Abstract:
A special purpose processor (SPP) for implementing a synthetic neural model of the biological anatomy of the human brain to control a brain-based device (BBD) that is movable in a real-world environment, including neural processing units (NPUs), each having a programmed processor and a local memory that stores data records of neural elements, a system memory for storing data about all the NPUs, and a finite state machine and a system bus for transferring data between the NPUs and system memory.

Description:
CLAIM OF PRIORITY 
     This application is a continuation of U.S. patent application Ser. No. 11/426,881 entitled “Neural Modeling and Brain-Based Devices Using Special Purpose Processor” filed Jun. 27, 2006 by Snook, et al., which claims priority to U.S. Provisional Application No. 60/694,532 entitled “Neural Modeling and Brain-Based Devices Using Special Purpose Processor,” filed Jun. 28, 2005, which applications are hereby incorporated by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     This invention was made with Government support under N00014-05-1-0205 awarded by the Office of Naval Research. The United States Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to neural modeling, especially to neural modeling that can be used with brain-based devices. 
     BACKGROUND OF THE INVENTION 
     Intelligent systems have been developed which are intended to behave autonomously, automate tasks in an intelligent manner, and extend human knowledge. These systems are designed and modeled based on essentially three distinct fields of technology known, respectively, as
         (1) artificial intelligence (AI);   (2) artificial neural networks (ANNs); and   (3) brain-based devices (BBDs).       

     The intelligent systems based on AI and ANN include digital computers which are programmed to perform tasks as far ranging as playing chess to robotics. AI algorithms are logic-based and preprogrammed to carry out complex algorithms implemented with detailed software instructions. ANNs are an oversimplified abstraction of biological neurons that do not take into consideration nervous system structure (i.e. neuroanatomy) and often require a supervisory or teacher signal to get desired results. BBDs, on the other hand, are based on different principles and a different approach to the development of intelligent systems. 
     BBDs are based on fundamental neurobiological principles and are modeled after the brain bases of perception and learning found in living beings. BBDs incorporate a simulated brain or nervous system with detailed neuroanatomy and neural dynamics that control behavior and shape memory. BBDs also have a physical instantiation, called a morphology or phenotype, which allows active sensing and autonomous movement in the environment. BBDs, similar to living beings, organize unlabeled signals they receive from the environment into categories. When a significant environmental event occurs, BBDs, which have a simulated neuronal area called a value system, adapt the device&#39;s behavior. 
     The different principles upon which logic-based intelligent systems and BBDs operate are significant. As powerful as they are, logic-based machines do not effectively cope with novel situations nor process large data sets simultaneously. By their nature, novel situations cannot be programmed beforehand because these typically consist of unexpected and varying numbers of components and contingencies. Furthermore, situations with broad parameters and changing contexts can lead to substantial difficulties in programming. And, many algorithms have poor scaling properties, meaning the time required to run them increases exponentially as the number of input variables grows. 
     SUMMARY OF THE INVENTION 
     For the present invention there is described a detailed hardware system, i.e., a special purpose processor, that implements a synthetic neural model of the biological anatomy of the human brain for use in a brain-based device or BBD that is movable in a real-world environment. 
     Thus, the present invention is a special purpose processor that has:
         (a) a plurality of neural processing units, each one of the neural processing units having (i) a programmed processor, and (ii) a local memory, in which
           (i) the programmed processor of one neural processing unit processes data corresponding to a plurality of distinct neural elements, and in which each of the plurality of distinct neural elements has a plurality of pre-synaptic inputs received from outputs of other neural elements and an output providing post-synaptic output activity data to be sent to other neural elements; and   (ii) the local memory stores a plurality of data records, each one of the data records having data corresponding to one of the neural elements of one of the neural processing units, in which each the data of each data record stores (a) a synaptic connection table defining synaptic connections between one of the neural elements and other of the neural elements, (b) a current weight data table having weight data corresponding to each synaptic connection through which the one neural element receives an input, and (c) an output storage table having post-synaptic output activity data resulting from processing by the one neural processing unit and provided on the output;   
           (b) first system memory storing an output storage table having post-synaptic output activity data corresponding to each output of each neural element of each of the plurality of neural processing units;   (c) second system memory for storing respective data records for each of the plurality of neural elements for each of the plurality of neural processing units, each of the data records having address pointers to the first system memory to access and output post-synaptic output activity data stored in the output storage table;   (d) a finite state machine for controlling writing of the post-synaptic output activity data into the output storage table from the plurality of neural processing units and for reading the post-synaptic output activity data stored in the output storage table in response to the address pointers from the second system memory;   (e) a system data bus for transferring data between the plurality of neural processing units and the first system memory and the second system memory;   (f) sensors for receiving and providing sensed data corresponding to the real-world environment in which the BBD moves, wherein the plurality of neural processing units process the sensed data to calculate the weight data; and   (g) actuators, responsive to the data processed by the plurality of neural processing units, for controlling movement of the BBD in the real-world environment; and   (h) wherein (i) the plurality of neural processing units process data for all of the plurality of neural elements over a given time epoch and (ii) during the given time epoch, the output storage table and the current weight table are accessed to provide the post-synaptic output data and the current weight data for one neural element of the same neural processing unit.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a diagram of a special purpose processor of one embodiment. 
         FIG. 1B  is a diagram showing inputs and outputs to a neural element of a neural model of one embodiment. 
         FIG. 1C  is a schematic diagram of an exemplary regional and functional neuroanatomy of neural model which can guide the behavior of a brain-based device in its environment. 
         FIG. 1D  is a diagram of a brain-based device including a special purpose processor. 
         FIG. 2  is a diagram of a neural model using a special purpose processor of one embodiment. 
         FIGS. 3A and 3B  are diagrams of a core of one embodiment for a special purpose processor. 
         FIG. 4  is a flowchart of the operation of one embodiment of a brain-based device using a special purpose processor. 
         FIGS. 5A-5D  are diagrams illustrating the transfer of inputs, outputs and weights in a special purpose processor of one embodiment of the present invention. 
         FIG. 6  is a diagram of a special purpose processor of one embodiment. 
         FIG. 7  is a diagram of a processor interface module of one embodiment. 
         FIG. 8  is a diagram of a finite state machine controller of one embodiment. 
         FIG. 9  is a diagram that shows a pin arrangement for the SRAM controller module of one embodiment. 
         FIG. 10  is a diagram of an SRAM controller of one embodiment. 
         FIG. 11  are exemplary read and write timing diagrams for the core. 
         FIG. 12  is a diagram of output storage tables of one embodiment. 
         FIG. 13  is a diagram of a system bus environment module of one embodiment. 
         FIGS. 14 and 15  are diagrams illustrating data paths of one embodiment. 
         FIG. 16A-16D  is a diagram of a rover for a brain-based device BBD. 
         FIG. 17  is a functional diagram of a rover of one embodiment. 
         FIG. 18  is a data processing device or module useful for implementing the brain-based device functionality described herein, according to an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     One embodiment of the present invention is a special purpose processor (SPP) which can include a chip to model multiple neural elements concurrently. The SPP can use a Field Programmable Gate Array (FPGA) to model large numbers of the neural elements. The use of FPGAs allows for parallel processing with relatively large input and output connectivity of the modeled neural elements. For the purposes of this application, an FPGA is any configurable logic device, such as a reconfigurable logic device, that can implement neural elements. An exemplary FPGA for use in the present invention is a Virtex™ series Xilinx™ FPGA available from the Xilinx Corporation of San Jose, Calif. 
     The Field Programmable Gate Array architecture lends itself to implementation in a number of other more power efficient and compact electronic devices. These devices include application specific integrated circuits (ASICs) and other applicable technologies. In an embodiment, ASICs are used to implement the invention. 
     It should be understood that, while embodiments of the invention are described herein as being implemented using SPPs, FPGAs, and/or ASICs, the invention is not limited to these example implementations. As will be appreciated by persons skilled in the relevant art(s), embodiments of the invention can be implemented using any data processing module, device or architecture. This includes, for example and without limitation, application specific integrated circuits (ASICs). 
     The neural model can include a relatively large number of neural elements. The neural elements each can execute a series of processes based on their inputs. The period for each series of processes serves as a cycle time called an epoch. The neural elements can perform their set of processes on their respective set of inputs within the epoch, making their outputs and any learning that they do available for use in the next epoch. The processes can include presynaptic calculation  102   a , postsynaptic calculation  102   b , and plasticity calculations  102   c . The core can use preloaded coefficients so that the core can model a specific type of neural element. 
     As shown in  FIG. 1A , the SPP  100  can have a number of neural processing units  102  (also called “cores”) that can implement the processes. The processes implemented by the cores  102  can include presynaptic calculations  102   a , postsynaptic calculations  102   b , and plasticity calculations  102   c.    
     The cores can use one or more groups of resources on the FPGA as required. As discussed below, cores can use resources, such as local memory, look-up tables, comparators and multipliers that can be arranged in a variety of ways on an FPGA. In one embodiment, each core uses multiple configurable logic blocks (CLBs) on the FPGA. 
     The SPP  100  can store the results of these processes, in on-chip or off-chip memory for the next epoch. In one embodiment, timeslices within the epoch allow each neural processing unit to model multiple neural elements. The total number of neural elements modeled can be given by (number of cores)*(number of timeslices in epoch). The more timeslices that are used, the larger the simulation, the longer the epoch, and the larger the neural element address required. 
     In neural modeling, each neural element can be considered to have a number of inputs. The inputs can be combined in a sum-of-products process, where each input is multiplied by a unique weight coefficient. This sum-of-products process is an example of a presynaptic calculation. The output of this sum-of-products, which can be a single value, can then be passed through a series of calculations, referred to as post-synaptic processing, to generate a single PostSynaptic Processing (PSP) output. Additionally, a series of plasticity calculations can be performed, which can include activity-dependent synaptic processes and value-dependent synaptic processes. These plasticity calculations can modify the weight values so that they have new learned values for the next epoch. 
     The PSP outputs of each neural element can be connected as an input of a number of other neural elements in the next epoch.  FIG. 1B  is a diagram that illustrates the inputs  122  and outputs  124  of a core  120 . 
       FIG. 2  shows an example of a neural model using an SPP. The cores  200  can model specific types of neural units. For example, core  0  could model visual neurons; core  1  could model audio neurons, core  2  could model hippocampus neurons and the like. The cores  200  can have coefficients that are unique to the neural type of the core and help define the type of neuron modeled by the core. In an FPGA, functions that depend on coefficients can be implemented as Look-Up Tables (LUTs). These LUTs can also be different for different neural types. 
     In one embodiment, the coefficients don&#39;t change between the different timeslices. Thus, if there are 256 timeslices, each core can model 256 of the same type of neural element. If more of the same type of neural element is desired, multiple cores can be used with the total number of neural elements of a specific neural type given by (number of cores of given neural type)*(number of timeslices in epoch). 
     The on-chip memory  202  and off-chip memory  204  and  206  can store current and initial weights; PSP outputs, such as in an output storage table (OST); and connection tables. Each neural element can have associated with it specific inputs, which can be the outputs from other neural elements of a previous epoch. In one embodiment, memory, such as ping-pong buffers, is used to store the outputs of all the neural elements that are provided as inputs in the next epoch. In one embodiment, two tables are used to store outputs, one table including outputs from the last epoch and one table which is filled with outputs from the current epoch. Once a new epoch starts, the functions of the tables can switch. 
     Neural elements in different timeslices can be interconnected using memory to store the PSP outputs for the next epoch rather than immediately sent to a core in the current timeslice. In one embodiment, the number of inputs for each neural element is a relatively large number, such as 100 or more (256 in one embodiment), to better model the highly connected neuronal structure of the brain. In one embodiment, the output of the neuronal elements is also sent to a relatively large number of neural elements, such as 100 or more (256 in one embodiment), in the next epoch. 
     The neural elements can also be loaded with weights for the inputs. In one embodiment, the current weights can be loaded into the neural elements along with the input values, PSP outputs of the last epoch. The weights can be modified due to plasticity calculations and updated to be used in the next epoch. In one embodiment, each weight is used by a single neural element so only a single weight table is needed which can be updated before being accessed again by the neural element. In one embodiment, the current weights are different for each neural element so each core will use a number of weights given by (number of weights per neural element)*(number of timeslices) which may make it more feasible to store the weights outside the core, such as in a BRAM (buffer random access memory), even though the weights are not used by any other core. 
     In one embodiment, the initial weights, which may be used in the plasticity calculations, are provided from an initial weight table. Alternately, the initial weights can be stored locally. If the initial weights are stored locally, the initial weights can be selected using a scheme that minimizes the amount of initial weight data stored locally. 
     A connection table can store indications of the connections. In one embodiment, a connection indicates that an output from a specified neural element of the last epoch is to be sent as an input to a specified neural element of the current epoch. The output table can be arranged with the position in the output table indicating the source of the output. The elements of the connection table can be pointers into the output table. In one embodiment, the connection table has m pointers into the output table for each neural element, where m is the number of inputs per neural element. 
     In one embodiment, the cores are first loaded with the coefficients and LUTs. Then, for each timeslice of each epoch, each of the neural elements of the timeslice is loaded with inputs and current weights. Within an epoch, the loading can go in an order, such as (Core  0 , timeslice  0 ), (Core  1 , timeslice  0 ) . . . (Core  255 , timeslice  0 ), (Core  0 , timeslice  1 ) . . . (Core  254 , timeslice  255 ), (Core  255 , timeslice  255 ). The PSP output and the updated weights can be sent out to memory after the neural element finishes the processing. The transfer of the PSP outputs and the updated weights from the neural elements to memory can be done in the same order as the loading. In one embodiment, cores can be loaded for one timeslice while other cores are calculating for the previous timeslice. For example, core  12  can be loaded for timeslice  10  while core  245  is still calculating or waiting to store to memory for timeslice  9 . In one embodiment, the system waits at least until the output storage table is completely filled before moving on to processing for a new epoch. 
     As shown in  FIG. 1D , a SPP  142  can be used to control a brain-based device (BBD)  140 . In one embodiment, some input values for the neural units can be provided from sensors  144 . Sensor signals, such as signals from video, audio, wheel, motor, tactile, suspension, accelerometer, gyro, and/or power management sensors, can be processed or fed directly as inputs to neural elements of an appropriate type. For example, some parts of the output storage table for the next epoch can be or be derived from sensor data. Additionally, some output storage table values can be used directly or be processed to control actuators  146 . In that way, the SPP can control a robot, or other BBD device. 
     A BBD of the present invention can include a physically instantiated mobile device which can explore its environment and develop adaptive behavior while experiencing it. The BBD can also include a neural model, such as the SPP, located at the mobile device or remotely, for guiding the mobile device in its real-world environment. 
     The BBD can develop or adapt its behavior by learning about the environment using the neural model, such as the neural model implemented on the SPP. The mobile device can move autonomously in its environment. A BBD can use sensor signals as input to the neural model, such as a neural model implemented on the SPP, so that the neural model can control the BDD. For example, the mobile device can approach and view multiple objects that share visual features, e.g. same color, and have distinct visual features such as shape, e.g. red square vs. red triangle. The mobile device can become conditioned through the learning experience to prefer one target object, e.g. the red diamond, over multiple distracters or non-target objects such as the red square and a green diamond of a scene in its vision. The mobile device can learn this preference behaviorally while moving in its environment by orienting itself towards the target object in response to an audible tone or other stimulus. 
     The brain-based device can utilize a wide variety of multi modal active and/or passive sensor inputs for real time interaction with a broad range of environmental conditions. The sensory input can encompass both monocular and binocular vision with inputs across the full electromagnetic spectrum. Other sensors can include, but are not limited to, haptic, olfactory, audio, acoustic, and thermal. For example, the brain-based device can have sensors, such as a camera for vision and microphones which can provide visual and auditory sensory input to neural model, as well as actuators, such as effectors or wheels for movement. It can also have an infrared (IR) sensor for obstacle avoidance by sensing differences in reflectivity of the surface on which it moves, and for triggering reflexive turns of the BBD in its environment. 
     A variety of presynaptic, postsynaptic and plasticity calculations can be used. The neural model is not to be limited to the presynaptic, postsynaptic and plasticity calculations in the examples given below. 
       FIG. 3A  is an embodiment that shows an example of a core  300 . In this example, the core  300  includes presynaptic calculations  302 , postsynaptic calculations  304  and plasticity calculations  306 . In one embodiment, the plasticity calculations  306  can include activity dependent synaptic activity  306   a  and value dependent synaptic activity  306   b .  FIG. 3A  also shows how the information can be passed into the core  300 . In this embodiment, the plasticity calculations  306  receive the PSP output signals S new  from the postsynaptic calculations  304 . The plasticity calculations  306  can use S new  and a value delay term, d, to produce updates for the weights in the weight table, which can be written back out to memory. The presynaptic calculation  302  can use the m weights and m input values to sum in a presynaptic calculation. This can then be sent to the postsynaptic calculation  304  that uses an output of the presynaptic calculations  302  as well as the previously stored PSP output for the last epoch, which can be stored locally. The PSP output from the core  300  can be sent back to the output storage table and the modified weights can be written back into the weight table. 
       FIG. 3B  illustrates an implementation of the core  320 . The m input data and m weights are looped through multiply unit  322  and then summed in the accumulator  324 . The postsynaptic processing of block  326  can include, in one embodiment, a multiplication and a shift or two multiplications along with a comparison and a lookup table operation. The postsynaptic calculations  328  can include a single table lookup plus m subtractions, m comparisons and up to m additions. The weight data can be written out to memory  330  for the next epoch. The PSP output can be stored locally and transferred to the output storage tables to be used by the other neural elements in the future. 
       FIG. 4  illustrates a flowchart of the operation of one embodiment of a BBD using a SPP. In step  400 , the neural stimulation begins. In step  402 , sensor data is received. The sensor data can be directly provided to or processed to provide input(s) to neural element(s). In step  403 , commands are accepted. These commands include quit commands, override commands or the like which can be done after the end of every epoch. In step  404 , it is checked whether the BPP is to be halted in step  405 . Steps  406 ,  407  and  408  illustrate calculations for one timeslice. In step  406  the presynaptic and postsynaptic calculations are done in each neural processing unit. In step  407 , the connection weights are updated. In step  408 , outputs and modified connections weights are sent to memory. As discussed above, these steps  406 - 408  can be done in parallel for each of the cores. In step  409 , if there is any remaining timeslices in the epoch, the next timeslice calculation begins. Steps  406 - 408  are repeated for each timeslice in the epoch. In step  412 , PSP outputs can directly provide or be processed to provide signals for actuators of a BBD. 
     In various embodiments, the PSP output can be a mean firing rate, s. In one embodiment, s can range from 0 (quiescent) to 1 (maximal firing). The state of a neuronal element can be updated as a function of its current state and contributions from other neuronal elements. 
     The m inputs for each neural element can be indicated as s 1  to s m . The s values can be an unsigned byte of data. The m weights for each neural element can be indicated as c 1  to c m . The c values can be a single signed byte. The presynaptic processing can be expressed by the equation: 
               A   ⁡     (   t   )       =       ∑     j   =   1     m     ⁢       c   ij     ⁢     s   j               
where t indicates the current epoch. This can be implemented by using a multiplier, such as the 18×18 multiplier on the Virtex™-II Xilix™ FPGA.
 
     The postsynaptic processing can be given by:
 
 S   new =φ(tan  h ( g ( A ( t )+ω S   old ))
 
where A(t) is the current presynaptic output given above, S new  is the current PSP output value of the neural element, S old  is the PSP output value of the neural element in the last epoch, g is a scale coefficient and t is a persistence coefficient. tan h(x) which provides compression into the range −1 to 1.
 
     φ(x) is a trigger function given by: 
               ϕ   ⁡     (   x   )       =           0   ;     x   &lt;   δ                 x   ;   otherwise                 
where δ is a trigger coefficient.
 
The trigger function φ(x) along with the tan h(x) function ensures that S new  is between 0 and 1. The S new  value can be sent to the output storage table. The S new  value can also be stored locally to be used as S old  in the next epoch.
 
     The postsynaptic processing can be implemented in the FPGA as follows. The S old  value can be multiplied by ω, the persistence parameter. Assuming that ω is restricted to a value in the series ½, ¼, ⅛. . . , the multiplication can be implemented by a shift. The result of the multiplication (or shift) can be added to the A(t) value from the presynaptic processing. The result of the addition can be multiplied by the scale coefficient, g, in a multiplier, such as the 18×18 multiplier of the Virtex™-II Xilinx™ FPGA to produce a temp value. The temp value can be used as an input to the function φ(tan h(temp)) implemented as LUT 1  to determine S new . Thus:
 
 S   new   =LUT   1   [g ( A ( t )+( S   old   &gt;&gt;W ))]
 
where S old   &gt;&gt;W is right shift W spaces which is the same as ωS   old , where ω=2 −W .
 
     Alternately, the temp value can be compared to tan h −1 (δ), which is a constant, and if temp&gt;=tan h −1 (δ), the temp value can be used as an input to the function tan h(temp) implemented as LUT 1′  to determine S new . Otherwise, S new =0. This alternate embodiment can allow sharing of the LUT 1′  between cores of different neural types. 
     Thus: 
     
       
         
           
             
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     The plasticity processing can be given by:
 
Δ c   j =ε( c   j (0)− c   j ( t ))+η SF ( S ); without value dependency
 
 Δc   j =ε( c   j (0)− c   j ( t ))+η SF ( S ) V ( d ); with value dependency
 
where Δc j =ε(c j (0)−c j (t)) is the forgetting rule, ηSF(S) is the value independent learning rule and ηSF(S)V(d) is the value dependent learning rule. c j (0) is the initial weight for the jth input and c j (t) is the current weight for the jth input. ε is a decay constant, η is a learning rate constant. S is a post synaptic output, such as S new .
 
     F(S) can be given by: 
               F   ⁡     (   S   )       =           0   ;             for   ⁢           ⁢   S     &lt;     θ   1                     κ   1     ⁡     (       θ   1     -   S     )       ;               for   ⁢           ⁢     θ   1       &lt;   S   &lt;         θ   1     +     θ   2       2       ⁢                           κ   1     ⁡     (     S   -     θ   2       )       ;             for   ⁢           ⁢         θ   1     +     θ   2       2       &lt;   S   &lt;     θ   2                     κ   2     ⁢     tanh   ⁡     (     ρ   ⁡     (     s   -     θ   2       )       )         ρ             for   ⁢           ⁢   S     &gt;     θ   2                   
Where θ 1  and θ 2  are threshold constants with (0&lt;θ 1 &lt;θ 2 &lt;1), κ 1  and κ 2  are inclination constants, and ρ is a saturation parameter, which can be 6 for all cores.
 
     V(d) can be a function that relates to the intensity of the value learning. This function or an associated look up table can be adjusted as desired. 
     In one embodiment V(d) is given by: 
               V   ⁡     (   d   )       =     1   +       f   ⁡     (   d   )       ⁢         S   _     +       V   ⁡     (     d   -   1     )       ⁢     (     d   -   1     )         d               
where d is a delay, such as the number of epochs since the start of the value dependent event. When no value learning is being done, d can be defined to be 0 with V(d=0) defined to be 1. The d values during value learning can range from 1 to d max , where d max *(epoch period) is the value learning period. Thus, in one example, an epoch is 10 ms and the desired value learning period is 900 ms, so d max  is 90. f(d) can be a function that starts at about 0, reaches a peak of 1 and returns to about 0 at d max . f(d) can be used to delay the initiation of and spread the operation of value learning. One possible series for f(d) can be defined by a curve including the points f(d max /9)=0.1, f(2d max /9)=0.1, f(3d max /9)=0.3, f(4d max /9)=0.7, f(5d max /9)=1.0, f(6d max /9)=1.0, f(7d max /9)=0.7, f(8d max /9)=0.3, f(d max )=0.1.  S  can be average activity value in an area S. V(d−1) can be the value of V in the previous epoch.
 
     The plasticity can be implemented on an FPGA as follows. The S new  value can be used as an input to the function ηS F(S) implemented as LUT 2  to get a Temp 1  value. If a Value_Enabled flag is set, the d, or Value_term, can be used as an input to the function 
             1   +       f   ⁡     (   d   )       ⁢         S   _     +       V   ⁡     (     d   -   1     )       ⁢     (     d   -   1     )         d             
implemented as LUT 3  to get a Temp 2  value and the learning rule term is given by Temp 1 *Temp 2 . Otherwise the learning rule term is given by Temp 1 .
 
     In one embodiment, the LUT 3  lookup and a multiplication is done when the Value_Enabled flag is not set so the processing time, and thus potentially the epoch length, is not longer during the value learning period. If it is desirable to have specific neural type(s) not implement value learning, these cores of these neural type(s) can have a LUT 3  that includes dummy values. 
     For each of the m weights, the forgetting rule portion can be approximated by doing a subtraction of a coefficient E from the current weight, checking whether this subtraction value is less than the original weight and then adding the greater of the original weight or the subtraction value to the forgetting rule portion. This approximation only requires a subtraction and a compare for each of the m weights rather than a multiplication. Thus: 
     
       
         
           
             
               
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                         ⁡ 
                         
                           [ 
                           S 
                           ] 
                         
                       
                       * 
                       
                         
                           LUT 
                           3 
                         
                         ⁡ 
                         
                           [ 
                           d 
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       for 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               c 
                               j 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           - 
                           E 
                         
                         ) 
                       
                     
                     &gt; 
                     
                       
                         c 
                         j 
                       
                       ⁡ 
                       
                         ( 
                         0 
                         ) 
                       
                     
                   
                 
               
               
                 
                   
                     
                       
                         c 
                         j 
                       
                       ⁡ 
                       
                         ( 
                         0 
                         ) 
                       
                     
                     + 
                     
                       
                         
                           LUT 
                           2 
                         
                         ⁡ 
                         
                           [ 
                           S 
                           ] 
                         
                       
                       * 
                       
                         
                           LUT 
                           3 
                         
                         ⁡ 
                         
                           [ 
                           d 
                           ] 
                         
                       
                     
                   
                 
                 
                   otherwise 
                 
               
             
           
         
       
     
     When the Value_Enabled flag is not set, d can have a value of 0 and LUT 3 [d=0] can have a value of 1, so that LUT 2 [S]*LUT 3 [d=0]=LUT 2 [S] which gives the value independent learning rule. Similarly, LUT 3 [x] can be 1 for all x in cores that don&#39;t do value learning. The size of LUT 3  can be kept small by using fewer values than the total number of epochs of the learning period. In one embodiment, groups of epochs since the initiation of value learning can have the same d value. For example, epochs 1-10 can correspond to d=1, epochs 11-20 can correspond to d=2 . . . and so on. 
     Coefficients that are unique to each core can include w (or W) and g which are post-synaptic scale factors, the Phi threshold and the tan h lookup table (LUT 1 ) for the post-synaptic calculations. For the plasticity function, the core specific variables can be the F*n lookup table (LUT 2 ), the decay constant E and the variables associated with value learning, such as LUT 3 . Exemplary code to implement the calculations is given in APPENDIX I. 
     The example given above doesn&#39;t use phase information in the neural model of the SPP. This simplifies the calculations and can allow the cores to run faster and use fewer FPGA resources. In one embodiment, the SPP can be a neural model that takes phase information into account and/or distinguish contributions of voltage-independent, voltage-dependent, and phase-independent synaptic connectors. 
     A phase can be associated with each of the PSP output values. For example, a phase (p) can be divided into discrete values representing the relative timing of activity of the neuronal units by an angle ranging from 0 to 2π. If five bits are used to encode the phase, 32 discrete phases can be encoded. In one embodiment, the output of each neuronal element can include a byte to encode the s value and a byte to encode the p value. The s and p values can be transferred as a pair in the SPP, effectively doubling the storage requirements in the output storage table and transmission requirements for the PSP outputs. The presynaptic, postsynaptic and plasticity calculations in the cores are also complicated when p values are used. Examples of phase-dependent presynaptic, postsynaptic and plasticity calculations that can be adapted for use in an SPP are given in the article, Seth et al., “Visual Binding Through Reentrant Connectivity and Dynamic Synchronization in a Brain-based Device” Cerebral Cortex V14 N11 p. 1185-1199, incorporated herein by reference. Exemplary coefficients, including coefficients for determining the LUTs, are given in Tables 1 and 2 for different neural types. 
     
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Neuronal unit parameters 
               
             
          
           
               
                 Area 
                 Size 
                 σ-fire 
                 σ-phase 
                 σ-vdep 
                 ω 
                 G 
               
               
                   
               
               
                 V1 (6) 
                 60 × 80 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 V2 (6) 
                 30 × 40 
                 0.10 
                 0.45 
                 0.05 
                 0.30 
                  1.0* 
               
               
                 V4 (6) 
                 15 × 20 
                 0.20 
                 0.45 
                 0.10 
                 0.50 
                  1.0* 
               
               
                 C 
                 15 × 20 
                 0.10 
                 0.10 
                 0.10 
                 0.50 
                 1.0 
               
               
                 IT 
                 30 × 30 
                 0.20 
                 0.20 
                 0.10 
                 0.75 
                 1.0 
               
               
                 S 
                 4 × 4 
                 0.10 
                 0.00 
                 0.00 
                 0.15 
                 1.0 
               
               
                 Mic- 
                 1 × 1 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 Mic-left 
                 1 × 1 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 A-left 
                 4 × 4 
                 0.00 
                 0.00 
                 0.10 
                 0.50 
                 1.0 
               
               
                 A-right 
                 4 × 4 
                 0.00 
                 0.00 
                 0.10 
                 0.50 
                 1.0 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Properties of anatomical projections and connection types 
               
             
          
           
               
                 Projection 
                 Arbor 
                 P 
                 c ij (0) 
                 type 
                 η 
                 θ 1   
                 θ 2   
                 k1 
                 k2 
               
               
                   
               
             
          
           
               
                 V1-&gt;V2 
                 [ ] 0 × 0 
                 1.00 
                 1, 2 
                 PI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V2→V2(intra) 
                 [ ] 3 × 3 
                 0.75 
                 0.45, 0.85 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V2→V2(inter) (X) 
                 [ ] 2 × 2 
                 0.40 
                 0.5, 0.65 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V2→V2(intra) 
                 Θ 18, 25 
                 0.10 
                 −0.05, −0.1 
                 VI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V2→V2(inter) 
                 [ ] 2 × 2 
                 0.05 
                 −0.05, −0.1 
                 VI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V2→V4 
                 [ ] 3 × 3 
                 0.40 
                 0.1, 0.12 
                 VI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V4→V2 (X) 
                 [ ] 1 × 1 
                 0.10 
                 0.25, 0.5 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V4→V4(inter) (X) 
                 [ ] 2 × 2 
                 0.40 
                 1.75, 2.75 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V4→V4(intra) 
                 Θ 10, 15 
                 0.10 
                 −0.15, −0.25 
                 VI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V4→V4(inter) 
                 Θ 10, 15 
                 0.10 
                 −0.15, −0.25 
                 VI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V4→V4(inter) 
                 [ ] 2 × 2 
                 0.03 
                 −0.15, −0.25 
                 VI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V4→C 
                 [ ] 3 × 3 
                 1.00 
                 0.002, 0.0025 
                 VI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 V4→IT 
                 special 
                 — 
                 0.1, 0.15 
                 VI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 IT→V4 (X) 
                 non-topo 
                 0.01 
                 0.05, 0.07 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 IT→IT 
                 non-topo 
                 0.10 
                 0.14, 0.15 
                 VD 
                 0.10 
                 0 
                 0.866 
                 0.90 
                 0.45 
               
               
                 IT→C # 
                 non-topo 
                 0.10 
                 0.2, 0.2 
                 VD 
                 1.00 
                 0 
                 0.707 
                 0.45 
                 0.65 
               
               
                 IT→S # 
                 non-topo 
                 1.00 
                 0.0005, 0.001 
                 VI 
                 0.10 
                 0 
                 0.707 
                 0.45 
                 0.45 
               
               
                 C→V4 (X) 
                 non-topo 
                 0.01 
                 0.05, 0.07 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 C→C 
                 Θ 6, 12 
                 0.50 
                 −0.05, −0.15 
                 PI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 C→Mleft 
                 non-topo 
                 1.00 
                 35, 35 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 C→Mright 
                 non-topo 
                 1.00 
                 35, 35 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 S→C 
                 non-topo 
                 0.50 
                 0.5, 05 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 S→S 
                 non-topo 
                 0.50 
                 0.7, 0.8 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 A-left→C 
                 left-only 
                 1.00 
                 0.5, 0.5 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 A-right→C 
                 right-only 
                 1.00 
                 0.5, 0.5 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 A-left→C 
                 right-only 
                 1.00 
                 −0.15, −0.15 
                 PI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 A-right→C 
                 left-only 
                 1.00 
                 −0.15, −0.15 
                 PI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 A-left→S 
                 non-topo 
                 1.00 
                 35, 35 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 A-right→S 
                 non-topo 
                 1.00 
                 35, 35 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 A-left ⇄A-right 
                 non-topo 
                 1.00 
                 −1, −1 
                 PI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 A-left ⇄A-right 
                 non-topo 
                 1.00 
                 −0.5, −0.5 
                 VD 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                 Mic-left, Mic-right→A-left, A-right 
                 non-topo 
                 1.00 
                 5, 5 
                 PI 
                 0.00 
                 0 
                 0 
                 0.00 
                 0.00 
               
               
                   
               
             
          
         
       
     
       FIG. 1C  is a schematic diagram of an exemplary regional and functional neuroanatomy of a neural model which can guide the behavior of the BBD in its environment. These regions can be implemented as cores of an SPP. The neural model can be modeled on the anatomy and physiology of the mammalian nervous system but, as can be appreciated, with far fewer neurons and a much less complex architecture. The neural model can include a number of neural areas labeled according to the analogous cortical and subcortical regions of the human brain. Thus,  FIG. 1C  shows respective neural areas labeled as V 1 , V 2 , V 4 , IT, S, A-left, Mic-left, A-right, Mic-right and C, whose activity controls the tracking of a BBD. Each neural area V 1 , V 2 , etc. contains different types of neuronal units, each of which represents a local population of neurons. Each ellipse shown in  FIG. 1C  (except “tracking”) denotes a different neural area, with each such area having many neuronal units. 
     The neuroanatomy of  FIG. 1C  also shows schematically various projections P throughout the neural model. A projection can be “feedforward” from one neural area to another, such as the projection P 1  from neural area V 1  to neural area V 2 . A projection P may also be “reentrant” between neural areas such as the reentrant projection P 2  from neural area IT to neural area V 4  and reentrant projection P 4  from neural area V 4  to neural area V 2 . Reentrant projections P marked with an “X” were removed from the neural model during “lesion” experiments as will be further described. Furthermore, projections P have properties as indicated by the legend in  FIG. 1C , which are (1) “excitatory voltage independent,” (2) “excitatory voltage dependent,” (3) “plastic,” (4) “inhibitory,” and (5) “value dependent.” 
     The neural model shown in  FIG. 1C  can be comprised of four systems: a visual system, a tracking system, an auditory system and a value system. Other systems with other inputs and outputs can also be used. 
       FIG. 1C : The Visual System. Neural Areas V 1 , V 2 , V 4 , IT 
     The visual system can be modeled on the primate occipitotemporal or ventral cortical pathway and includes neural areas V 1 →V 2 →V 4 →IT in which neurons in successive areas have progressively larger receptive fields until, in the inferotemporal cortex, receptive fields cover nearly the entire visual field. Visual images from a camera can be filtered for color and edges and the filtered output directly influences neural activity in area V 1 . V 1  can be divided into subregions (not shown) each having neuronal units that respond preferentially to green (V 1 -green), red (V 1 -red), horizontal line segments (V 1 -horizontal), vertical line segments (V 1 -vertical), 45-degree lines (V 1 -diagonal-right), and 135-degree lines (V 1 -diagonal-left). This visual system provides a computationally tractable foundation for analyzing higher-level interactions within the visual system and between the visual system and other cortical areas. 
     Subregions of neural area V 1  can project topographically to corresponding subregions of neural area V 2 . The receptive fields of neuronal units in area V 2  can be narrow and correspond closely to pixels from the image of a camera. Neural area V 2  can have both excitatory and inhibitory reentrant connections within and among its subregions. Each V 2  subregion can project to a corresponding V 4  subregion topographically but broadly, so that neural area V 4 &#39;s receptive fields are larger than those of neural area V 2 . Neural area V 4  subregions can project back to the corresponding neural area V 2  subregions with non-topographic reentrant connections. The reentrant connectivity within and among subregions of area V 4  is similar to that in area V 2 . V 4  projects in turn non-topographically to neural area IT so that each neuronal unit in neural area IT can receive input from three V 4  neuronal units randomly chosen from three different V 4  subregions. Thus, while neuronal units in IT respond to a combination of visual inputs, the level of synaptic input into a given IT neuronal unit is fairly uniform; this prevents the activity of individual IT neuronal units from dominating the overall activity patterns. IT neuronal units project to other IT neuronal units through plastic connections, and back to neural area V 4  through non-topographic reentrant connections. 
       FIG. 1C : The Tracking System. Neural Area C 
     The tracking system allows the BBD to orient towards auditory and visual stimuli. The activity of neural area C (analogous to the superior colliculus) can dictate where the BBD directs its camera gaze. Tracking in the BBD can be achieved by signals to wheels or tracks based on the vector summation of the activity of the neuronal units in area C. Each neuronal unit in area C can have a receptive field which matches its preferred direction, and the area has a topographic arrangement such that if activity is predominately on the left side of area C, signals to the BBD wheels are issued that evoke a turn towards the left. The auditory neural areas (A-left and A-right) can have strong excitatory projections to the respective ipsilateral sides of area C causing the BBD to orient towards a sound source. Neural area V 4  projects topographically to area C, its activity causing the BBD to center its gaze on a visual object (e.g. a red triangle). Both neural areas IT and the value system S project to area C, and plastic connections in the pathways IT-&gt;C and IT-&gt;S facilitate target selection by creating a bias in activity, reflecting salient perceptual categories (see Value System, below). As will be described below, prior to a conditioning or training stage, because of a lack of bias, the BBD will direct its gaze predominately between two objects in its environment (e.g. a red triangle and a red square). After learning to prefer a visual object (e.g. a red triangle), changes in the strengths of the plastic connections can result in greater activity in those parts of area C corresponding to the preferred object&#39;s position. 
       FIG. 1C : The Auditory System, Neural Areas Mic-left, Mic-right, A-left, A-right 
     This system converts inputs from microphones into simulated neuronal unit activity. In one embodiment, Neural areas Mic-left and Mic-right can be respectively activated whenever the corresponding microphones  16 ,  18  detect a sound of sufficient amplitude within a specified frequency range. Mic-left/Mic-right project to neuronal units in areas A-left/A-right. Sound from one side can result in activity on the ipsilateral side of the auditory system, which in turn produces activity on the ipsilateral side of area C causing orientation of the BBD towards the sound source. 
       FIG. 1C : The Value System, Neural Area S 
     Activity in the simulated value system can signal the occurrence of salient sensory events and this activity contributes to the modulation of connection strengths in pathways IT→S and IT→C. Initially, in the learning stage to be described below, neural area S is activated by sounds detected by the auditory system (see A-left→S and A-right→S of nervous system  12 ). Activity in area S can be analogous to that of ascending neuromodulatory systems in that it is triggered by salient events, influences large regions of the neural model (described below in the section Synaptic Plasticity), and persists for several cycles. In addition, due to its projection to the tracking area C, area S has a direct influence on the behavior of the BBD in its real-world environment. 
     Details of the values of certain parameters of the neuronal units within the respective neural areas V 1 , V 2 , etc. shown in  FIG. 1C  are given in Table 1, described above. Details of the anatomical projections and connection types of neuronal units of the neural areas V 1 , V 2 , etc. are given in Table 2, described above. As is known, a neuronal unit can be considered pre- or post-a synapse (see “Universe of Consciousness” by Edelman and Tononi, Basic Books, 2000, FIG. 4.3, for a description of a synapse and pre- and post-synaptic neurons). 
     Neuronal Units Generally 
     In one embodiment, a neuronal unit within a neural area V 1 , V 2 , etc. of the neural model  12  is simulated by a mean firing rate model. The state of each neuronal unit is determined by both a mean firing rate variable (σ) and a phase variable (P). The mean firing rate variable of each neuronal unit corresponds to the average activity or firing rate of a group of roughly 100 neurons during a time period of approximately 100 milliseconds. The phase variable, which specifies the relative timing of firing activity, provides temporal specificity without incurring the computational costs associated with modeling of the spiking activity of individual neurons in real-time (see Neuronal Unit Activity and Phase, below). 
     Synaptic Connections—Generally 
     In one embodiment, synaptic connections between neuronal units, both within a given neural area, e.g. V 1  or C, and between neural areas, e.g. V 2 →V 4  or C→V 4 , are set to be either voltage-independent or voltage-dependent, either phase-independent or phase-dependent, and either plastic or non-plastic. Voltage-independent connections provide synaptic input to a post-synaptic neuron regardless of the post-synaptic state of the neuron. Voltage-dependent connections represent the contribution of receptor types (e.g. NMDA receptors) that require post-synaptic depolarization to be activated. In other words, a pre-synaptic neuron will send a signal along its axon through a synapse to a post-synaptic neuron. The post-synaptic neuron receives this signal and integrates it with other signals being received from other pre-synaptic neurons. 
     A voltage independent connection is such that if a pre-synaptic neuron is firing at a high rate, then a post-synaptic neuron connected to it via the synapse will fire at a high rate. 
     A voltage dependent connection is different. If the post-synaptic neuron is already firing at some rate when it receives a pre-synaptic input signal, then the voltage-dependent connection will cause the post-synaptic neuron to fire more. Since the post-synaptic neuron is active, i.e. already firing, this neuron is at some threshold level. Therefore, the pre-synaptic connection will modulate the post-synaptic neuron to fire even more. The voltage-dependent connection, no matter how active the pre-synaptic neuron is, would have no effect on the post-synaptic neuron if the latter were not above the threshold value. That is, the post-synaptic neuron has to have some given threshold of activity to be responsive or modulated by a voltage-dependent synaptic connection. 
     In the neural model of  FIG. 1C , all within-neural area excitatory connections and all between-neural area reentrant excitatory connections can be voltage-dependent (see  FIG. 1C  and Table 2). These voltage-dependent connections, as described above, play a modulatory role in neuronal dynamics. 
     Phase-dependent synaptic connections influence both the activity, i.e. firing rate, and the phase of post-synaptic neuronal units, whereas phase-independent synaptic connections influence only their activity. All synaptic pathways in the neural model can be phase-dependent except those involved in motor output (see Table 2: A-left/A-right→C, C→C) or sensory input (see Table 2: Mic-left/Mic-right→A-left/A-right, A-left→A-right, V 1 →V 2 ), since signals at these interfaces are defined by magnitude only. Plastic connections are either value-independent or value-dependent, as described below. 
     Neuronal Unit Activity and Phase Details 
     As shown in Table 1, area V 1  can be an input neural area and its activity can be set based on the image of a camera. Neural areas V 1 , V 2  and V 4  can have six sub-areas each with neuronal units selective for color (e.g. red and green), and line orientation (e.g. 0, 45, 90 and 135 degrees). Neural areas Mic-left and Mic-right can be input neural areas and their activity is set based on inputs from microphones. 
     Table 1 also indicates the number of neuronal units in each neural area or sub-area (“Size” column). Neuronal units in each area apart from neural areas V 1 , Mic-left and Mic-right have a specific firing threshold (σ-fire), a phase threshold (σ-phase), a threshold above which voltage-dependent connections can have an effect (σ-vdep), a persistence parameter (ω), and a scaling factor (g). 
     Table 2 shows properties of anatomical projections and connection types of the neural model. A pre-synaptic neuronal unit connects to a post-synaptic neuronal unit with a given probability (P) and given projection shape (Arbor). This arborization shape can be rectangular “[ ]” with a height and width (h×w), doughnut shaped “θ” with the shape constrained by an inner and outer radius (r 1 , r 2 ), left-only (right-only) with the pre-synaptic neuronal unit only projecting to the left (right) side of the post-synaptic area, or non-topographical (“non-topo”) where any pairs of pre-synaptic and post-synaptic neuronal units have a given probability of being connected. The initial connection strengths, C i (0), are set randomly within the range given by a minimum and maximum value (min, max). A negative value for C i (0), indicates inhibitory connections. Connections marked with “intra” denote those within a visual sub-area and connections marked with “inter” denote those between visual sub-areas. Inhibitory “inter” projections connect visual sub-areas responding to shape only or to color only (e.g. V 4 -red→V 4 -green, V 4 -horizontal→V 4 -vertical), excitatory “inter” projections connect shape sub-areas to color sub-areas (e.g. V 4 -red→V 4 -vertical). Projections marked # are value-dependent. A connection type can be phase-independent/voltage-independent (PI), phase-dependent/voltage-independent (VI), or phase-dependent/voltage-dependent (VD). Non-zero values for η, θ 1 , θ 2 , k 1 , and k 2  signify plastic connections. The connection from V 4  to IT was special in that a given neuronal unit in area IT was connected to three neuronal units randomly chosen from three different V 4  sub-areas. 
     In this model of a neuronal unit, post-synaptic phase tends to be correlated with the phase of the most strongly active pre-synaptic inputs. This neuronal unit model facilitates the emergence of synchronously active neuronal circuits in both a simple network and in the full neural model ( FIG. 1C ), where such emergence involves additional constraints imposed by reentrant connectivity, plasticity, and behavior. 
     Synaptic Plasticity 
     Synaptic strengths are subject to modification according to a synaptic rule that depends on the phase and activities of the pre- and post-synaptic neuronal units. Plastic synaptic connections are either value-independent (see IT→IT in  FIG. 1C ) or value-dependent (see IT→S, IT→C in  FIG. 1C ). Both of these rules can be based on a modified BCM learning rule in which thresholds defining the regions of depression and potentiation are a function of the phase difference between the pre-synaptic and post-synaptic neuronal units (see  FIG. 1C , inset). 
     Looking at  FIG. 2 , which is a diagram of a neural model using a special purpose processor, the host PC  208  can initialize the tables and the coefficients. It can then download this data to the processor  210 , such as a Power PC, which can be part of the FPGA. The host PC  208  can maintain an interactive connection to the processor to monitor the network and upload the ‘learned’ data. In an alternate embodiment, the FPGA can act independently of a host PC. 
     The processor  210 , such as Power PC, can provide administrative services for the network. The processor can maintain an interactive connection with the host PC  208 . The processor  210  can download initial weights, PSP data, and connection tables into off-chip memory  204  and  206 , such as DRAM, can also initialize the on-chip memory  202 , such as Block Random Access Memory (BRAM), with the various LUTs for the equations, as well as coefficients and any indices. The processor  210  can also perform real time metrics on the health and activity of the network, i.e. databus usage, percentage of offchip connections, mean PSP values etc. 
     The off-chip memory  204  and  206 , such as the DRAM, can hold the stored data of the neural simulation. This data can include but is not limited to the weights for the presynaptic processing, the output data, also called “Post-Synaptic Potential” (PSP) data, and the connection table that indicates the interconnection of the neural elements. 
     The on-chip memory  202 , such as BRAM, can hold small coefficients and LUTs as well as be a FIFO for the PSP and weight data being processed by each element. In addition to the Weights, PSP data, and Connection Tables that are loaded at execution time each element can have stored locally a unique Original weight and its PSP from the previous epoch. APPENDIX II shows exemplary memory requirements for a system of one embodiment. 
       FIGS. 5A-5D  illustrate the transfer of inputs, outputs and weights of one embodiment of the present invention. The transfers of the inputs, outputs and weights can be in a predetermined order that does not require a complex addressing scheme for the data. The inputs, outputs and weights can be transferred in the predetermined order so that the memory knows what core is the source of the data, for example. The data in the output storage tables, current weight table and connection table can be addressable according to this predetermined order. In one embodiment the data is written into these tables according to a neural element number. For example, the data can be transferred according to the order, (Core  0 , timeslice  0 ), (Core  1 , timeslice  0 ) . . . (Core  255 , timeslice  0 ), (Core  0 , timeslice  1 ) . . . (Core  254 , timeslice  255 ), (Core  255 , timeslice  255 ) and then loop to repeat the order for the next epoch. 
     Looking at  FIG. 5A , the connection table  502  can be instructed to get the next m pointers, which are the pointers to the source neural elements for the current core, in this case core  58 . The m pointers from the connection table  502 , indicating the source neural elements, can be sent to an output storage table  504  to get the PSP input data for core  58 . The next m weights can be obtained from the current weights table  506  to be provided to the core  58 . These m weights can be ordered such they correspond to the PSP input data. The m PSP values and m weights can then be processed by the core  58 .  FIG. 5B  shows these steps repeated for core  59 . 
       FIG. 5C  shows the writing of data back to an output storage table  508  and the current weight table  506 . The core can write the data to memory following the predetermined order. In the example of  FIG. 5C , the output of core  35  is written into the output storage table  508  while the m updated weights of core  34  are written to the current weight table  506 .  FIG. 5D  shows these steps repeated for the next cores. 
     One embodiment of the present invention is a scalable FPGA based architecture to model the neural elements and their interconnections. The architecture can simulate as many elements as possible on a single chip, and can provide an interconnection scheme to allow for connections to a large number of similar chips. The high speed of the FPGA circuitry can provide the ability to share resources to model large numbers of neural elements. The resources to be shared can include the calculating engines that perform the presynaptic (such as the sum-of-products), postsynaptic, and plasticity (such as activity-dependent and value-dependent processes) calculations. The sharing and some parallel replication of circuitry can allow for the modeling of large quantities of elements. Along with all of this, a means to preload the elements&#39; initial conditions and read their final state of the simulation can be provided. Finally, in order to make this a useful tool for simulating a variety of neural processes, a means to reconfigure the interconnections at the beginning of the simulation can be provided. 
     One challenge in the design is representing all of the elemental computation units and routing the data between all the elements in the network. In one embodiment, each element can have as many as 256 inputs (and associated weights). A simple network of connections, tying together a pool of elemental computation units, would use up the available routing resources rather quickly. This approach would also require significant reconfiguring of the FPGA for each new model of interconnections. 
     Instead of each element having its own computation engine and all of its inputs and outputs routed individually on the chip, a scheme of shared computation engines (neural processing units, also called or NPU&#39;s or “cores”) and a common data distribution bus is proposed. Over the course of a single epoch period, an individual neural element&#39;s inputs and their respective weights can be delivered to a core. The core can execute the sum-of-products, and post-synaptic and learning processes, creating a single output and updated weights for the neural element. This data set can be returned to a storage table to be used in the next epoch, while another element&#39;s data is passed to the core. Given the length of the epoch and the speed in which the core can calculate an element&#39;s processes, a single core can serve many elements. If the number of elements is increased, larger quantities of elements&#39; calculations can be executed. In one embodiment, with 128 cores on a chip, each can serve up to 256 elements in the time period of the epoch, resulting in the simulation of 32768 neural elements. Fewer cores can be used and still permit the modeling of the same number of neural elements, if each core is shared amongst a larger number of elements. 
     The common data distribution bus can deliver the input values for each element along with the weight factor for each input to the assigned NPU. The weight data values can be strictly associated with each element, so they can delivered sequentially from an SDRAM large storage memory. As each element&#39;s data is needed in sequence, the SDRAM will be addressed and the data sent along the data bus to the core being used for that element. The input data values represent the outputs of other elements from the previous epoch. 
     In one embodiment, there can be 32768 elements on each chip which means the same number of stored values are available as possible inputs to any given element. In order to accommodate the future expansion of the simulation to include outputs from other elements located on other chips, an additional amount of storage for those off chip sourced values is needed. For now, the amount of data needed for that purpose is assumed to be no more than 32768. This gives a pool of 65536 data values to pull the inputs for the elements from. They can be kept in what are called the Output Storage Tables (OST). Each element will need up to 256 of these values, selected from throughout the data set, as e.g. element # 1  could have inputs from elements  34 ,  456 ,  1093 , etc., while elements # 2  could have inputs from elements  1 ,  6 ,  12 ,  456 , etc. Other configurations determined for models of other neural anatomy could redefine these connections. 
     Because of this, a means of supplying a list of input sources picked from among the 65536 values in the table is proposed. Another large storage SDRAM memory can be used. The SDRAM can be accessed sequentially, similar to the weight table, but the data that will be presented by each address in the SDRAM will be a pointer to the Output Storage Tables. The data in the OST will be the outputs of each element during an epoch and the data in the SDRAM, which will be static, will be a pointer to a location in the OST that holds the value to be used be the element at the time. The data in this SDRAM is called the Input Pointers. The additional advantage of this approach is that to reconfigure the neural simulation for another model involving different connections will require only reloading the SDRAM with a different set of addresses in the OST. No reconfiguration of the FPGA would be needed. 
     In order for a given neural system model to run on this system, the weight tables and input pointers can be loaded in SDRAM. Also, the coefficients used in the post synaptic and learning processes can be pre-loaded. A processor on the FPGA can be employed for this. As the system is powered up, the processor will load the data from files it can receive via a network connection (e.g. TCP/IP). After the data is loaded, the processor will set a flag and the neural simulation can run on its own. The sequence of fetching and loading the inputs and weights from memory can repeat for every element as output values are generated and returned to memory to be used in the next epoch. The Process will repeat as long as the experiment calls for at which point the processor can intervene to stop the process and download the data from the tables for analysis. 
     The success of this design relies on the ability to pre-configure the interconnections between the elements offline before the process is executed. The offline software can work through an input list of desired connections and translate these connections to the element/NPU architecture of the FPGA based system. This place-and-route tool can place elements that share many connections together in the same chip to minimize inter-chip data transfer. The tool will also need to translate that placement into a list of data values that would be loaded into the input pointer table and the off-chip link module. 
     The processor interface module  602  ( FIG. 6 ) responds to the processor  604  program environment. It can be connected to the processor  604  via the on-chip peripheral bus  606  and feature an address decode space that can allow the processor  604  to set operating modes and download and upload information from the Neural Processing System registers and memory. 
     FMS controller module  608  can run in a continuous loop setting System Bus Addresses and other flags to actuate latches and mux&#39;s to route the data to and from the SDRAM and Output Storage Tables  610 . It can be able to be started and interrupted by commands sent to the processor interface  602 . 
     The SDRAM controller module  612  can oversee all interaction with the SDRAM. It can buffer page streams, both reading and writing, with the SDRAM. The SDRAM Controller module  612  can provide a simple synchronous port to the rest of the neural processing system  600  for reading and writing 32 bit words from or to the SDRAM&#39;s buffered data. SDRAM controller module  612  can also manage the auto-refresh cycle for the SDRAM. 
     The output storage table  610  can be a large block of BRAM that holds the output PSP values from the neural processes. The BRAM can be dual port, allowing reading and writing from each port. Each BRAM block can be 65,536 bytes. This number is derived from the need to store the outputs of 128 cores×256 element&#39;s outputs per each core (256 timeslices) and to store an equal number of data values from off-chip element outputs. There can be two banks of these memories; one is for storing data from the current epoch and the other is for writing the output from the current epoch. The role of each bank (reading or writing) can be exchanged with each epoch providing a so called ping-pong buffer. 
     Neural Processing Unit (CPU or core)  614  can include the calculation engine for the neural simulation. Each core can serve to perform the calculations for 256 neural elements. The data from the SDRAM and the PSP storage table can be routed to each core sequentially, and the core can perform the algorithm on this input data. The results of the calculations can be routed back to the memories, freeing the core up to calculate a subsequent neural element&#39;s data. One current architecture calls for 128 of these cores to be instantiated. 
     The system bus environment module  616  collects together the system bus access logic, providing registers and mux&#39;s to direct the data, address and control flags between the cores  614  and the output storage tables  610  and SDRAM. The system bus  618  will be the instantiated interface between the scattered NPU&#39;s and the FSM controller  608 . 
     The off chip link module  620  can provide an interconnection to other copies of this chip, located on other boards or in future designs, collocated on the same board. The data from the PSP output storage table can be provided to this link to supply other chips and this chip can receive data from the other chips in the network via this link. A moderately fast serial link could transmit all the output data in a 256 chip network within the epoch time allotted. 
     The program flash memory interface module  622  can be an Embedded Development Kit (EDK) library module which can provide interface to a program storage space for the processor software. It can be a OPB peripheral in the EDK design environment. 
     The TCP/IP Link module  624  can be another EDK Library module, providing a path between the processor and Ethernet connection hardware on the PC board that holds the system. 
     This processor interface module  700  is shown in  FIG. 7 . This module is designed to be a custom IP in the Xilinx EDK environment. It can have a PLB interface to allow the processor interaction. A 32 bit mode register can allow the processor to set modes in the cores. The module can route data to and from the processor to the cores via the system bus, the OST&#39;s and the SDRAM which holds the weights and the pointers to the OST for the elemental inputs. 
     The EDK environment that the chip will be developed in provides library functions for interfacing to the processor internal bus structure. The OPB can be used for this interface. A library module for that facilitates linking custom logic to the OPB can be employed. It is shown above as OPB_IPIF. On its left in the sketch the OPB interface is given, on the right are the various signals that need to be translated into the system space. The functions of this module can be mapped to address space in the processor through parametric definitions in the OPB_IPIF module  702 . The OPB_IPIF module  702  can generate one of many chip enable flags depending on which addresses the processor targets. Address banks can be allotted for:
         Mode register access   Input pointer SDRAM access   Weight SDRAM access   OSTA access (on-chip outputs)   OSTB access (off-chip outputs)   NPU constants access (via the NPS system bus)       

     Writing to the Mode register can set flags to direct the flow of data in the system and set the FIFO sync flags indicated for the SDRAM access. The interaction with the SDRAM can leverage the FIFO&#39;s built into the SDRAM controller module. Data can be burst to the SDRAM controllers sequentially, with no addressing requirements from the OPB_IPIF module  702 . The software can stream the data to the SDRAM according to the intended address sequence. PpcSdramxAck flags can be sent to the SDRAM controller to increment the FIFO&#39;s address counters. Two separate addresses in the processor space can be used, one for the input pointers and the other for the weights. 
     The interaction with the Output Storage Tables (OST) can be through direct addressing with a 16 bit address. These writes and reads on the part of the PPC can be either burst or single beat transactions (TBD). An addressing scheme to the OST can be used, either provided by the processor through the bus or via a sequential counter in this module. The last connection for this module is to the cores, to load their initial states and constants. This can involve writing to the BRAM blocks located in each NPU via the system bus. The addressing of each location can be determined by the processor, although, there will be opportunities for burst mode writing and sequential addressing could permit a counter addressing scheme as well. A provision for reading through this connection may also use error detection and final state downloading of some possible non-static data in the cores. 
     A FSM module  800  is shown in  FIG. 8 . The FSM module  800  can control the neural processing cycle. The FSM module  800  can repeat the sequence of memory read, system bus write, system bus read and memory write steps needed for loading and unloading the element data and weights. The FSM module  800  can count through the elements and cores, setting addresses in the output storage table and on the system bus as needed for each element. The FSM module  800  overall process cycle time counts through all the elements and takes one epoch time period. 
     The FSM Controller module  800  can do the following tasks:
         Count through the steps, elements and cores of the epoch,   Provide the necessary sequence of flags for pipeline registers, memory and system bus accesses,   Provide needed addresses for the output storage table and system bus devices,   Possibly provide sequencing for processor streaming access.       

     At the start of an epoch, the FSM controller module  800  can trigger a reset in each SDRAM control module to set their address generators to the top of memory. The SDRAM controllers can flag the FSM controller  800  when they have data ready to read in their FIFO&#39;s. At this point the FSM controller  800  can start the sequence of flags that will pass the data through the pipeline, steering various mux&#39;s that present the data to the system bus. The input pointer data from one of the SDRAM&#39;s is routed to the address line of the output storage table BRAM to select the correct data to be used as the inputs to the core processes. The FSM controller  800  can steer the output of one of its counters to the system bus address lines to signal which NPU&#39;s will receive the data. A system bus read can also occur to take from the cores their output data. The FSM will step this data through the pipeline to the SDRAM controller or OST, depending on the source. This cycle can be repeated for all 256 inputs of the selected elements. Then the element loading/unloading process is repeated for all 256 elements of each of the 128 cores. An additional possible role for the FSM controller module  800  is to execute the sequencing of pipeline pulses and mux select lines for processor reads and writes. A simple finite state machine along with several counters can be used to achieve the sequence. However, the process can require numerous flags to control the pipeline registers and counters. One approach to assuring that all of the required flags are synchronous is to place the state machine in a BRAM. The BRAM can hold the output flag sets in its 32 bit wide cells. The control of the FSM then would be realized by clocking through the addresses of the FSM BRAM, sending out the desired flags as bits in the BRAM output data. A 512×32 BRAM would provide 32 flags to be used for both external pipeline control (approx. 16 needed) and internal state machine loop control. 
     The Neural Processing Unit ( FIG. 1A ; also Neural Processing System (NPS) or “neural core”) can store its weight data in SDRAM. The SDRAM can also hold pointers to the output storage table data. The data can be streamed sequentially to and from memory in large blocks at system bus speeds of 125 MHz. The SDRAM access can accommodate this high speed access if it is read or written in page bursts of 512 words. Accessing the memory in this fashion can reduce the time spent in CAS latency and other timeouts. The data use in the system can be compatible with this as it can be accessed sequentially and the return values for writing can also be presented in the same sequence. The SRAM controller, besides providing the standard sequenced pulses for synchronous control of the SDRAM I/O, can also provide a means of buffering the streamed pages of data both on their way to and from the memory. In this manner, the system can access the data in a less continuous manner than the page streaming provides. There can be two instantiations of this memory controller, each driving two memory chips configured into 32 Mb blocks. The memory used can be the HYB25L128160AC-8 from Infinion which is compatible with the signals and their timing. All read, write and auto-refresh commands can be designed per the data specifications for this memory. The memory is configured as a 32 Mb block. The controller can be initially implemented in a Xilinx X2VP50F1152 on a pre-existing demo board. The pin connections from the Xilinx part to the memory parts can be pre-assigned. 
     The cores can be the primary user of the data from the SDRAM. The cores can use effectively continuous streaming of data from the SDRAM via this SRAM controller ( FIG. 10 ). The data can be sequential from the memory (no random access). When the RDACK flag is high, during a rising edge of the system clock, the data on the read bus should be valid. On a subsequent rising edge of the clock with the RDACK flag high, the next data word from the memory should be available. The controller can provide data under a condition of the RDACK being high continuously, supplying data sequentially at the system clock rate of 125 MHz. There can be breaks in the reading, enough for the controller to supply subsequent pages to a read buffer. In addition, the controller can accept a data word on the write bus when the WRACK flag is high during a rising edge of the system clock. The controller can receive a continuous stream of data from the write bus when the WRACK flag is high continuously. There can be breaks in the writing, enough for the controller to empty pages from a write buffer to the SDRAM. The controller can be able to process the read and write requests, buffering the data as needed, while at the same time pulling data from the SDRAM or writing it to the SDRAM as needed. The overall system timing can mean that the access to the SDRAM be page mode, therefore, it is anticipated that buffering can be provided for both directions. Overall system timing can be provided for alternating page write/page read access to the SDRAM where needed as well as for accommodation of pipeline loading at the beginning and end of any cycle. 
       FIG. 9  shows a pin arrangement for the SRAM controller module  900 . 
     The following chart lists the pins and their descriptions of one embodiment. 
     
       
         
               
               
               
             
               
             
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                   
                 Input/ 
                   
               
               
                 Pin Name 
                 Output 
                 Description 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 SDRAM Interface Pins 
               
             
          
           
               
                 SDRAM_DQ(31:0) 
                 I/O 
                 Data bus in/out of SDRAM 
               
               
                 SDRAM_A(13:0) 
                 O 
                 Address Bus to SDRAM 
               
               
                 SDRAM_BA(1:0) 
                 O 
                 Bank Select to SDRAM 
               
               
                 SDRAM_DQM(3:0) 
                 O 
                 Data mask to SDRAM 
               
               
                 SDRAM_RASn 
                 O 
                 Row address select to SDRAM - active low 
               
               
                 SDRAM_CASn 
                 O 
                 Column address select to SDRAM - active  
               
               
                   
                   
                 low 
               
               
                 SDRAM_WEn 
                 O 
                 Write enable command to SDRAM - active  
               
               
                   
                   
                 low 
               
               
                 SDRAM_CSn 
                 O 
                 Chip select to SDRAM - active low 
               
               
                 SDRAM_CKE 
                 O 
                 Clock enable to SDRAM 
               
               
                 SDRAM_CLK 
                 O 
                 Phase corrected clock to SDRAM 
               
               
                 SDRAM_CLKFB 
                 I 
                 Feedback from SDRAM clock trace for  
               
               
                   
                   
                 DCM 
               
             
          
           
               
                 NPU Interface Pins 
               
             
          
           
               
                 WRDBUS(31:0) 
                 I 
                 Data bus from NPU 
               
               
                 WRACK 
                 I 
                 Flag indicates data on WRDBUS is to be  
               
               
                   
                   
                 written 
               
               
                 WRSYNC 
                 I 
                 Optional command flag from NPU to  
               
               
                   
                   
                 synchronize write addresses to 0 
               
               
                 WRFULL 
                 O 
                 Flag from SDRAM control module  
               
               
                   
                   
                 indicating that the WR FIFO is full.  
               
               
                   
                   
                 Probably indicates an error has occurred 
               
               
                 RDDBUS(31:0) 
                 O 
                 Data bus from controller to NPU 
               
               
                 RDACK 
                 I 
                 Flag from NPU indicating the data was read 
               
               
                 RDSYNC 
                 I 
                 Optional command flag from NPU to  
               
               
                   
                   
                 synchronize read addresses to 0 
               
               
                 RDRDY 
                 O 
                 Flag from controller indicating that the NPU  
               
               
                   
                   
                 can start reading data from the FIFO. 
               
               
                 ARCMD 
                 I 
                 Optional external command to the SDRAM  
               
               
                   
                   
                 controller to prompt the start of an auto- 
               
               
                   
                   
                 refresh cycle. 
               
               
                 ARCOMP 
                 O 
                 Optional flag from the controller indicating  
               
               
                   
                   
                 the commanded auto-refresh is complete 
               
               
                 SYSRSTn 
                 I 
                 Global reset - low means reset active 
               
               
                 SYSCLK 
                 I 
                 Global 125 MHz clock 
               
               
                   
               
             
          
         
       
     
     The following tables indicate the off chip pin numbers on a Veritex™ II Xilinx FPGA. Since there are 2 instantiations of the controller, 2 sets of pin numbers are given. In each table the top row is the pin name (without the SDRAM_prefix) and the second row is the pin number on the FPGA. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Module 1 Pinouts 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 CSn 
                 CKE 
                 RASn 
                 CASn 
                 WEn 
                 CLK 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 P5 
                 P6 
                 U5 
                 R7 
                 T5 
                 T7 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 DQM 
                  0 
                  1 
                  2 
                  3 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
                 K4 
                 H2 
                 P3 
                 N2 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 BS 
                  0 
                  1 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
                 J7 
                 R6 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 A 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
               
               
                   
                 T6 
                 M6 
                 L5 
                 U6 
                 M7 
                 F7 
                 L6 
                 L7 
                 N7 
                 N6 
                 N5 
                 R9 
                 P7 
                 U7 
               
               
                 DQ 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                   
                   
                   
                   
                   
                   
               
               
                   
                 M3 
                 F5 
                 N4 
                 F4 
                 M4 
                 K5 
                 L3 
                 L4 
                   
                   
                   
                   
                   
                   
               
               
                 DQ 
                  8 
                  9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                   
                   
                   
                   
                   
                   
               
               
                   
                 H1 
                 K2 
                 J2 
                 L2 
                 K1 
                 M2 
                 L1 
                 M1 
                   
                   
                   
                   
                   
                   
               
               
                 DQ 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
                 23 
                   
                   
                   
                   
                   
                   
               
               
                   
                 R3 
                 T3 
                 T4 
                 U3 
                 U4 
                 P4 
                 N3 
                 R4 
                   
                   
                   
                   
                   
                   
               
               
                 DQ 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                   
                   
                   
                   
                   
                   
               
               
                   
                 N1 
                 P1 
                 P2 
                 R1 
                 R2 
                 U2 
                 T2 
                 V2 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Module 2 Pinouts 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 CSn 
                 CKE 
                 RASn 
                 CASn 
                 WEn 
                 CLK 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 AB5 
                 AB6 
                 AH5 
                 AC6 
                 AD8 
                 AC7 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 DQM 
                  0 
                  1 
                  2 
                  3 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
                 Y3 
                 W2 
                 AD3 
                 AD1 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 BS 
                  0 
                  1 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
                 V6 
                 AD5 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 A 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
               
               
                   
                 AD6 
                 W5 
                 V5 
                 AH8 
                 Y6 
                 V7 
                 W6 
                 W7 
                 Y7 
                 AA6 
                 AA5 
                 AB7 
                 AA7 
                 AD7 
               
               
                 DQ 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                   
                   
                   
                   
                   
                   
               
               
                   
                 AB3 
                 V4 
                 AB4 
                 W3 
                 AA4 
                 W4 
                 AA3 
                 Y4 
                   
                   
                   
                   
                   
                   
               
               
                 DQ 
                  8 
                  9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                   
                   
                   
                   
                   
                   
               
               
                   
                 Y1 
                 AA1 
                 Y2 
                 AB1 
                 AA2 
                 AC1 
                 AB2 
                 AC2 
                   
                   
                   
                   
                   
                   
               
               
                 DQ 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
                 23 
                   
                   
                   
                   
                   
                   
               
               
                   
                 AE4 
                 AF4 
                 AF3 
                 AK4 
                 AK3 
                 AC4 
                 AC3 
                 AD4 
                   
                   
                   
                   
                   
                   
               
               
                 DQ 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                   
                   
                   
                   
                   
                   
               
               
                   
                 AD2 
                 AE2 
                 AE1 
                 AG1 
                 AF2 
                 AL1 
                 AG2 
                 AL2 
               
               
                   
               
             
          
         
       
     
     The SDRAM controller  1000  of  FIG. 10  can be comprised of these five modules:
         SDRAM registered outputs  1010     Write FIFO  1002     Read FIFO  1004     Address generator  1006     Controller finite state machine  1008         

     The SDRAM Interface Registers  1010  can be as a Xilinx I/O block clocked to provide the correct timing to the SDRAM chip (90˜180 clock phase shift). Optional clock feedback may be used with a Delay Control Module (DCM) if more sophisticated clock control is needed. The bi-directional port for the data can also be de-mux&#39;d in this block. 
     The Write FIFO  1002  can be at least 512 words deep (possibly 1024) and can buffer the data in from the core until enough data to stream a page is stored. At that point it can send an “Empty_Me” request to the controller  1008 . The controller  1008 , after accommodating any arbitration it may be doing, can send the necessary sequence of commands to the SDRAM for page writing, while strobing the FIFO to write its output to the SDRAM  1000 . The FIFO  1002  will be realized with dual port BRAM in a Xilinx chip. 
     The Read FIFO  1004  can be at least 512 words deep (possibly 1024) and can supply data per core read requests until its data level is low enough to receive another page from the SDRAM  1000 . When its contents are low enough to accommodate another 512 word page burst from the SDRAM, it can send a “Fill_Me” request to the controller  1008 . The controller  1008 , after accommodating any arbitration it may be doing, can send the necessary sequence of commands to the SDRAM  1000  for page reading, while strobing the FIFO  1004  to read its input from the SDRAM. The FIFO  1004  can be realized with dual port BRAM in a Xilinx chip. 
     The Address Generator  1006  can keep a row-to-be-written and row-to-be-read value in its registers, incrementing each after a page is written or read. A sync input can allow for the resetting of these addresses in the event of a fault or at power up or just periodically to assure synchronicity. An additional provision can be a mux to select per command from the controller, whether the write address or read address is to be sent to the SDRAM  1010 . The address generator can also provide the command value to the SDRAM during power-up mode register loading of the SDRAM. This can be done through an additional command from the controller  1008 . 
     Finally, the Controller Finite State Machine  1008  can arbitrate the FIFO service commands and initiate page streams to or from the SDRAM  1010  per the timing requirements of the SDRAM. It can also initiate auto-refresh cycles either through an internal timer or per an external command from the core. Depending on the needs to provide synchronizing, the controller may also respond to the sync pulses from the core and either pass them to the address generator or perform a more elaborate process as determined upon further system analysis. 
       FIG. 11  shows exemplary read and write timing diagrams for the core. The SDRAM interface timing can be per the data sheet for the device that is being used. For the core side the timing diagrams of  FIG. 11  give an idea of the WRDBUS vs. WRACK and RDDBUS vs. RDACK. 
     During the execution of the neural simulation process, the neural elements can require input data that represents the output signals from other neural elements generated in the previous epoch. On each chip, there can be 32,768 elements. That represents 256 elements assigned to each of 128 NPU&#39;s. Each of these elements can generate a single output that will be used as an input for other elements in the subsequent epoch. The output storage tables can store all of the data used by the elements on the chip. It can feature a section that holds the output data from the elements on the chip and it can also have a section that holds output data from other chips that will be used as input data for the elements on this chip. The data can be byte sized. In order to hold the outputs of all the elements on the chip the size can be 32 kB. Data from off chip elements can provide an additional 32 kB, so the overall size can be 64 kB. Since the neural simulation system can be generating outputs at the same time that it is using inputs for the current epoch, a ping-pong buffer scheme can be used to provide a memory to write to while the current epoch uses data that was written in the previous epoch from a separate memory. This can double the memory requirement to 128 kB. This memory can be organized as two 64 kB BRAM tables. Each table can use 32 BRAM blocks. In the ping-pong scheme, the 2 tables can be in either a read phase or a write phase. In order to maximize the access speed to feed the inputs to the elements, the output storage table BRAM can be configured as dual port. A byte can be read from each port simultaneously during the read phase. During write phase, one side of the dual port access can be used for writing the outputs of the current epoch, while the other side can be used for writing the output data from the off-chip elements that is used on the chip. Each table can be generated using a Core-generator of the Xilinx tools. The block and its I/O appear in  FIG. 12 . 
       FIG. 13  shows a system bus environment module  1300 . This module  1300  can hold the miscellaneous routing facilities for connecting the data between the memories and the system bus. It also can define the pipelines that have been designed in to pass the data along between its various endpoints. In terms of number of signals it is the most complex, but the logic can be relatively simple, involving a collection of mux&#39;s and registers and flags.  FIG. 13  shows the inputs and outputs. 
     There can be four main data paths through this block which will be discussed individually. These four paths are:
         OST and weight data to the System bus   OST and weight data from the System bus   PPC data writing   PPC data reading.       

     In the OST and weight data to the system bus path, the data is retrieved from memory and sent to the system bus. For this path, the weight and OST data are handled differently. The weight data is read directly from its SDRAM. For the OST data the input pointer SDRAM is first read. The data record obtained from the SDRAM holds 2 16 bit values. Each of these ‘pointers’ is used to address the OST, with one 16 bit pointer addressing the A port on the OST and the other pointer addressing the B port. These addresses will be applied to the appropriate memory, depending on the ‘ping-pong’ selection described above. Since 4 elements are served with each System Bus write and each address in the OST only holds 1 value, it can take 2 OST accesses to get the 4 bytes needed for the system bus write. The OST data can then be available with the weight data to be sent to the system bus via an additional register. There can be an intervening mux and register that permits the PPC data to be sent to the system bus when that mode is active. The address for the write to the system bus, which selects which of the cores the data will be written, is applied to the bus by the FSM controller, via a mux which selects between the FSM address or the processor address, and a register. An example of this process is shown in  FIG. 14 . 
     In the path, the data is received from the system bus and routed to the proper memory. The address can be applied to the system bus address lines to select the source. The address applied can be passed through a mux which would allow the processor sourced address to be applied in that mode. When addressed, the cores present their output data on the 32 bit system bus read data lines. The cores can be connected to the data lines in groups of 4, such that 1 of the 4 is tied to bits  0  to  7 , the next to bits  8  to  15 , the next to bits  16  to  24  and the fourth to bits  24  to  31 . The 32 bit read data can be registered first. The data from the cores is either a weight bound for the SDRAM or a PSP output to be sent to the output storage table. Alternating registers take either the weight data or the OST data. The weight values are passed through a mux which selects between this data or the processor data and then on to the SDRAM, where a WRACK pulse cues the SDRAM controller to record the value into its FIFO. Since there is only 1 PSP output value (compared to 256 weight outputs), it can be handled more slowly. Each of the 4 bytes contained in the 32 bit data record can be individually written to the output storage table. The address for the output storage table is sequentially generated by the FSM controller and passed through a mux that would allow the processor address to be applied in that mode. The data for the output storage table is demuxed to byte size, registered and passed to the output storage table via a mux for the processor access as well.  FIG. 15  shows an example of this system. 
     The SPP can receive programmed instructions, but more generally it can also receive inputs from sensors and have outputs to actuators.  FIG. 16A-D  shows an off-road capable robotic base (“rover”) for a brain-based device (BBD). The rover can be a BBD that can navigate to a goal, via various waypoints, in an unknown, harsh, three-dimensional environment. The rover can give its controlling neural simulation a robust set of real-time inputs from numerous embedded sensors, together with adjustable effectors to enable controlled movements. These diverse connections with the neural simulation can help the BBD navigate in a novel environment. The rovers can be any size. The rover  1600  can have many unique features to provide maximum flexibility for operation of the neural simulation. 
     The rover  1600  can include multiple pods. The pods can be modular, extensible, interchangeable, and easily replaced. The pods and central unit can be connected through a central connector axis. In one embodiment, the rover can allow for the addition and subtraction of pods from the central connector axis and different sized central connector axes can be used. The central connector can include a conduit to send power, sensor and actuator signals to and from a central unit. The conduit can include a bus, such as a two-line bus, to allow a large number of sensors and actuators to communicate with the central unit. The pods can include sensors and actuators which interact with the neural model. Some of the pods can be drive pods including a wheel controlled by a motor. 
     The pods can have bi-directional suspension systems  1602 . The bi-directional suspension can allow the pods to have a functional suspension system even when the rover is flipped over. The bi-directional suspension system can include gas charged shocks arranged in opposition to one another. The bi-directional suspension system can also include sensors to monitor the compression at each of the shocks. 
     In addition to wheels on some of the pods, the rover can include treads  1604 , such as tank-type treads. The treads  1604  can be a part of a central unit. In one embodiment, the treads  1604  are not normally engaged. The treads  1604  can allow the rover  1600  to crawl out of an otherwise immobilizing situation. In most situations, the rover will be driving on terrain in which wheels are most efficient. However, on occasions where wheels are not viable, the rover can switch to using the treads  1604  to get out of difficult situations (e.g., climb out of a ravine). If the rover  1600  is stuck, the rover  1600  can move the pods such that the treads  1604  engage the ground. In one embodiment, the rover  1600  can move the pods to a fully extended position to allow the treads to engage the ground. 
     A sensor pod  1606 , can house a camera and other sensors. The sensor pod  1606  can be constructed using some of the subassemblies used in the drive pods. In one embodiment, the sensor pod  1606  can be attached to the center portion  1610  that includes the treads  1604 . The sensor pod can move to protect itself between the drive pods when the rover senses a freefall type situation. 
     The articulating drive and camera pods can provide the BBD with the ability to drive in an inverted orientation and increase the overall stability of the entire camera system. In one embodiment the pods can be rotated about a range of motion by motors at the pods. 
     The power management system  1608  can constantly monitor power consumption from its multiple power sources. In one embodiment, power management system  1608  includes sensors, such current sensors to measure the power consumed by motors and voltage sensors to measure the output of a battery. 
       FIG. 17  is a functional diagram of an exemplary rover  1700 . The rover  1700  can include drive pods, such as drive pod  1702 . Drive pod  1702  can include a number of sensors and actuators. Wheel sensor  1704  can optically sense the position of the wheel  1706 . The motor  1708 , such as a brushless motor, can power the wheel  1706  and can include an associated motor sensor. A number of position sensors can be used such as gyros and accelerometers  1710 . The suspension  1712 , which can be a bi-directional suspension, can have associated sensors. The drive pod  1702  can have a motor  1714  and associated sensors for rotating the drive pod  1712  about the central axis  1716 . The drive pod  1702  can include an associated power sensor  1718 , at the drive pod  1702  or at the central unit  1720 , to monitor the power consumption by the drive pod  1702 . The sensor pod  1722  can include sensors such as a video camera, an IR sensor, a laser sensor or the like. The central unit  1720  can include treads  1724 . The sensors  1726  can include tread position and tread motors sensors. The central unit  1720  can also include a power supply  1728 , such as a battery. 
     The rover  1700  can be controlled by a neural model, such as a neural model run by SPP  1730 , that receives sensor input and provides actuator outputs. The neural elements of the neural model can learn through the plasticity calculations how to react to situations in the environment. These plasticity calculations can modify the connection weights and thus the behavior of the neural model in response to inputs. 
     The behavior reactions are not explicitly programmed in by a programmer but instead learned by the BBD. The BDD can engage in unforeseen behavior as it reacts to the environment with the neural model. The neural model of rover  1700  can receive a large number of inputs from sensors and can learn by itself what inputs are the most relevant in different situations. For example stuck wheels can result in value type plasticity signals that inhibit the operation of behaviors that caused the stuck wheels. Smooth terrain as sensed by the video camera can be associated with good operation of the wheels and low power consumption and can thus result in positive learning. Rough terrain as sensed by the video camera can be associated with poor operation of the wheels and high power consumption and can thus result in inhibitory learning. 
     The neural model can include sensors and actuators in logical groupings. For example the response of the actuators to control output can be monitored by the sensors. In this way the BBD can learn to control its actions, with feedback, in a similar manner to the way animals learn to control the movements of their limbs. 
     The design or phenotype of the rover can be closely coupled with the neural simulation. Successful traversal over uneven terrain can use the neural model to monitor traction, rotation, and vibration sensors from the drive system and adjust the suspension compliance, speed of the wheels, and pod positions of the drive system to keep the rover moving efficiently over terrain. The cameras and other sensors, such as infrared and laser range finders, can feed into the neural model and allow the BBD to recognize a terrain and associate the near environment with a degree of difficulty. After experience, the BBD can learn to avoid areas of the environment that are difficult to traverse and seek areas where it can make efficient progress. A motor control loop, based on a model of cerebellar adaptation, can learn to keep the camera and sensor housing steady by moving the articulating pod appropriately due to terrain changes. 
     BBDs can adapt their behaviors based on environmental cues that trigger their value or reward system. The value system in the rover can be closely coupled with the power management system. Efficient use of power (or low current draw) is of positive value and high current draw is negative in value. Typically, an area where traction is poor or the surface is rough will draw more current than a smooth road. Therefore, the BBD, based on its value-dependent learning, can seek smooth, high traction surfaces when available. 
     The body of the rover can have room for computers, communication electronics, and batteries. Because of the number and bandwidth of the on-board sensors, the neural simulation of the BBD may have high performance computational requirements (such as a 32-node Beowulf cluster) The rover  1700  can include a corn link  1732  to wirelessly communicate with a neural model running remotely. 
     In an embodiment, in order to navigate over moderate to long distances, beyond the range of wireless communication, special onboard computing will be necessary. Conventional computers require too much power and are too large fit on an autonomous rover device. In one embodiment, a Special-Purpose Processor (SPP)  1730 , such as that discussed above specifically designed for rapid and efficient computation of neural simulations can be used by the rover. 
     The neural simulation control running on an SPP, which is closely coupled with the unique, actively suspended rover design, can allow the BBD to complete its goals of traversing a novel environment, learning the salient objects and locations in the environment, and then using its experience to navigate in an efficient and reliable manner. The rover  1700  can also have override logic to protect the rover when the rover is in danger. 
     While embodiments of the invention have been described at times herein as being implemented using special-purpose processors and field programmable gate arrays, it should be understood that those examples have been provided only for purposes of illustration. The invention is not limited to those example implementations. As will be appreciated by persons skilled in the relevant art(s), embodiments of the invention can be implemented using any data processing/computing element, module, device or architecture. This includes, for example and without limitation, application specific integrated circuits (ASICs). 
     In an embodiment, the present invention is implemented using one or more well known data processing devices or modules, such as a computer  1802  shown in  FIG. 18 . The computer  1802  includes one or more processors (also called central processing units, or CPUs), such as a processor  1806 . The processor  1806  is connected to a communication bus  1804 . 
     The computer  1802  also includes a main or primary memory  1808 , such as random access memory (RAM). The primary memory  1808  has stored therein control logic  1828 A (computer software), and data. 
     The computer  1802  also includes one or more secondary storage devices  1810 . The secondary storage devices  1810  include, for example, a hard disk drive  1812  and/or a removable storage device or drive  1814 . The removable storage drive  1814  represents a floppy disk drive, a magnetic tape drive, a compact disk drive, an optical storage device, tape backup, etc. 
     The removable storage drive  1814  interacts with a removable storage unit  1816 . The removable storage unit  1816  includes a computer useable or readable storage medium  1824  having stored therein computer software  1828 B (control logic) and/or data. Removable storage unit  1816  represents a floppy disk, magnetic tape, compact disk, DVD, optical storage disk, or any other computer data storage device. The removable storage drive  1814  reads from and/or writes to the removable storage unit  1816  in a well known manner. 
     The computer  1802  also includes input/output/display devices  1822 , such as monitors, keyboards, pointing devices, etc. 
     The computer  1802  further includes a communication or network interface  1818 . The network interface  1818  enables the computer  1802  to communicate with remote devices. For example, the network interface  1818  allows the computer  1802  to communicate over communication networks or mediums  1824 B (representing a form of a computer useable or readable medium), such as LANs, WANs, the Internet, etc. The network interface  1818  may interface with remote sites or networks via wired or wireless connections. 
     Control logic  1828 C may be transmitted to and from the computer  1802  via the communication medium  1824 B. More particularly, the computer  1802  may receive and transmit carrier waves (electromagnetic signals) modulated with control logic  1830  via the communication medium  1824 B. 
     Any apparatus or manufacture comprising a computer useable or readable medium having control logic (software) stored therein is referred to herein as a computer program product or program storage device. This includes, but is not limited to, the computer  1802 , the main memory  1808 , the hard disk  1812 , the removable storage unit  1816  and the carrier waves modulated with control logic  1830 . Such computer program products, having control logic stored therein that, when executed by one or more data processing devices, cause such data processing devices to operate as described herein, represent embodiments of the invention. 
     Accordingly, the brain-based device functionality described herein can be achieved in many ways, including but not limited to FPGAs, ASICs, special purpose processors, general purpose processors, computing elements, etc., and combinations thereof. The scope and spirit of the invention includes all of these embodiments. 
     Also, alternative embodiments of the invention may operate with virtual inputs and/or virtual outputs. For example, in certain embodiments, a BBD may operate with a virtual input received from a computer application (such as but not limited to a computer game) or other source, where such virtual input does not represent a real-world input from a real-world sensor. For example, instead of receiving input from the real-world haptic, olfactory, audio, acoustic, thermal, visual, and/or auditory sensors described above, a BBD embodiment can receive input from a computer application (or other source) that simulates such haptic, olfactory, audio, acoustic, thermal, visual, and/or auditory sensors. Also, instead of interacting with real-world actuators, such as effectors or wheels for movement, a BBD embodiment can interact with virtual actuators, such as virtual wheels that are part of a virtual rover. Accordingly, the description above of the rover is provided for purposes of illustration, not limitation. For example, alternative BBD embodiments can be part of virtual rovers that are simulated by computer applications, wherein BBDs send output to virtual actuators. 
     The invention can work with software, hardware, and/or operating system implementations other than those described herein. Any software, hardware, and operating system implementations suitable for performing the functions described herein can be used. 
     The foregoing description of preferred embodiments of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to one of the ordinary skill in the relevant arts. The embodiments were chosen and described in order to best explain the principles of the invention and its partial application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications that are suited to the particular use contemplated. It is intended that the scopes of the invention are defined by the claims and their equivalents. 
     
       
         
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
             
           
               
                 APPENDIX I 
               
               
                   
               
             
             
               
                 Void neural_core(void) 
               
               
                 { 
               
             
          
           
               
                  unsigned byte 
                 I; 
                  // this index is used in many places 
               
               
                  // 
                   
                   
               
               
                  signed 16bit word 
                 A; 
                 // accumulator for input_data*weight 
               
               
                  unsigned byte 
                 input_data[256]; 
                  // these values are read from DRAM at 
               
               
                  signed byte 
                 weight[256]; 
                 // run time and are unique for each 
               
               
                  // 
                   
                   // element but are not stored locally 
               
               
                  // 
                   
                   // between epochs 
               
               
                  // 
                   
                   
               
               
                  signed 16bit word 
                 temp; 
                 // temp variable 
               
               
                  unsigned byte 
                 old_S; 
                  // this is unique for each element and 
               
               
                   
                   
                  // is stored locally 
               
               
                  unsigned byte 
                 S; 
                  //  this is the PSP which is propagated 
               
               
                   
                   
                  // but not stored except as Old_S 
               
               
                  bit 
                 send_enabled; 
                 //  this is a bit set by the memory 
               
               
                   
                   
                  // controller to enable PSP data to be sent 
               
               
                  constant 3bits 
                 w; 
                  //  this is a divisor which is applied to 
               
               
                   
                   
                  // Old_S. It is unique to each Core 
               
             
          
           
               
                  constant unsigned byte g; 
                  // this is a scale multiplier applied 
               
             
          
           
               
                   
                   
                  // A and is unique to each Core 
               
               
                  unsigned byte 
                 Tan_Lut[ ] = 
                  // this is the Tanh lookup and is 
               
               
                   
                 0,1,2,3,4...256; 
                  // unique to each core 
               
               
                  unsigned byte 
                 Phi_Threshold; 
                  // unique to each core 
               
               
                  // 
                   
                   
               
               
                  signed byte 
                 Fn_Lut[ ] = 
                  // unique to each core 
               
             
          
           
               
                   
                 −100,−99,−98...130; 
               
             
          
           
               
                  signed byte 
                 E; 
                  // this is the decay constant that 
               
               
                   
                   
                  // is unique to each core 
               
               
                  unsigned byte 
                 Original_Weight; 
                  // this will either be one variable per 
               
               
                   
                   
                  // element or an array per core 
               
               
                  unsigned byte 
                 Value_term; 
                  // index of our value table 
               
               
                  unsigned byte 
                 Value_max; 
                  // max number of value table 
               
               
                  unsigned byte 
                 Value_table[ ] = 
                  // table applied over succesive 
               
               
                   
                 0,1,2,3,4,3,2,1,0; 
                  // epochs 
               
               
                  signed byte 
                 C; 
                  // temp variable for weight calculation 
               
               
                  bit 
                 Value_Enabled; 
                  // this bit is set by the value system 
               
               
                  // 
                   
                   
               
             
          
           
               
                  unsigned 32bit word 
                 connection_table[256]; // these are unique for each element 
               
             
          
           
               
                   
                   
                   // they are loaded into BRAM from DRAM 
               
               
                  unsigned byte 
                 element; 
                   // this is the element index 
               
             
          
           
               
                  // 
               
               
                  // loop through the 256 elements per core 
               
               
                  for(element = 0;element&lt;=255;element++) 
               
               
                  { 
               
               
                   Read_in_weights_from_DRAM(element[&amp;weight]); 
               
               
                   Read_in_input_data_from_DRAM(element[&amp;weight]); 
               
               
                   Read_in_connection_table_from_DRAM(element[&amp;weight]); 
               
               
                   // 
               
               
                   ///////////////////////////////////// 
               
               
                   //  this is the pre-synaptic activity 
               
               
                   //  or neuronal activity 
               
               
                   // 
               
               
                   ///////////////////////////////////// 
               
               
                   A = 0; 
               
               
                   for(I = 0;I&lt;=255;I++) 
               
               
                   { 
               
               
                    A += input_data[I]*weight[I]; 
               
               
                   } 
               
               
                   // 
               
               
                   ///////////////////////////////////// 
               
               
                   //  this is the post-synaptic activity 
               
               
                   // 
               
               
                   // 
               
               
                   ///////////////////////////////////// 
               
               
                   temp = A*g; 
               
               
                   temp += old_S[element]&gt;&gt;w; 
               
               
                   // 
               
               
                   here we need to adjust a 16 bit ‘temp’ to be an 8 bit value 
               
               
                   for now we just save the top 8 bits so we get 
               
               
                   temp = temp&gt;&gt;8; 
               
               
                   // 
               
               
                   S = 0; 
               
               
                   if(temp &gt;= Phi_Threshold) 
               
               
                   { 
               
               
                    S = Tan_Lut[temp]; 
               
               
                   } 
               
               
                   old_S[element] = S; 
               
               
                   Send_PSP_data(S); 
               
               
                   // 
               
               
                 ///////////////////////////////////// 
               
               
                   //  this is activity-dependant synaptic plasticity 
               
               
                   //  with provisions for value plasticity 
               
               
                   // 
               
               
                   ///////////////////////////////////// 
               
               
                   // the learning rule with value added in 
               
               
                   temp = Fn_Lut[S]; 
               
               
                   if(Value_Enabled) 
               
               
                   { 
               
               
                    temp = temp * Value_table[Value_term] 
               
               
                   } 
               
               
                   if(++Value_term &gt; Value_max) 
               
               
                   { 
               
               
                    Value_term = 0; 
               
               
                    Value_Enabled = 0; 
               
               
                   } 
               
               
                   // 
               
               
                   for(I= 0;I&lt;255;I++) 
               
               
                   { 
               
               
                    C = weight[I] − E;    // this is the forgetting rule 
               
               
                    if(C &lt; Original_Weight[element]) // 
               
               
                    {        // 
               
               
                     C = Original_Weight[element]; // 
               
               
                    } 
               
               
                    weight[I] = C + temp;    // new weight to be stored 
               
               
                   } 
               
               
                   Write_out_new_weights_to_DRAM(&amp;weight); 
               
               
                  } 
               
               
                 } 
               
               
                 /////////////////////////////////////////////////////////////////////////////// 
               
               
                 void Write_out_new_weights_to_DRAM(signed byte &amp;weight) 
               
               
                 { 
               
               
                  for(I = 0;I&lt;=255;I++) 
               
               
                  { 
               
               
                   write(element[weight[I]]); 
               
               
                  } 
               
               
                 } 
               
               
                 /////////////////////////////////////////////////////////////////////////////// 
               
               
                 void Send_PSP_data(unsigned byte S) 
               
               
                 { 
               
               
                  while(!send_enabled) 
               
               
                  { 
               
               
                   // wait for our signal to send 
               
               
                  } 
               
               
                  for(I = 0;I&lt;=255;I++) 
               
               
                  { 
               
               
                   send(concatenate(connection_table[I],S)); 
               
               
                  } 
               
               
                 } 
               
               
                   
               
             
          
         
       
     
     APPENDIX II 
     In one exemplary embodiment with 256 cores and 256 timeslices, the weights can use a single signed byte with:
         256 bytes per element=&gt;256 bytes   256 timesliced elements per core=&gt;256*256=65536 bytes   256 cores per chip=&gt;256^3=16,777,216 bytes
 
(16 Meg by 8) total
       

     The PSP output data can each have a single unsigned byte with:
         256 bytes per element=&gt;256 bytes   256 timesliced elements per core=&gt;256*256=65536 bytes   256 cores per chip=&gt;256^3=16,777,216 bytes
 
(16 Meg by 8) total
       

     The connection table can have 16 bits for each connection. 8 bits for destination neural core ID, and 8 bits for destination timeslice ID. Thus: 
     256 connections per element=&gt;2*256=516 bytes 
     256 timesliced elements per core=&gt;2*256^2 connection bytes 
     256 cores per chip=&gt; 2*256^3  connection bytes 
     (16 Meg by 16) total