line or source line can be used as the output for the output neuron. Alternatively, the non-volatile memory cells of VMM arrays described herein can be used in all regions or a combination thereof (sub threshold, linear, or saturation). Any of the above described current to voltage conversion circuits or techniques can be used with any of the embodiments herein so that the current output from any given neuron in the form of current can then be used as an input after adjusted by an activation function circuit for the next subsequent VMM array stage. 
       FIG.  18    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  18    are the same as that in the array of  FIG.  16   . However, the matrix voltage inputs Vin 0 -Vin 3  are placed on the select gate lines  28   a , and the matrix current outputs Iout 0  . . . IoutN are produced on the source lines  14   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the column). As with the previous embodiment (and any other embodiment described herein), the output of any given neuron is in the form of current, which can then be used as an input after adjusted by an activation function circuit for the next subsequent VMM array stage. 
       FIG.  19    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a drain summing matrix multiplier. The lines for the array of  FIG.  19    are the same as that in the array of  FIG.  16   . However, the matrix voltage inputs Vin 0 -Vin 3  are placed on the control gate lines  22   a , and the matrix current outputs Iout 0  . . . IoutN are produced on the bit lines  16   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the column). 
       FIG.  20    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a drain summing matrix multiplier. The lines for the array of  FIG.  20    are the same as that in the array of  FIG.  16   . However, the matrix voltage inputs Vin 0 -Vin 3  are placed on the select gate lines  28   a , and the matrix current outputs Iout 0  . . . IoutN are produced on the bit lines  16   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the column). 
       FIG.  21    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a drain summing matrix multiplier. The lines for the array of  FIG.  21    are the same as that in the array of  FIG.  16   , except that the source lines  14   a  run horizontally instead of vertically. Specifically, each row of memory cells includes a source line  14   a  connecting together all the source regions  14  for the memory cells in that row. The matrix voltage inputs Vin 0 -Vin 3  are placed on the select gate lines  28   a , and the matrix current outputs Iout 0  . . . IoutN are produced on the bit lines  16   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the column). 
       FIG.  22    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a drain summing matrix multiplier. The lines for the array of  FIG.  22    are the same as that in the array of  FIG.  21   . The matrix voltage inputs Vin 0 -Vin 3  are placed on the control gate lines  22   a , and the matrix current outputs Iout 0  . . . IoutN are produced on the bit lines  16   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the column). 
       FIG.  23    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a drain summing matrix multiplier. The lines for the array of  FIG.  23    are the same as that in the array of  FIG.  21   . The matrix voltage inputs Vin 0 -Vin 1  are placed on the source lines  14   a , and the matrix current outputs Iout 0  . . . IoutN are produced on the bit lines  16   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the column). 
       FIG.  24    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  24    are the same as that in the array of  FIG.  21   . The matrix voltage inputs Vin 0 -Vinn are placed on the bit lines  16   a , and the matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the row). 
       FIG.  25    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  25    are the same as that in the array of  FIG.  21   , except that each bit line includes a bit line buffer transistor  60  connected in series with the bit line (i.e., any current on the bit line flows through the transistor between its source and drain). The transistor  60  acts as a graduated switch that selectively and gradually turns on the bit line as the input voltage on the transistor&#39;s gate terminal is increased (i.e., the transistor couples the bit line to its current or voltage source). The matrix voltage inputs Vin 0  . . . Vinn are provided to the gates of the transistors  60 , and the matrix current outputs Iout 0  . . . Iout 1  are provided on the source lines  14   a . The advantage of this configuration is that the matrix inputs can be supplied as voltages (to operate transistors  60 ), instead of supplying inputs directly to the bit lines in the form of electrical voltages. This allows for the use of constant voltage sources to operate the bit lines, using transistors  60  to gradually couple them to the bit lines in response to the input voltages Vin supplied to the transistors&#39; gates, thus negating the need to supply electrical voltage inputs to the memory array. Transistors  60  can be included on the bit lines for receiving the inputs on their gates instead of the inputs being applied to the bit lines, for any of the embodiments herein for the memory cells  10  of  FIG.  15    where the bit lines receive the inputs. 
       FIG.  26    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  26    are the same as that in the array of  FIG.  21   , except that the control gate lines  22   a  run vertically instead of horizontally. Specifically, each column of memory cells includes a control gate line  22   a  connecting together all the control gates  22  in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vinn and are placed on the control gate lines  22   a . The matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the row. 
       FIG.  27    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  27    are the same as that in the array of  FIG.  21   , except that the control gate lines  22   a  run vertically instead of horizontally. Specifically, each column of memory cells includes a control gate line  22   a  connecting together all the control gates  22  in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vinn and are placed on the bit lines  16   a . The matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the row. 
       FIG.  28    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  28    are the same as that in the array of  FIG.  21   , except that the select gate lines  28   a  run vertically instead of horizontally. Specifically, each column of memory cells includes a select gate line  28   a  connecting together all the select gates  28  in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vinn and are placed on the select gate lines  28   a . The matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the row. 
       FIG.  29    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  15    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  29    are the same as that in the array of  FIG.  21   , except that the select gate lines  28   a  run vertically instead of horizontally. Specifically, each column of memory cells includes a select gate line  28   a  connecting together all the select gates  28  in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vinn and are placed on the bit lines  16   a . The matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the row. 
       FIGS.  30 - 31    illustrate another configuration of an array of three-gate memory cells of a different configuration, arranged as a drain summing matrix multiplier. The three-gate memory cell is shown in  FIG.  30   , and is the same as that of  FIG.  6   , except there is no control gate  22 . The select gate  28  as shown lacks any portion extending up and over the floating gate  20 . However, the select gate  28  could include an additional portion extending up and over a portion of the floating gate  20 . 
     Read, erase, and program is done in a similar manner, but without any bias to a control gate (which is not included). Exemplary, non-limiting operating voltages can include those in Table 4 below: 
                                     TABLE 4                   SG 28a   BL 16a   EG 30a   SL 14a                                                                    Read 1   0.5-2   V   0.1-2   V   0-2.6   V   0   V       Read 2   0.5-2   V   0-2   V   0-2.6   V   2-0.1   V                                             Erase   −0.5 V/0 V   0   V   8-12   V   0   V                                                 Program   1   V   1   uA   4.5-7   V   4.5-7   V                    
Read 1 is a read mode in which the cell current comes out on the bit line. Read 2 is a read mode in which the cell current comes out on the source line.
 
       FIG.  31    shows a memory cell array architecture using the memory cell  10  of  FIG.  30   , with all the lines extending in the horizontal/row direction except the bit lines  16   a . After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a bit line summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vin 3  and are placed on the select gate lines  28   a . The matrix outputs Iout 0  . . . Ioutn are produced on the bit lines  16   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the column. 
       FIG.  32    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  30    arranged as a drain summing matrix multiplier. The lines for the array of  FIG.  32    are the same as that in the array of  FIG.  31   . The matrix voltage inputs Vin 0 -Vin 1  are placed on the erase gate lines  30   a , and the matrix current outputs Iout 0  . . . IoutN are produced on the bit lines  16   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the column). 
       FIG.  33    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  30    arranged as a drain summing matrix multiplier. The lines for the array of  FIG.  33    are the same as that in the array of  FIG.  31   . The matrix voltage inputs Vin 0 -Vin 1  are placed on the source lines  14   a , and the matrix current outputs Iout 0  . . . IoutN are produced on the bit lines  16   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the column). 
       FIG.  34    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  30    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  34    are the same as that in the array of  FIG.  31   . The matrix voltage inputs Vin 0 -Vinn are placed on the bit lines  16   a , and the matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a  (i.e., each output Iout is a sum of the cell current which is proportional to the weight W stored in the cell, for all the cells in the row). 
       FIG.  35    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  30    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  35    are the same as that in the array of  FIG.  31   , except that each bit line includes a bit line buffer transistor  60  connected in series with the bit line (i.e., any current on the bit line flows through the transistor between its source and drain). The transistor  60  acts as a graduated switch that selectively and gradually turns on the bit line as the input voltage on the transistor&#39;s gate terminal is increased (i.e., the transistor couples the bit line to its current or voltage source). The matrix voltage inputs Vin 0  . . . Vinn are provided to the gates of the transistors  60 , and the matrix current outputs Iout 0  . . . Iout 1  are provided on the source lines  14   a . The advantage of this configuration is that the matrix inputs can be supplied as voltages (to operate transistors  60 ), instead of supplying inputs directly to the bit lines in the form of electrical voltages. This allows for the use of constant voltage sources to operate the bit lines, using transistors  60  to gradually couple them to the bit lines in response to the input voltages Vin supplied to the transistors&#39; gates, thus negating the need to supply electrical voltage inputs to the memory array. Transistors  60  can be included on the bit lines for receiving the inputs on their gates instead of the inputs being applied to the bit lines, for any of the embodiments herein for the memory cells  10  of  FIG.  30    where the bit lines receive the inputs. 
       FIG.  36    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  30    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  36    are the same as that in the array of  FIG.  31   , except that the select gate lines  28   a  run vertically instead of horizontally. Specifically, each column of memory cells includes a select gate line  28   a  connecting together all the select gates  28  in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vinn and are placed on the select gate lines  28   a . The matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the row. 
       FIG.  37    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  30    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  37    are the same as that in the array of  FIG.  31   , except that the select gate lines  28   a  run vertically instead of horizontally. Specifically, each column of memory cells includes a select gate line  28   a  connecting together all the select gates  28  in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vinn and are placed on the bit lines  16   a . The matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the row. 
       FIG.  38    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  30    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  38    are the same as that in the array of  FIG.  31   , except that the erase gate lines  30   a  run vertically instead of horizontally. Specifically, each column of memory cells includes an erase gate line  30   a  connecting together all the erase gates  30  in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vinn and are placed on the erase gate lines  30   a . The matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the row. 
       FIG.  39    illustrates another configuration of an array of three-gate memory cells  10  of  FIG.  30    arranged as a source summing matrix multiplier. The lines for the array of  FIG.  39    are the same as that in the array of  FIG.  31   , except that the erase gate lines  30   a  run vertically instead of horizontally. Specifically, each column of memory cells includes an erase gate line  30   a  connecting together all the erase gates  30  in that column. After each of the memory cells is programmed with the appropriate weight value for that cell, the array acts as a source summing matrix multiplier. The matrix voltage inputs are Vin 0 -Vinn and are placed on the bit lines  16   a . The matrix current outputs Iout 0  . . . Iout 1  are produced on the source lines  14   a . Each output Iout is a sum of the cell current that is proportional to the weight W stored in the cell, for all the cells in the row. 
     Regarding the embodiments of  FIGS.  15 - 20   , namely an array of the memory cells of  FIG.  15   , wherein each of the arrays in  FIGS.  16 - 20    includes a source line  14   a  extending vertically (in the column direction) instead of horizontally (in the row direction), the arrays of  FIGS.  16 - 20    would equally apply for the memory cell of  FIG.  30    which has an erase gate  30  instead of a control gate  22 . Specifically, the arrays of  FIGS.  16 - 20    would be of memory cells  10  in  FIG.  30    instead of memory cells  10  in  FIG.  15   , where in each array the control gate lines  22   a  would be replaced with erase gate lines  30   a  (i.e., each of the erase gate lines  30   a  would connect together all the erase gates  30  for a row of the memory cells  10 ). All the other lines in  FIGS.  16 - 20    would remain the same. 
     All of the above functionality can be performed under the control of a controller  100 , which is connected to the memory array(s) of the above described memory cells  10  used for the neural net functionality. As shown in  FIG.  40   , the controller  100  is preferably on the same semiconductor chip or substrate  110  as the memory array(s)  120 . However, controller  100  could also be located on a separate semiconductor chip or substrate, and could be a collection of multiple controllers disposed in different locations on or off semiconductor chip or substrate  110 . 
     It is to be understood that the present invention is not limited to the embodiment(s) described above and illustrated herein, but encompasses any and all variations falling within the scope of any claims. For example, references to the present invention herein are not intended to limit the scope of any claim or claim term, but instead merely make reference to one or more features that may be covered by one or more claims. Materials, processes and numerical examples described above are exemplary only, and should not be deemed to limit the claims. Single layers of material could be formed as multiple layers of such or similar materials, and vice versa. While the outputs of each memory cell array are manipulated by filter condensation before being sent to the next neuron layer, they need not be. Lastly, for each of the matrix multiplier array embodiments described above, for any lines not being used for the input voltages or the output currents, the nominal read voltages disclosed in the tables herein for that configuration of memory cell can be (but not necessary be) applied to those lines during operation. 
     It should be noted that, as used herein, the terms “over” and “on” both inclusively include “directly on” (no intermediate materials, elements or space disposed there between) and “indirectly on” (intermediate materials, elements or space disposed there between). Likewise, the term “adjacent” includes “directly adjacent” (no intermediate materials, elements or space disposed there between) and “indirectly adjacent” (intermediate materials, elements or space disposed there between), “mounted to” includes “directly mounted to” (no intermediate materials, elements or space disposed there between) and “indirectly mounted to” (intermediate materials, elements or spaced disposed there between), and “electrically coupled” includes “directly electrically coupled to” (no intermediate materials or elements there between that electrically connect the elements together) and “indirectly electrically coupled to” (intermediate materials or elements there between that electrically connect the elements together). For example, forming an element “over a substrate” can include forming the element directly on the substrate with no intermediate materials/elements there between, as well as forming the element indirectly on the substrate with one or more intermediate materials/elements there between.