NSL: Neural Simulation Language, Version 2.1
Contents
1. window_layer specifies the particular layer to be displayed window_graph specifies the particular type of graph to utilize for displaying create The create command creates a new display window according to the current settings update The update command update an existing display window according to the current settings 7 1 4 display_canvas A display_canvas is the visual display object where graphics are actually drawn There are different kinds of graphics items which may be drawn ona canvas graphs grids lines and text as shown by the class structure tree in Figure 14 30 When we talk about a frame we talk about an X windows screen frame while a display frame refers to NSL s window interface display entity Alfredo Weitzenfeld NSL 2 1 50 canvas_item temporal spatial temporal_graph area_level_graph spatial_graph_2 spatial_graph_3 Figure 14 NSL display canvas item classes 2 or The set command assigns canvas related parameters window_graph specifies the type of graph to be used for the display window Graphs may be either temporal or spatial and there are three different types of spatial graphs mimi Dg wyma 7 00 t5 9 40 COLA ia 11 7 rasa WAT LAYER wymi i og wy mas 1 00 t5 9 40 AT Figure 15 Alfredo Weitzenfeld NSL 2 1 51 vector area_level_graph vs spatial_graph_2 Spatial graphs area_level_graph displays a layer as levels of rectangular area r2. SLsaturation nsl_vector amp nsl_vector amp nsl_vector amp nsl_vector amp nsl_vector amp SLsaturation nsl_vector amp nsl_vector amp nsl_vector amp nsl_data amp nsl_data amp SLsaturation nsl_vector amp nsl_data amp nsl_data amp nsl_data amp nsl_data amp SLsaturation nsl_matrix amp nsl_matrix amp nsl_matrix amp nsl_matrix amp nsl_matrix amp SLsaturation nsl_matrix amp nsl_matrix amp nsl_matrix amp nsl_data amp nsl_data amp NSLsaturation nsl_matrix amp nsl_data amp nsl_data amp nsl_data amp nsl_data amp ZAZZLZLAZZ NSLsigmoid num_type NSLsigmoid nsl_datad NSLsigmoid nsl_vector amp NSLsigmoid nsl_matrix z NSLsigmoid num_type num_type nnum_type num_type num_type NSLsigmoid nsl_data amp nsl_data amp nsl_data amp ns _data amp nsl_data amp NSLsigmoid nsl_vector amp nsl_vector amp nsl_vector amp nsl_vector amp nsl_vector amp NSLsigmoid nsl_vector amp nsl_vector amp nsl_vector amp nsl_data amp nsl_data amp NSLsigmoid nsl_vector amp nsl_data amp nsl_data amp nsl_data amp nsl_data amp NSLsigmoid nsl_matrix amp nsl_matrix amp nsl_matrix amp nsl_matrix amp nsl_matrix amp NSLsigmoid nsl_matrix amp nsl_matrix amp nsl_matrix amp nsl_data amp nsl_data amp NSLsigmoid nsl_matrix amp nsl_data amp nsl_data amp nsl_data amp nsl_data amp
3. file POSTSCRIPT output will be saved as postscript ps file dump_ras_index n ras dump file suffix number dump_ps_index n ps dump file suffix number dump_auto_name ON output file name is composed dump_file dump_type index OFF output file name is same as dump_ file 11 6 reset reset type reset display objects type description window_interface reset window interface Alfredo Weitzenfeld NSL 2 1 17 11 7 set set type option set buffer for objects in the next categories type class description display_frame display frame information display_window window_item canvas_item panel_item display frame set modifier option modifier display window information window item information canvas item information panel item information option description display_frame frame_name frame_X0 frame_YO frame_width frame_height frame_auto_resize type frame_rows frame_cols n display window set modifier option modifier current display frame name display frame by name index display frame by index name frame s name n frame s left corner s location on the screen pixels n frame s top corner s location on the screen pixels n frame s width pixels n frame s height pixels ON automatic resize OFF no automatic resize n number of window rows automatic redraw number of window columns automatic redraw
4. m2 elem i j m elem i j 1 else this else part is not really necessary since m was initialized to 0 m elem i j 0 return m Note that structures can be passed by value or by reference In this case the matrices were passed by reference permitting any changes on the argument matrices to take effect outside the function although this was not the case Passing by reference is also more efficient than passing by value where the structure gets copied for passing by value omit the amp in the argument declaration 9 3 Adding Simulation Commands New simulation commands may be added to NSL command interpreter This is achieved by writing the following command reading function in a file to be linked via nsl_link include nsl_include h extern int new_command_function istream amp C declaration of your command function int my_command_function istream amp in string str int status 0 34 NSL keeps global structures independent from locally declared structures Alfredo Weitzenfeld NSL 2 1 67 if nsl_get_str in str 0 cmd_error Empty command string return 1 if stremp str new_command 0 status new_command_function in else cmd_error Unknown command str return status Every time nsl_get_str gets called a new string is read from the interpreter new_command_function will contain the code that actually performs the command including rea
5. option description display_window window_name window_X0 window_Y0 window_width window_height window_step window_layer window_layer_i0 window_layer_il window_layer_j0 window_layer_j1 window_graph current display window name display frame by name index display frame by index name window s name n window s left corner s location on the screen pixels n window s top corner s location on the screen pixels n window s width pixels n window s height pixels n window update step default 1 name layer s name to be displayed n layer s i0 unit to be displayed n layer s il unit to be displayed n layer s j0 unit to be displayed n layer s j1 unit to be displayed type area_level_graph Alfredo Weitzenfeld NSL 2 1 window_wymin window_wymax window_t0 window_tl window_val_in window_pulse window_vec_type window_hidden_line window_ax window_by window_cz window_sx window_sy window_sz 11 8 status status type option spatial_graph_2 spatial_graph_3 temporal_graph value graph s min layer unit value value graph s max layer unit value value temporal graph starting time value temporal graph ending time value interactive mouse input value draw using pulse type lines ON OFF vector drawing type HORIZONTAL VERTICAL draw 3D with hidden line removal ON OFF value 3D graph x reference point value 3D graph y reference po
6. raster format is the local workstation picture format WindowDump gt PostScript Save the window dump into a postscript file ps specified by the dump_file variable postscript is the standard printer language where dump_file is a file name automatically generated by NSL composed of a number suffix an inffix of ras or ps depending on what type of file it represents and a preffix containing the model s name For example the first time a raster ras is created from the didday model the following name will be generated didday ras 1 The other two entries in the menu are as follows The UpdateGraph entry is used for updating the window with any new information The ControlPanel entry is used for recalling the Control Panel window if not present Interactive input assignment The user may interactively modify the values data_value from any layer in the network This can be done with the help of the two mouse buttons when pressed over any window displaying a layer as an area_level_graph type of graph By clicking the left button over a layer element the value specified by the window control panel s val_in entry is assigned while by clicking the middle button the layer s element value is reset to 0 0 To assign a value other than the one currently shown in val_in simply modify the text entry to the right of val_in and the new value will be used instead To find out the values or the element s in
7. nsl_matrix NSLstep num_type nsl_data nsl_vector nsl_matrix num_type nsl_data nsl_vector nsl_vector nsl_vector nsl_matrix nsl_matrix nsl_matrix NSLramp num_type nsl_data nsl_vector nsl_matrix num_type nsl_data nsl_vector nsl_vector nsl_vector nsl_matrix nsl_matrix nsl_matrix NSLsaturation NSLsaturation num_type num_type nsl_data nsl_vector N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N SLmax nsl_data amp num_type SLmax nsl_vector amp nsl_vector amp NSLmax nsl_vector amp nsl_data amp NSLmax nsl_vector amp num_type N N N SLmax nsl_matrix amp nsl_matrix amp JSLmax nsl_matrix amp nsl_data amp JSLmax nsl_matrix amp num_type SLmin nsl_vector amp JSLmin nsl_matrix amp JSLmin nsl_data amp nsl_data amp SLmin nsl_data num_type JSLmin nsl_vector amp nsl_vector amp SLmin nsl_vector amp nsl_data amp JSLmin nsl_vector amp num_type JSLmin nsl_matrix amp nsl_matrix amp JSLmin nsl_matrix amp nsl_data amp SLmin nsl_matrix num_type SLstep num_type SLstep nsl_data amp SLstep nsl_vector amp SLstep nsl_matrix amp SLstep num_type num_type num_type num_type SLstep nsl_data amp nsl_data amp nsl_data amp nsl_data amp SLstep nsl_vector amp nsl_vector amp nsl_vector amp nsl_vector amp SLstep nsl_vector amp nsl_vector
8. open a file write write a file proc processing info cont process modules starting at current time init process modules for t 0 run process modules for t 0 step process once through all modules reset reset commands set set commands shell unix shell commands cd change model directory csh execute a c shell command sh execute a shell command status print status information on the model update update model objects user call a user defined command 10 2 create The create command is utilized for creating model class objects The syntax is as follows create type type description block_stim create block type stim object icon_stim create icon type stim object time_stim create time interval for existing stim object 10 3 disable disable type l option disable processing for object type type option description network disable current model name disable a particular model by name index disable a particular model by index module disable current module name disable a particular module by name index disable a particular module by index layer disable current layer update name disable a particular layer update by name index disable a particular layer update by index input_layer disable current input layer name disable an input layer by name index disable an input layer by index input_stim disable current input stim name disable an input stim by name Alfr
9. 1 set end_time 20 0 which gives a total of 200 20 0 0 1 simulation steps processing To process a simulation there are the following commands command description init process INIT_MODULE s and MODULE s for t 0 run n process all modules from t 0 similar to init and all RUN MODULE s and MODULE s for t gt 0 until t n or t end_time if no n is specified step n process modules n steps or step for one iteration if no n is specified Alfredo Weitzenfeld NSL 2 1 44 cont 11 continue module processing from current t until t 1 or t end_time if no n is specified Control C AC serves as processing interrupt 6 3 Data files Data produced by a simulation may be stored into external files The data stored in these files can be used as input to other simulations or simply as a means of analyzing the simulation output in numerical detail Besides the load command the user has available commands for opening and closing files either for input or output output data file In order to create a a file for output the user may execute the following command open OUTPUT file_name where file_name is the name of the file to be created If the command is executed without a file name then the current model name is used as file name If the file_auto_name flag is ON set file_auto_name ON then NSL will append an increasing numerical index suffix to every newly opened data file For example if the
10. 5 0 5 0 5 1 0 5 0 5 0 5 1 22 Due to the current implementation the has lower precedence than the other arithmetic operators making it necessary to add parentheses around the multiplication expression Alfredo Weitzenfeld NSL 2 1 32 5 6 5 Convolution Three types of convolution edge effect are treated by NSL zero effect The edge effect is treated as 0 Default action For example having layer X and mask M as follows X 1 1 1 1 1 1 2 2 2 2 1 2 4 4 4 1 2 4 8 8 1 2 4 8 0 M 1 1 1 1 2 1 1 1 1 will result in Y M X as follows first a larger matrix is created with 0 values for the edges the size of the new matrix depends on both the size of the mask and the convolved matrix for example for a 2d 1 x 2d 1 mask the border of zeroes must be d deep X0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 2 2 2 2 0 0 1 2 4 4 4 0 0 1 2 4 8 8 0 0 1 2 4 8 0 0 0 0 0 0 0 0 0 second we overlap M on the left top corner of XO with M 0 0 on top of X0 0 0 so the first convolution will be given by Y 0 0 0 1 0 1 0 1 0 1 1 2 1 1 0 1 1 1 2 1 6 and so on for the other elements The function for this kind of effect would be called as Y NSLconv_zero M X or Y M X mel since the default operation is the zero edge convolution wrap around Alfredo Weitzenfeld NSL 2 1 33 The layer is replicated successively so values are wrapped around For example having layer X and mask M as befor
11. Simulation commands may be called from the model file in the following manner NSL lt lt command lt lt command lt lt ENDL where NSL is the command interpreter command is the desired command and ENDL specifies the end of an expression without ENDL the command wouldn t be processed There may be as many lt lt command as necessary this is particularly useful for sending commands composed of part string and part numerical values For example you could execute a status command from inside a FUNC_MODULE by having the following expression NSL lt lt status data_value ALL lt lt ENDL which will show the data values for all layers when the function containing this line gets executed 9 6 Adding Graphics New graphics libraries may be incorporated as part of NSL35 10 NSL Simulation Command Summary The next sections provide a summary of all NSL simulation commands 10 1 help help command command option NSL help on simulation related commands command description help help command create create model objects disable disable objects enable enable objects exec execute a particular function module exit quit exit NSL file file info file_enable enable layer filing file_disable disable layer filing close close a file 35 separate document will show a sample creation of new types of graphics libraries Alfredo Weitzenfeld NSL 2 1 69 load read read a file open
12. are four classes of panel items text menus buttons and messages The panel class structure is shown in Figure 17 panel_item Figure 17 NSL display panel item classes A typical control panel as the one controlling window WN11 in Figure 12 is shown in Figure 18 The different entries are control parameters which can also be set from the window interface interpreter33 UpdateGraph LAYER 7 GRAPH area_level_graph wyinin 0 000000 WyYMAX 2 000000 33 These parameters are preceded by window_ when called from the commands interpreter The control panel functions and parameters are a subset from those available from the commands interpreter Alfredo Weitzenfeld NSL 2 1 53 Figure 18 NSL display window control panel To disable the control panel from the command interpreter do disable display_panel name and to enable it do enable display_panel name where name is the name of the window to which the control panel belongs 7 2 Window Mouse Interaction Until now we have described the window interface display objects and how they can be manipulated from the command interpreter In these sections we explain how to interact with the window interface in a graphical way 7 2 1 Drawing Frame Every frame includes a frame menu along its boundary The Frame Menu contains the regular X windows menu e g for moving resizing and closing the frame resize The graphs in the different displays may be auto
13. brain in a faithful way and artificial neural networks intended to apply neural networks computing techniques including different learning algorithms into various technological applications Rumelhart and and McClelland 1986 Different languages have been written for the simulation of neural networks with different modelling capabilities and for different application areas Goddard et al 1987 Teeters 1989 Wilson et al 1989 Wang and Hsu 1990 One important contrasting point is how networks are syntactically described in our particular simulation language we describe neural networks in the form of mathematical equations Alfredo Weitzenfeld NSL 2 1 9 3 1 Neurons and Links A neural network is in our abstraction a set of interconnected concurrent processing units neurons having a non linear dynamic behavior Therefore a model description includes 1 declarations of the units in the model 2 connections between the units 3 descriptions of inputs external to the network and 4 descriptions of network outputs A basic neuron is shown in Figure 2 It may receive input from many different neurons while it has only a single output ease input neuron output Figure 2 A Basic Neuron We will focus on neurons whose internal state is described by a single scalar quantity its membrane potential m whose time course is described by a differential equation dm t Ty ue f S pmt depending on its input Sm The choi
14. can do this by defining the modules in a different way so input to layers will get processed first and only after all layers have their input processed will the output then get computed RUN_MODULE didday_mem_pot DIFF eq u tu u w1 U w2 V h1 5 DIFF eq v tv v U sum h2 RUN_MODULE didday_firing U NSLstep u k V NSLramp v Alfredo Weitzenfeld NSL 2 1 25 By combining the update of all neuron firing layers layers into the last module we simulate parallel update since no output values will be computed until every layer has its input processed 5 4 Expressions Layer dynamics in the form of mathematical equations describe the interactions among the different layers in the network On the left hand side of the equation the layer being described is specified On the right hand side of the equation an expression is given specifying the particular input for that layer where the expression may be composed of sub expressions Positive sub expressions describe an excitatory effect while negative sub expressions describe an inhibitory effect on the layer For example equations can be as follows DIFF eq u tu u w1 U w2 V h1 S U NSLstep u k The general form of the equation is Ihs expression where lhs is the left hand side of the equation and may be one of the following lhs gt layer lhs gt var lhs gt diff where layer is either a data vector or matrix structure var i
15. currently simulated model is called DIDDAY then a call to open without arguments will create an output data file named DIDDAY nsl 0 the next call to open without arguments will create an output data file named DIDDAY nsl 1 and so on The information stored into these data files is basically all the data values computed during the simulation NSL will store data from all those layers currently enabled where enable layer refers to which layer is enabled for file interaction To enable a layer specified by name to be written do file_enable layer name Layers may be disabled by using the file_disable command in a similar way The ALL reserved string serves as name modifier specifying all layers in the network To close file execute the following command close file_name where file name is the name of the file to be close If the command is executed without a file name then the current open file is closed input data file In order to create a a file for input the user may execute the following command open INPUT file_name Alfredo Weitzenfeld NSL 2 1 45 where file_name is the name of the file to be created If the command is executed without a file name then the current model name is used as file name The information to be read is basically depends on what s stored in the file and what layers are currently enabled NSL will read data to all those layers currently enabled where enable layer refers to w
16. details are completely hidden away from the rest of the network Figure 3 A network of interconnected neurons For example Figure 3 shows a network composed of three neurons where the input to neuron m1 is given by specifying S1 in the following manner S1 W21 M2 W31 M3 where W21 and W31 specify the connection weights for the links between m2 and m1 and the links between m3 and m1 respectively S1 adds together the factors from the output of neurons M2 and M3 multiplied by their respective connection weights 3 2 Layers and Masks As part of our modelling primitives we have extended the basic neuron abstraction into neuron layers and connection masks describing spatial arrangements among homogeneous neurons and their connections respectively The reason for defining such abstractions is that in the brain as well as in many neural engineering applications we often find neural networks structured into two dimensional layers with regular connection patterns between various layers The computational advantage of introducing such concepts when describing a neural network is that neural layers and interconnection masks can then be concisely described as higher level data structures Instead of describing neurons on a one by one basis a layer can be described as an array and similarly the connections between layers can be described by a mask storing synaptic weights An interconnection among neurons would then be process
17. inf aay esther r cdas 30 5 6 1 ATOME das an dan en dater aai RE A Ea A Sir 30 5 6 2 SUDITACHON tdi dt nn den ee de a ete 30 5 6 3 Multiplication rl dr des dr redire de 31 5 6 4 Division bald 31 5 6 5 Convolution A za 32 5 6 6 A See nn PR nn al RS 34 5 6 7 A ne EE E a a SU MONTANT 37 Dala Numerical M odS usines es ln io 38 5 7 1 Euler ss seen O Concho drames a aan eee 38 5 7 2 Interpol ii tion 38 5 7 3 RUNAS UA A ds a AD taa 39 G Learning Methods ia 39 6 NSE Simulation Command ai ccs 39 6 1 Model Object Classes 5e ne nn ral Ona cdo 40 6 1 1 NELWOLK A nr Mn Re M en ne dt dr re dd ed dde dette a 40 6 1 2 layers ata ano ES SEE RERO 41 6 1 3 Moli o coaching dite ddr ten tr s abs 42 6 2 A est nine re etes 43 Alfredo Weitzenfeld NSL 2 1 6 3 Data less nl sites 44 6 4 Simulation Management 45 65 INumerical Methods La Re an en iii dadas 45 60 TR ET NS Ruel cence Res tia til oboe beste 46 Z NSL Window Interface user int E ot toes ita eb Noa re 46 7 1 Display Object Classes in uns ennemies AS e TEER S EAS 47 7 1 1 Window interface iaa 47 7 1 2 display frames hands de ms Ci su then items 48 7 1 3 display wind OW ss inst ta picas E 48 7 1 4 display canvas ss cites lees ner hentai nn etienne in 50 7 1 5 display panel orteses riore ne rente nette Sea aio Nado etienne 52 Leds Window Mouse Interaction 53 7 2 1 Drawing Frame 53 7 2 2 Drawing Canvas sisi cease deeded ied ae in tent
18. layer DATA layer_name DATA S a data layer with a single element Vector layer VECTOR layer_name size VECTOR INP 10 a 10 element vector layer Matrix layer MATRIX layer_name rows columns MATRIX A 10 8 a 10x8 element layer where layer_name specifies the name of the layer size specifies the length of the vector rows specifies the number of rows of a matrix layer and columns represent the number of columns of a matrix layer For our sample model we should enter the following declarations after the NETWORK line VECTOR S 10 network input S VECTOR u 10 membrane potential u VECTOR U 10 firing rate U DATA v membrane potential v DATA V firing rate V 12 Vectors may also be declared as column vectors COL_VEC layer_name size or row vectors which corresponds to the default VECTOR declaration type ROW_VEC layer_name size Alfredo Weitzenfeld NSL 2 1 23 S is the network input layer while u and U represent the membrane potential and firing rate layer respectively and v and V represent the membrane potential and firing rate layer respectively The convention followed here which is not enforced is to name membrane potential layers with lower case letters while firing layers are named with upper case letters The following seven declarations although similar to those of v and V represent network parameters DATA tu u time constant DATA tv v time const
19. several model files may be compiled together it is required to name each module differently this requirement is for the present system release and will be discarded in the future Different naming can be achieved by concatenating the particular model name with a local separate name For example for a model called didday a module could be called didday_mod1 Alfredo Weitzenfeld NSL 2 1 24 RUN_MODULEs are processed during the entire simulation with the exception of the initialization time when t gt 0 RUN_MODULE module_name layer dynamics For our sample model and after having declared the layers in the network we define the processing modules The first one is an INIT_MODULE resetting the dynamic layers to zero every time the network is re computed INIT_MODULE didday_init 0 0 0 S x dade Il Y Two RUN_MODULEs are declared for the didday model one for layer U and another one for layer V Each module calculates new membrane potentials and firing rates The layer dynamics are all in the form of mathematical descriptions These expressions will be explained in the next sections RUN_MODULE didday_U DIFF eq u tu u w1 U w2 V h1 S U NSLstep u k RUN_MODULE didday_V DIFF eq v tv v U sum h2 V NSLramp v Processing is sequential so in this case layer U would get computed before layer V If we wanted to simulate parallel neural update we
20. the firing rates The mapping from the first layer to the second is simply the neuron s nonlinearity e g a step ramp or sigmoidal function A convention is to use the same name for each layer in lower case for the membrane potential layer and in upper case for the firing rate layer This convention aids the user but is not enforced by the compiler In NSL 2 1 an array x is declared as DATA x if it has a single element VECTOR x n if it one dimensional with n elements and ARRAY x m n if it is a 2 dimensional mxn array Each declaration is terminated by a semi colon Thus the introduction to the model looks as follows ae Re nae tee ee aye mig ae eae Je didday c 3 PR SRE EE SEER ape eT include nsl_include h NETWORK DIDDA Y VECTOR S 10 network input VECTOR u 10 membrane potential VECTOR U 10 firing rate DATA v membrane potential DATA V firing rate We next declare some of the constants needed to define the model whose values will be set in didday nsl If a constant is really constant we may write the numerical value directly into the program However it is often good practice to name these model parameters a so that the user may better understand the role that it plays in the model and b to make it easy to change values when running experiments on how different features of the model affect its behavior DATA k DATA tu DATA tv DATA h1 threshold for u DATA h2
21. the neural network has been completely described Different numerical methods keep on evolving and they may be more appropriate according to the sophistication of the model and the processing power of the computing machine 5 7 1 Euler The Euler method which is the default NSL method replaces the above differential equation by m t dt 1 dt tm m t dt tm Sm t where dt is the integration time step delta 5 7 2 Interpolation The interpolation method replaces the above differential equation by m t dt p m t 1 p Smt Alfredo Weitzenfeld NSL 2 1 39 where p exp dt t 5 7 3 Runge Kutta The Runge Kutta numerical method is included as a separate document 5 8 Learning Methods Learning methods are included as NSL libraries built on top of the main layer structures Back propagation sample networks are included as a separate document 6 NSL Simulation Commands In order to process and interact with the model it is necessary to set up a suitable simulation environment including the window interface for graphics displays This section will concentrate on how model parameters are interactively assigned the simulation is run and other simulation related commands are used the window interface will be described in the next section Commands may be read from batch files or interactively entered and any number of command files can be associated with a single model file precedes all comm
22. the order of commands is very important the set network command should precede all other commands in the file The simulation file for the previously described DIDDAY model should then begin with set network DIDDAY status The interpreter provides status information on different aspects of the system If several models have been compiled together the status command can give a listing of them showing their names and indices and information on which one is currently enabled In what follows nsl gt is the system s prompt nsl gt status system A sample response would look as follows total linked models 11 1 TUTORIAL disabled 2 TECTUM_88 disabled 3 TECTUM_11 disabled 4 STRETCH disabled 25 Currently NSL 2 1 lets only one model be run at any time in the future several model could be run together Alfredo Weitzenfeld NSL 2 1 41 5 RETINA disabled 6 LOOM21 disabled 7 LIMULUS disabled 8 DIDDAY enabled 9 DEV disabled 10 CUE INTERACTION disabled 11 BEKESY disabled 6 1 2 layer The following are commands affecting network layers set Layers can be assigned data interactively at any time during the simulation Data may also be assigned through the graphics interface as will be explained in the window interface section To assign data set data_value name value value where name is the name of an existing layer Immediately follo
23. threshold for inhibitory unit DATA w1 DATA w2 The description of the model is now given in two parts the INIT_MODULE and the RUN_MODULEs The current release requires the user to include the line include nsl_include h at the beginning of the file This line tells NSL to incorporate all object declarations and macro definitions Alfredo Weitzenfeld NSL 2 1 15 4 1 2 INIT MODULE INIT MODULE didday_init tells the program how to initialize appropriate variables and constants we shall later discuss how other parameters are initialized INIT MODULE runs just once at the beginning of a run of the model and we shall later discuss how the length and grain of the run is specified Following the header INIT MODULE didday_init starts with and ends with Each line is terminated with a semi colon Note that in the spirit of array processing we may where appropriate specify all values of an array in a single assignment INIT_MODULE didday_init These expressions are called every time the model is re run and should include any model initialization lines such as resetting layer values to zero 4 1 3 RUN MODULES RUN _MODULE didday_x has as many parts as there are natural submodules which comprise the module We could have an x for every variable in the module or one x for the whole module However in this example we specify two RUN_MODULEs one called didday_U to specify how uand U are updated an
24. void operator nsl_data amp void operator num_type void print void print _status 9 1 3 2 vector The macro declaration of VECTOR name size translates to nsl_vector name name size Alfredo Weitzenfeld NSL 2 1 63 where nsl_vector is the name of the object class and name is the name of the instantiation variable name is used for linking the compiled code with the run time interpreted environment size is simply the size of the vector which also gets passed as argument to the nsl_vector class constructor The vector structure is as follows class nsl_vector public nsl_layer num_type v int i0 il int size public nsl_vector int nsl_vector nsl_vector amp nsl_vector nsl_model char int nsl_vector nsl_model amp char int nsl_vector char int nsl_vector int get_i0 int get_il int get_size num_type get_vector num_type amp elem int void operator nsl_vector amp void operator nsl_data amp void operator num_type num_type max num_type min num_type sum nsl_vector get_sector int int nsl_vector put_sector nsl_vector amp int void print void print int int void print_status k 9 1 3 3 matrix The macro declaration of MATRIX name rows columns translates to nsl_matrix name name rows columns where nsl_matrix is the name of the object class and name is the name of the instantiation variable name is used for linkin
25. with the following script set input_layer IN reset stim_list set stim_val 1 0 create block_stim set stim_t0 0 0 set stim_t1 0 3 create time_stim set stim_t0 3 0 set stim_t1 3 3 create time_stim These lines will be explained in the next sections 8 2 1 input layer The first step in describing an input object is to set the appropriate input layer e g set input_layer IN then the mapping characteristics between the layer and the input stimulus coordinates have to be given For example Alfredo Weitzenfeld NSL 2 1 58 set input_xz 0 set input_yz 16 set input_dx 1 set input_dy 1 specify the origin of the coordinate system to lie over IN 0 16 element 0 16 of layer IN while the distance among adjacent layer elements is equivalent to 1 either in x or y Figure 22 shows the general schematics of an input layer and input stimulus specification characteristics input_xz input_yz stim_x0 stim_y0 stim_xc stim_yc stim_x1 stim_yl stim_dx stim_dy Figure 22 NSL input stim objects The summary of input layer specifications is given in section 10 the input stimulus specifications will be explained in the next section 8 2 2 input_stim The following is the input object specification as shown in Figure 19 reset stim_list which resets the stimuli list to a new one set stim_val 1 5 Alfredo Weitzenfeld NSL 2 1 59 which assigns the value of 1 5 to the input layer elements corresponding to t
26. 0 1 0 A A 1 0 1 0 NSLsaturation NSLsigmoid Figure 11 NSL threshold functions To get arbitrary threshold functions as shown in Figure 12 the following function call can be given step B ky2 ky1 NSLstep A kx1 ky1 or B NSLstep A kx1 ky1 ky2 corresponds to an iteration over all i j for if A ij lt kxl Bli j ky1 Alfredo Weitzenfeld NSL 2 1 36 else if A i j kx1 Bi jl ky2 B ky2 ky1 NSLramp A kx1 ky1 or B NSLramp A kx1 ky1 ky2 corresponds to an iteration over all i j for if Ali j lt kx1 Bli j kyl else if Ali j kx1 Blij Alij kx1 ky2 saturation B ky2 ky1 NSLsaturation A kx1 kx2 kx1 ky1 or B NSLsaturation A kx1 kx2 ky1 ky2 corresponds to an iteration over all ij for if Ali j lt kx1 Bfi j ky1 else if kx1 lt Afi j lt kx2 Bli j ky2 ky1 Afi j kx1 kx2 kx1 ky1 else if Afi j kx2 Bfi j ky2 sigmoid B ky2 ky1 NSLsigmoid s2 3 2s ky1 where s A kx1 kx2 kx1 or B NSLsigmoid A kx1 kx2 ky1 ky2 corresponds to an iteration over all i j for if A ij lt kxl Bli j ky1 else if kx1 lt Ali j lt kx2 Bli j s2 3 2s where s A i j kx1 kx2 kx1 else if Ali j kx2 Bli j ky2 Alfredo Weitzenfeld NSL 2 1 37 B ky2 kyl kx1 ie NSLstep B ky2 kyl kx1 kx2 A NSLsaturation B ky2 ky1 kxl da NSLramp B ky2 kyl kx1 kx2 A NSLsigmoid Arbitrary threshold functions 5 6 7 Other Othe
27. 54 7 2 3 Control Panel ess ras REL IDS Gs its MANS Che Ne ne ir nee 55 0 UN SLs Input Rac tyres sn frise nt TU OM Sal Mere remettent eA ea denim serie Ends 55 8 1 Modellangtage iii tandil ANN Rene e rt 56 8 1 1 INput day Olano nan rer a ie nent rada 56 8 1 2 processe RS A Me mr tee M e dre nes terne lanta ere dise 57 8 2 Simulation Commands ss sessist eyii aeae eA e EA OKD ES N As EEES 58 8 2 1 Input layer toto MA N AE es A dass tuk 58 8 2 2 ANP Ut SEL S25 Posie ii ed rade rose secs di 59 9 Advanced NSL Programming 61 9 1 ModelEanguages i tin trs ne Mt rta deeds 61 9 1 1 TEEWOLK stress mat Men iio lERR nn 61 9 1 2 modules eea ONO 62 9 1 3 NAV OTS E EEN 62 ONS Ms data SERRE EE EE e a Aar Aea A e 63 A anea n E E a S ens Sore eeaaahenechueh exe 63 D S MAD e nr AA or a AA eee 64 9 1 4 INPUt ENE E T T E Cid A S 65 gsls O s su peie R e A E Sedona EE e OEN Ea 65 91 42 A innn o a R tetes ten ee 66 9 1 43 input_matrix s 66 9 2 Adding NSL Language Functions 67 9 3 Adding Simulation Commands ss 67 9 4 Adding Simulation Functions in C 68 9 4 Calling Simulation Commands from C 69 96 5 Adding Grapes 5 en AE Le Re Oc Scat AR a ee te 69 10 NSL Simulation Command Summary 69 O A ne ne nr nr UN nn ce 69 1022 TN 70 10 3 ET 70 104 enables ti netas 71 TOS eee 71 LOG A ras a a was vied O Oa re tn ttre tated ier 71 e iera li
28. NSL Neural Simulation Language Version 2 1 Alfredo Weitzenfeld Technical Report 91 05 August 1991 Brain Simulation Laboratory Center for Neural Engineering University of Southern California Preparation of this document was supported in part by grant 1R01 NS24926 from NINDS of the National Institutes of Health Michael A Arbib Principal Investigator and in part by a grant from Rockwell International to the USC Center for Neural Engineering NSL Neural Simulation Language Version 2 1 The software described in this document and the document itself are copyrighted and may not be copied or otherwise distributed without the prior written consent of the Brain Simulation Laboratory The information in this document is subject to change The Brain Simulation Laboratory assumes no responsibility for any errors that may appear in this document Users are requested to advise Alfredo Weitzenfeld at the address given below of any comments or suggestions for improvements To get copies of the software contact Alfredo Weitzenfeld Brain Simulation Laboratory Center for Neural Engineering University of Southern California Los Angeles CA 90089 2520 e mail alfredo usc edu The lab will charge a fee of 50 for tape user s manual and delivery For FTP send a request to the above e mail address Copyright 1991 Brain Simulation Laboratory All Rights Reserved Alfredo Weitzenfeld NSL 2 1 Table of Contents I Introd
29. Vectors can be added with other vectors of the same size or with data and with float values Matrices can be added with other matrices of the same size with data and with float values Vectors and matrices cannot be added together When a vector or matrix is added to a data or num_type value this value is added to every component of the vector or matrix For example having matrices X and Y X 1 1 1 Y 2 2 2 1 2 1 1 3 1 1 1 2 22 2 X Y 3 3 3 X 1 2922 2 5 2 2 3 2 3 3 4 2 2 3 5 6 2 Subtraction Subtraction operator is a pointwise subtraction among corresponding elements of similar layers The NSL function corresponding to it is NSLsub a b Vectors can be subtracted from other vectors of the same size from data and from float values Matrices can be subtracted from other matrices of the same size from data and from float values Vectors and matrices cannot be subtracted from each other When a vector or matrix is subtracted from to a data or num_type value this value is subtracted from to every component of the vector or matrix 5 6 3 Multiplication Multiplication can be of different forms 21 Matrix values are entered row by row Alfredo Weitzenfeld NSL 2 1 31 Pointwise multiplication operator 22 among corresponding elements of similar layers The NSL function corresponding to it is NSLmult a b Vectors can be multiplied with other vectors of the same size with data an
30. aded to provide the right functionality For example adding two matrices a b operators is similar to calling NSLadd a b which returns a matrix containing the added pointwise matrix values Operations not covered here by the above operators e g regular matrix multiplication are achieved by function calling Some of these functions provide the nonlinear mappings between the neuron s membrane potential and firing rate which are needed in neural net modeling Direct value assignment to layers may be achieved in two ways By specifying a single value for the whole layer available to all layer types as included in the above description layer_name value e g S 1 5 By specifying a value for a particular layer unit and depending on the type of layer Data layer layer_name elem value Vector layer layer_name elem index value Matrix layer layer_name elem row_index col_index value in order to ensure proper operation This shortcoming should be overcome in the next NSL release Alfredo Weitzenfeld NSL 2 1 27 where index specifies a vector element row_index specifies a matrix row element and col_index specifies a matrix column element All indices start from 0 5 5 Layer Class Functions There are two types of functions layer class functions and layer library functions Layer class functions are of the form layer function while layer library function are of the form function layer Layer c
31. al equation in going from u t to u t At etc The code in didday nsl to be described in section 4 2 provides the missing information for a given run of the model as well as the information on how to set up the graphics for displaying the results of the simulation 4 1 4 Compilation We will name the model file didday c although more generally a model file should be called file c where file totally arbitrary name and what s important is the c suffix Compilation and linkage of this file is done by executing the following line the file nsl_main c should be present in the directory where compilation is taking place nsl_link file c The system will then create an executable file called nsl if no errors were made in the model file which is ready for running Several model files may be linked with NSL by simply adding their names to the nsl_link command file list 9 At this point the model has been linked with NSL and it can be run by typing nsl 7 This compilation requires the availability of a C compiler 8 nsl_main c contains the C C main routine where nsl initialization takes place Linking to any other C C programs can be included inside this file as explained in the advanced programming section A copy of this file should exist in the directory where compilation is taking place and can be obtained by running nsl_init which also copies the sample didday model files 9 If running graphics rem
32. amp nsl_data amp nsl_data amp SLstep nsl_vector amp nsl_data amp nsl_data amp nsl_data amp SLstep nsl_matrix amp nsl_matrix amp nsl_matrix amp nsl_matrix amp SLstep ns _matrix amp nsl_matrix amp nsl_data amp nsl_data amp SLstep nsl_matrix amp nsl_data amp nsl_data amp nsl_data amp SLramp num_type SLramp nsl_data amp SLramp nsl_vector amp SLramp nsl_matrix amp NSLramp num_type num_type num_type num_type JSLramp nsl_data amp nsl_data amp nsl_data amp nsl_data amp JSLramp nsl_vector amp nsl_vector amp nsl_vector amp nsl_vector amp JSLramp nsl_vector amp nsl_vector amp nsl_data amp ns _data amp SLramp nsl_vector amp nsl_data amp nsl_data amp nsl_data amp JSLramp nsl_matrix amp nsl_matrix amp nsl_matrix amp nsl_matrix amp JSLramp nsl_matrix amp nsl_matrix amp nsl_data amp nsl_data amp JSLramp nsl_matrix amp nsl_data amp nsl_data amp nsl_data amp SLsaturation nsl_data amp NSLsaturation nsl_vector amp Alfredo Weitzenfeld NSL 2 1 83 nsl_matrix num_type nsl_data nsl_vector nsl_vector nsl_vector nsl_matrix nsl_matrix nsl_matrix NSLsigmoid num_type nsl_data nsl_vector nsl_matrix num_type nsl_data nsl_vector nsl_vector nsl_vector nsl_matrix nsl_matrix nsl_matrix NSLsaturation nsl_matrix amp SLsaturation num_type num_type num_type num_type num_type NSLsaturation nsl_data nsl_data nsl_data nsl_data nsl_datad
33. ant DATA k step function threshold DATA w1 DATA w2 DATA h1 DATA h2 These parameters will be assigned values through the nsl file to be read by the commands interpreter 5 3 3 Module The MODULE class is utilized by declaring any of the following in the form of macro declarations MODULE INIT MODULE and RUN MODULE The module contains the code describing the equations that are to be processed by NSL differing only in the time intervals on which the modules are applied depending on the above declaration types If there are no modules no processing will be done There may be as many modules as desired having any number of equations in each of them including having a single module for all the equations or one module per equation 3 The order of processing is the same order in which the modules are declared Currently these modules are serially processed although the goal in the future is to distribute them and take advantage of their concurrent nature In what follows module_name is the name of the modulel4 MODULES are processed for every time iteration t 0 MODULE module_name layer dynamics INIT_MODULEs are processed only at t 0 and should contain initialization code which gets called every time the model is reset INIT_MODULE module_name layer initialization 13 The current version doesn t support layer declarations inside a module only expressions 14 Since
34. as display_panel update display panel canvas_item update canvas item panel_item update panel item 12 References Amari S Arbib M A 1977 Competition and Cooperation in Neural Nets Systems Neuroscience J Metzler ed pp 119 165 Academic Press Arbib M A 1989 The Metaphorical Brain 2 Neural Networks and Beyond Wiley Didday R L 1976 A Model of Visuomotor Mechanisms in the Frog Optic Tectum Math Biosci Vol 30 pp 169 180 Goddard N Lynne KJ Mintz T 1987 Rochester Connectionist Simulator User s Manual University of Rochester Department of Computer Science Hebb D O 1949 The Organization of Behavior Wiley Hodgkin A L Huxley A F 1952 A Quantitative Descriptionof Membrane Current and its Application to Conduction and Excitation in Nerve J Physiol London Vol 117 pp 500 544 Kandel E R Schwartz J H 1985 Principles of Neural Science Elsevier Kernighan B W Ritchie D M 1978 The C Programming Language Prentice Hall McCulloch W S Pitts W H 1943 A Logical Calculus of the Ideas Immanent in Nervous Activities Bull Math Biophys Vol 5 pp 115 133 Rumelhart D E McClelland J L 1986 Parallel Distributed Processing Vol I amp IL MIT Press Stroustrup B 1987 The C Programming Language Addison Wesley Teeters J 1989 A Simulation System for Neural Networks and Model for the Anuran Retina TR 89 01 PhD Thesis Center for Neural Engineering University
35. ays for treating edge effects which is basically the convolution with out of bound layer elements We will address the following three main alternatives treat edges effects as zero do a wrap around of layer elements replicate boundary layer elements NSL deals with these three types of convolution as will be described more details in later sections 3 3 Numerical Methods Up until now we have left out the internal neural model detail One widely used neuron model is the leaky integrator Arbib 1989 whose membrane potential is described by the following differential equation Alfredo Weitzenfeld NSL 2 1 12 dm t Ty nz m t Sm t where S t incorporates the input from all the other cells and Ty is the time constant The overall dynamics will depend upon the actual choice of excitatory and inhibitory weights in each Sy t and of the time constants While different numerical methods may be used to solve a particular neuron model the neural network architecture and connection weights should not have to change depending on this Different numerical methods keep on evolving and they may be more appropriate according to the sophistication of the model and the processing power of the computing machine Many methods use a constant time step At As an example consider two different methods the Euler method and interpolation method for solving the previous differential equation The Euler method replace
36. ce of f defines the particular neural model utilized including the dependence of m on the neuron s previous history The firing rate or output of the neuron M is obtained by applying some threshold function to the neuron s membrane potential M t o m t where o could be for example a non linear sigmoid saturation function When building neural networks the output of a neuron serves as input to other neurons Links among neurons carry a connection weight which describes how neurons affect each other Links are called excitatory or inhibitory depending on whether the weight is positive or negative The most common formula for the input to a neuron is n Sm D wi Milt i 1 where M_ t is the firing rate of the neuron whose output is connected to the ith input line to the neuron and w is the weight on that link Alfredo Weitzenfeld NSL 2 1 10 It is important to realize that neurons may be modelled with different levels of detail from sophisticated biophysical models to simple binary models where the neuron is either on or off at each time step such as the McCulloch Pitts neuron model McCulloch and Pitts 1943 The Leaky Integrator see section 3 3 provides a simple yet more natural neuron model In terms of more detailed neuron models we have compartmental models Kandel and Schwartz 1985 and the Hodgkin Huxley model Hodgkin and Huxley 1952 In any event neurons are best suited to be treated as objects whose internal
37. computed by in the case of the corner location tx0 ts stim_vx stim_x0 ty0 ts stim_vy stim_y0 where ts is the current simulated time The summary of input stimulus specifications is given in section 10 9 Advanced NSL Programming To write more developed code in NSL the user is encouraged to become familiar with the C language The current release compiles NSL an extended version of C so user written C code should compile in a straight forward manner and may be integrated with any NSL code In these sections we will describe NSL classes and their most important public methods Calls to these methods can be done from the model language by writing any C expressions inside the different processing modules or by writing totally independent C routines which may be called from an expression Many files may be linked together the only requirement is that each contain an include nsl_include h line which contains all the header and macro definitions necessary for linking NSL code 9 1 Model Language Following C conventions an object s public method is called as follows object method where object is the name of the object and method the desired member function If the object is referenced as a pointer to it then the call would be object gt method 9 1 1 network The macro declaration of NETWORK name translates to a C declaration of nsl_network name name where nsl_network is the name
38. current form row or col to the opposite one do vector vector transpose applying it twice consecutively brings the vector to its original form Other functions set or get matrix rows and columns vector matrix get_row i vector matrix get_col j 18 Previously known as NSLmat_to_row_vec and NSLmat_to_col_vec 19 NSL will automatically draw vectors on the screen in the direction they are defined Internally all vectors are stored a unified way having simply an internal flag which tells what type they are row or column vectors 20 Currently there is no matrix transpose function Alfredo Weitzenfeld NSL 2 1 29 matrix matrix set_row vector i matrix matrix set_col vector j where i is a row index and j is a column index For example if A B set_row b i then Alij bij while Alk j B k j for k i 5 5 2 Sectors Sector functions deal with parts of layers either for setting them or to get part of them get_sector returns a sector of the respective vector or matrix while put_sector returns a larger vector or matrix with a copy of the specified vector or matrix inside and the rest of the elements left to zero The return layers are of size equal to the layer in front of the member function Currently the sector s starting point is specified and the whole sector is either copied or retrieved from the layer Vector sectors vector vector get_sector i0 j0 vector vector put_sector vector0 i0 wh
39. d another called didday_V for v and V RUN_MODULE didday_U DIFF eq u tu u w1 U w2 V h1 S U NSLstep u k RUN_MODULE didday_V DIFF eq v tv v U sum h2 V NSLramp v Note the NSL syntax for a differential equation We simply rewrite tau du dt f u x as DIFF eq u tau f u x where the differentiated variable u is followed by its time constant tau on the left hand side and f u x is simply the right hand side of the differential equation rewritten in NSL syntax the present Alfredo Weitzenfeld NSL 2 1 16 n n example the only convention to be noted is that gt f uj which is just D U is rewritten as i 1 i 1 U sum with the sigma summator written as a layer member function The nonlinear functions that transform a membrane potential into its firing rate are provided by functions that are included in the NSL library Thus 1 u gt 0 f u lo 20 is given by NSLstep u 0 while Ge SE is given by NSLramp v This completes didday c the actual specification of the model in NSL The INIT MODULE initializes the state of the computer for the run An actual run has a given time step and a given duration and proceeds by running each of the RUN_MODULEs at each time step in order to update the values of all the variables from the start to the end of the time step The user may specify which numerical method is to be used in approximating the solution of each differenti
40. d interpreter If the commands were stored into a file called didday nsl then this file can be loaded by typing nsl gt load didday To run the model simply type the output of a simulation is shown in Figure 7 nsl gt run WY MiG 00 why Max 00 ts 20 00 jog i1 9 imax 10 WAT2 LAYERU WY mina ag wyma 3 00 ts 20 00 Figure 7 The output of Didday model The user may stop the simulation at any time by typing C To resume the simulation from the interrupt point type Alfredo Weitzenfeld NSL 2 1 20 nsl gt cont 5 NSL Model Language NSL is built following an object oriented programming paradigm NSL provides a set of basic network object classes intended to give the user simple yet powerful constructs without restricting in any way the complexity and the type of models which can be described It is the goal of NSL to provide tools in a bottom up fashion where future system versions will incorporate more sophisticated network structures built on top of the currently available ones The following sections will give the user an introduction to NSL basic object structures 5 1 Object Oriented Programming Since NSL is designed as an object oriented language it is worth understanding the concepts behind this kind of programming methodology We will put emphasis on C due to its important role as NSL s implementation language Specifically the reader may want to become familiar with C as a programming language by referenc
41. d with float values Matrices can be multiplied with other matrices of the same size with data and with float values Vectors and matrices cannot be pointwise multiplied together When a vector or matrix is pointwise multiplied to a data or num_type value this value is multiplied to every component of the vector or matrix NSL also supports vector dot product and matrix multiplication scalar multiplication is supported by both The NSL function corresponding to it is NSLprod a b If X and Y are two vectors of the same size then NSLprod X Y xTy returns a data value size 1 equal to the dot product of the two vectors If X and Y are two matrices of sizes nxm and mxr respectively then NSLprod X Y XY returns a matrix of size nxr 5 6 4 Division Pointwise division operator among corresponding elements of similar layers The NSL function corresponding to it is NSLdiv a b Vectors can be divided with other vectors of the same size with data and with float values Matrices can be divided with other matrices of the same size with data and with float values Vectors and matrices cannot be pointwise divided together When a vector or matrix is pointwise divided with to a data or num_type value this value is divided with to every component of the vector or matrix For example having matrices X and Y X 1 1 1 Y 2 2 2 1 2 1 1 3 1 1 1 2 2 2 2 X Y 0 5 0 5 0 5 1 0 67 1 0 5 0 5 1 X 2 0 5 0
42. dex of the different layer elements simply drag the mouse without clicking any button over the different units and their respective values with their respective unit locations will be shown on val_out this entry value cannot be modified by the user 7 2 3 Control Panel The control panel as shown in Figure 14 contains two sections a static top section and a dynamic bottom section The top section contains the following entries The UpdateGraph button used for updating the corresponding display window with new information The Layer menu from which a layer is selected The Graph menu from which a graph is selected The lower section is scrollable and contains different entries depending on the Layer and Graph type currently selected 8 NSL Input Facility NSL 2 1 includes a facility for dealing with a special type of INPUT_LAYER An input layer serves as the world where many different objects or stimuli may be set with constrains on their location and time on which they are valid While this functionality may be obtained using regular NSL language constructs such a task is greatly simplified by the use of NSL s input facility In the next sections we explain how to interact with this module Alfredo Weitzenfeld NSL 2 1 55 For example Figure 19 shows an area_level_graph of an input layer INPUT_MAT made of 32x32 elements containing an object of size 8x4 joa Figure 19 NSL input stim object
43. dex 27 For example set all_data_value S 0 set elem_i 4 set elem_data_value S 1 set elem_i 6 set elem_data_value S 0 5 is equivalent to set data_value S 0000100 5000 status To show the data values status data_value name For example if we want to show the values of layer S then nsl gt status data_value S The system response would be as follows set data_value S 00001005000 6 1 3 module The following are commands affecting network modules Initially all modules are enabled for processing yet the user has the option to disable or enable individual modules from being processed enable To enable module processing 27 NSL 2 2 will have single element assignment in the form of v i val for vectors and m i j val for matrices Alfredo Weitzenfeld NSL 2 1 43 enable module name where name is optional and should match an existing module name disable To disable module processing disable module name where name is optional and should match an existing module name 6 2 Simulation Processing The following are commands affecting network simulation processing set To set the simulation time step or delta set delta value value specifies the simulation delta time step To set the simulation end time set end_time value value specifies the simulation end time which divided by delta gives the total number of steps the simulation is going to run For example for the didday model we have set delta 0
44. ding any other command line parameters via more nsl_get_str The name of the command is new_command The file nsl_main c has to be edited so it would look as follows include nsl_include h extern int my_command_function istream z main int argc char argv NSLinit argc argv NSL_USER_CMD my_command_ function NSLmain argc argv These commands may then be called from the interpreter with the following syntax user new_command optional modifiers 9 4 Adding Simulation Functions in C In order to permit greater flexibility from the command interpreter NSL permits the addition of general purpose simulation command functions to be written in C code This is achieved by declaring a special type of module in the model file called FUNC_MODULE The purpose of this module is to provide the link between the model language and the command interpreter A FUNC_MODULE may include any C code or it may call regular simulation commands see next section The interpreter itself would call the function by exec function_name No arguments may be passed to the function Any C expressions may be included inside this module such as conditionals and iterative loops The syntax is as follows FUNC_MODULE function_name function specification Alfredo Weitzenfeld NSL 2 1 68 Calling simulation commands from inside a module is described in the next section 9 4 Calling Simulation Commands from C
45. e will result in Y M X as follows first a larger matrix is created with wrapped around values for the edges the size of the new matrix depends on both the size of the mask and the convolved matrix 23 X0 0 1 2 4 8 0 0 1 1 1 1 1 1 1 2 1 2 2 2 2 1 4 1 2 4 4 4 1 8 1 2 4 8 8 1 0 1 2 4 8 0 1 0 1 1 1 1 1 0 second we overlap M on the left top corner of XO with M 0 0 on top of X0 0 0 so the first convolution will be given by Y 0 0 0 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 2 1 12 and so on for the other elements The function for this kind of effect would be called as Y NSLconv_wrap M X copy edge The edge element values of the layers are replicated as if it was an infinite layer For example having layer X and mask M as before will result in Y M X as follows first a larger matrix is created with copied values for the edges the size of the new matrix depends on both the size of the mask and the convolved matrix X0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 2 4 4 4 4 1 1 2 4 8 8 8 1 1 2 4 8 0 0 1 1 2 4 8 0 0 second we overlap M on the left top corner of XO with M 0 0 on top of X0 0 0 so the first convolution will be given by Y 0 0 1 1 1 1 1 1 1 1 1 2 1 1 141 1 1 2 1 11 and so on for the other elements 23 Edge corners are currently assigned zero Alfredo Weitzenfeld NSL 2 1 34 The function for this kind of effect would be called as Y NSLconv_co
46. ect classes window_interface display_frame display_window display_canvas and display_panel 7 1 1 window_interface The window_interface is a non visual object type instantiated automatically by the system s graphical environment Figure 13 shows the window interface structure composed of a list of display frames Each display frame is made up of a list of display windows which themselves are composed of a display canvas where graphs are drawn and a data panel where the user can interface with the window control attributes display_frame display_window display_panel display_canvas Figure 13 NSL display classes In order to initialize a window interface the following call should be entered if the call doesn t appear new frames will be added to any currently existing ones create window_interface Alfredo Weitzenfeld NSL 2 1 48 7 1 2 display_ frame A display_frame is a visual display unit manipulated as a single entity on the screen which can be moved resized and printed A display frame can be physically composed of any number of display windows as will be explained in the next section For example the display frame on Figure 12 FW1 is created by the following commands set frame_name FW1 set frame_X0 200 set frame_YO 100 set frame_width 500 set frame_height 335 set frame_rows 2 create display_frame The set command assigns values to the different environment variables frame_name specif
47. ed by computing a spatial convolution of a mask and a layer For example if A represents an array of outputs from one layer of neurons and B represents the array of inputs to another layer and if the mask W k l for d lt k l lt d represents the synaptic weight from the A i k l for msk lsm elements to B i j element for each i and j we then have d d Bij Y S WE DAGE AD k d l d which can be expressed by the single array operation of convolution Alfredo Weitzenfeld NSL 2 1 11 B WxA giving greater computing power to a simple descriptive expression Figure 4 A discrete spatial convolution among mask W and layer A with B W A As shown in Figure 4 mask W stores the different connection or synaptic weights performing a discrete spatial convolution over A to obtain B In this example both the layers and the mask are square although they could be of any size as a matter of fact a layer may have any shape while 2D rectangular shapes are the most commonly used ones In terms of syntax the equations for the network shown in Figure 2 would be exactly the same if it was describing neuron layers instead of single neurons The only difference would be that now the factors representing connection weights will now represent connection masks and the variables representing neurons will now represent neuron layers The multiplication operator now means convolution It is important to realize that there are different w
48. ede all other declarations in the model file NETWORK model_name where model_name is the name to be used when identifying this particular model 1 For our sample network the first line of the c file would be NETWORK DIDDAY Note that this entry is required in every model file Without it the model file will not be translated 5 3 2 Layer The LAYER is a super class from which three data layer classes are derived DATA VECTOR and MATRIX classes These three classes vary according to the number of dimensions they contain A data layer represents a layer with a single unit a vector layer represents a one dimensional array of units and a matrix layer represents a two dimensional array of units Higher numbers of dimensions may be incorporated into new data structures if so desired similarly a user may define classes of objects which may have a structure other than the traditional rectangular ones although this is beyond the scope of this manual Figure 9 shows the layer class hierarchy 11 model_name doesn t have to be the same as the name of the file model_name is used to refer to the model from the simulation environment Alfredo Weitzenfeld NSL 2 1 22 VECTOR MATRIX Figure 9 NSL layer classes The LAYER super class is not directly utilized in specifying a network instead the user utilizes the derived layer classes DATA VECTOR and MATRIX The following is the syntax for each class declaration Data
49. edo Weitzenfeld NSL 2 1 index disable an input stim by index name is either a string name or ALL index is an integer 10 4 enable enable type l option enable processing for object type type option description network enable current model name enable a particular model by name index enable a particular model by index module enable current module name enable a particular module by name index enable a particular module by index layer enable current layer update name enable a particular layer update by name index enable a particular layer update by index input_layer enable current input layer name enable an input layer by name index enable an input layer by index input_stim enable current input stim name enable an input stim by name index enable an input stim by index name is either a string name or ALL index is an integer 10 5 exec exec execute a function module defined in the model file 10 6 exit exit quit exit NSL 10 7 file emd l option name commands for dealing with external i o cmd option description Alfredo Weitzenfeld NSL 2 1 71 file_enable file_disable load read write open close 10 8 proc emd l option process model enable layer name for file in out disable layer name for file in out read from file name write into filename open file name according to current file_type INPUT open
50. elatively few human readable lines which be understood and appreciated both by users with little programming background and by those with more extensive programming expertise For this purpose we have designed the language in the form of basic mathematical equations where the user may either program at a high level or include more sophisticated programming code Although NSL has been principally developed with a certain type of biological modelling in mind we have kept it as general as possible letting the user define diverse types of networks including those concerned with learning As will be discussed in more detail in later sections any network that can be described as a set of equations to be updated after each simulation iteration can be modelled by NSL The system includes the following features An object oriented simulation language with built in model object classes A library with the common neural network functions A library with sample neural network models Methodology for extending the libraries A command language interpreter for describing the simulation environment Interactive and batch processing of commands and data Management of simulation versions An interactive X windows graphical interface Temporal and spatial displays 2D and 3D graphics The flexibility of a system written in the UNIX C C environment NSL 2 1 offered as public domain software is the second release for the
51. eld NSL 2 1 49 set window_layer S set window_graph area_level_graph set window_wymin 0 set window_wymax 2 create display_window set window_name WN12 set window_layer u set window_graph temporal_graph set window_wymin 3 set window_wymax 3 set window_t1 20 create display_window The first window WN11 will display layer S as an area_level_graph with a y axis value range between 0 and 2 The second window WN12 will display layer u as a temporal_graph with y axis value range between 3 and 3 The time scale for the temporal graph is from 0 to 20 Each window automatically opens a display panel control panel on an independent screen frame 9 set The set command assigns values to the different environment variables window_name specifies the name to be used for the display window window_width specifies the width of the display canvas contained in the display window window_height specifies the height of the display canvas contained in the display window window_X0 specifies the left pixel location of the display canvas contained in the display window where the coordinate is zero on the left of the frame and increments towards the right until the frame s maximum width is reached window_Y0 specifies the top pixel location of the display canvas contained in the display window where the coordinate is zero on the top of the frame and increments towards the bottom until the frame s maximum height is reached
52. ent library functions available in NSL describing the number and type of arguments accepted by each one of them nsl_data nsl_vector and nsl_matrix are NSL layer classes while num_type is a simple data type currently defined to be a float arithmetic addition nsl_ data operator nsl_data z nsl_data operator nsl_data amp nsl_data amp nsl_data operator nsl_data amp num_type nsl_data operator num_type nsl_data amp nsl_vector operator nsl_vector amp nsl_vector amp nsl_vector operator nsl_vector amp nsl_vector operator nsl_vector amp num_type nsl_vector operator num_type nsl_vector amp nsl_vector operator nsl_vector amp nsl_data amp nsl_vector operator nsl_data amp nsl_vector amp nsl_matrix operator nsl_matrix amp nsl_matrix operator nsl_matrix amp nsl_matrix amp nsl_matrix operator nsl_matrix amp nsl_data amp nsl_matrix operator nsl_data amp nsl_matrix amp nsl_matrix operator nsl_matrix amp num_type nsl_matrix operator num_type nsl_matrix z subtraction nsl_data operator nsl_data amp nsl_data operator nsl_data amp nsl_data amp nsl_data operator nsl_data num_type nsl_data operator num_type nsl_data amp nsl_vector operator nsl_vector amp nsl_vector operator nsl_vector z nsl_vector z nsl_vector operator nsl_vector amp num_type nsl_vector operator num_type nsl_vector amp nsl_vector operator nsl_vector am
53. ents The most important commands will be described in these sections while a summary of all simulation commands is included at the end of the manual There are three important commands worth mentioning here before getting into any of the other ones command description help on line help quit or exit exit the simulator load file load a nsl file to be interpreted help Provides extensive on line information where information is available as a general command listing help or per command giving more detailed information on each command help command exit quit Provides the way of exiting the simulator 4 24 control C AC is used to interrupt simulation runs Alfredo Weitzenfeld NSL 2 1 40 load The load command is used to read in any nsl files containing simulation commands For example a file called didday nsl may be loaded as follows the nsl suffix may be omitted load didday 6 1 Model Object Classes Interaction with NSL s model language objects is done via the simulation environment In these sections we will provide a sample simulation file for the previously described DIDDAY model stored in didday c 6 1 1 network The following are commands affecting initial network setup set To set up the desired simulation model include the following line set network name where name matches the one in NETWORK name for the corresponding model Since this file is interpreted
54. epresenting the activity of the different elements in the layer spatial_graph_2 displays a layer as a two dimensional graph only vector layers should be displayed with this option Figure 15 shows an area_level_graph and a spatial_graph_2 for a similar vector layer spatial_graph_3 displays a layer as a three dimensional graph only matrix layers should be displayed with this option Figure 16 shows an area_level_graph and a spatial_graph_3 for a similar matrix layer Temporal Graphs a vector temporal graph is shown in Figure 12 inside window WN12 temporal_graph displays temporal layer information Every layer element is displayed as an independent temporal graph where the complete graph will contain as many rows and columns as there are elements in that layer i0 lt gt il jO lt gt j1 each graph being a temporal display t0 lt gt t1 of the respective layer s element 32 Figure 16 matrix area_level_graph vs spatial_graph_3 31 An area_level_graph may be used both for displaying and reading input as will be described later in more detail 32 For efficiency considerations the model data produced is not automatically stored by the system For this reason temporal graphs can only be fully displayed while the simulation is being run At the end of a simulation all layer temporal data is lost Alfredo Weitzenfeld NSL 2 1 52 7 1 5 display_panel The display_panel contains varied window control items There
55. ere i0 i1 specifies a vector sector Matrix sectors matrix matrix get_sector i0 i1 j0 j1 matrix matrix put_sector matrix0 i0 j0 where 10 11 j0 j1 specifies a matrix sector 5 5 3 Other To get the sum of all elements in either a data vector or matrix layer returning a num_type float value num_type layer sum To get the max or min values from either data vector or matrix layers and returning a num_type float value num_type layer max num_type layer min Alfredo Weitzenfeld NSL 2 1 30 5 6 Layer Library Functions The layer library includes a list of functions which usually take more than one layer as argument to the functions These functions are independent from the layer classes themselves and provide further extensibility Among these functions there are arithmetic functions including convolution and threshold functions Efficiency of these functions is of major importance since the system spends most of its CPU time around these functions All functions have a NSL prefix to distinguish them from any user defined functions The user may define additional functions to be written in either C Stroustrup 1987 or C Kernighan and Ritchie 1978 as will be explained in the advanced NSL programming section 5 6 1 Addition Addition operator is a pointwise addition among corresponding elements of similar layers The NSL function corresponding to it is NSLadd a b
56. es a set of display object classes and graphics libraries In order to be able to efficiently interact with the window interface the user should become familiar with the different types of display objects available In the following sections we will explain how to design such a graphics interface by either storing all commands on a nsl file or by interactively typing into the nsl interpreter Figure 12 shows the window interface created for the didday model at the end of the simulation WY MINI 00 why Ma 00 ts 20 00 Tene i1 9 imax 10 WAT2 LAYERU wy MIN 3 00 WM MAX 3 00 ts 20 00 Figure 12 The window interface for the didday simulation model The code creating this frame is as follows set frame_name FW1 set frame_X0 200 set frame_YO 100 set frame_width 500 set frame_height 335 set frame_rows 2 create display_frame set window_name WN11 set window_layer S set window_graph area_level_graph set window_wymin 0 set window_wymax 2 create display_window set window_name WN12 set window_layer u set window_graph temporal_graph set window_wymin 3 Alfredo Weitzenfeld NSL 2 1 47 set window_wymax 3 set window_t1 20 create display_window The next sections will describe the different interface object classes and describe their manipulation via the command interpreter A summary of all available window interface commands is given in section 11 7 1 Display Object Classes There are five types of display obj
57. file name for input OUTPUT open file name for output close file name cmd option description init process modules for t 0 run process modules for 0 lt t lt end_time ts process modules for 0 lt t lt ts cont process modules for current time lt t lt end_time ts process modules for current_time lt t lt ts step process modules 1 iteration n process modules n iterations 10 9 reset reset type reset object type type description stim_list reset stimuli list 10 10 set set type option set buffer for objects in the next categories network information input layer information stimulus information type class description network module module information layer layer information input_layer input_stim network Alfredo Weitzenfeld NSL 2 1 72 set modifier option set simulation end_time to value set simulation current_time to value current delta time step set simulation delta to value current integration numerical method set simulation numerical method to method modifier option description network current network name network by name index network by index end_time current end_time value current_time current time value delta value integration method module set modifier option modifier option description module current module name module by name index module by index layer set modifier option
58. g the compiled code with the run time interpreted environment rows and columns are simply the size of the matrix which also gets passed as arguments to the nsl_matrix class constructor The matrix structure is as follows class nsl_matrix public nsl_layer Alfredo Weitzenfeld NSL 2 1 64 num_type v int i0 i1 j0 j1 int rows cols public 9 1 4 There are three types of input layers derived from the regular layer classes nsl_matrix int int nsl_matrix nsl_matrix amp nsl_matrix nsl_model char int int nsl_matrix nsl_model amp char int int nsl_matrix char int int nsl_matrix int get_i0 int get_il int get_j0 int get_j1 int get_rows int get_cols num_type get_matrix num_type amp elem int int void operator nsl_matrix amp void operator nsl_data amp void operator num_type num_type max num_type min num_type sum nsl_matrix get_sector int int int int nsl_matrix put_sector nsl_matrix amp int int void print print layer data void print int int int int void print_status input_layers 9 1 4 1 input_data The macro INPUT_DAT name translates to where nsl_input_data is the name of the object class and name is the name of instantiation variable name is utilized for linking the compiled code with the run time interpreted environment nsl_input_data name name The data structure is as follows class n
59. he current input object location set stim_x0 4 set stim_y0 0 which sets the input object upper left corner location to 4 0 on the input layer coordinate system and which maps to layer elements 4 16 set stim_dx 8 set stim_dy 4 which sets the input object size to 8x4 and create block_stim which actually creates the specified object The object shown in figure 20 is specified by reset stim_list which resets the stimuli list to a new one set stim_val 1 0 which assigns the value of 1 0 which is really the default value create block_stim which creates the specified object since this is a single element layer there is no need to specify stimulus size or location set stim_t0 0 0 set stim_t1 0 3 create time_stim this creates a time interval between 0 0 and 0 3 simulated time set stim_t0 3 0 set stim_t1 3 3 create time_stim while this creates a time interval between 3 0 and 3 3 The temporal output is shown in Figure 20 The location of the stimulus may be specified either by using its corner or its center as reference position where the relation among them in a any rectangular object is as follows stim_xc stim_x0 stim_dx 2 stim_yc stim_y0 stim_dy 2 Objects may also be specified with velocity stim_vx Alfredo Weitzenfeld NSL 2 1 60 stim_vy where the object s velocity is calculated as distance per simulated time or in other words the current stimulus position at any given time is
60. hich layer is enabled for file interaction To enable a layer specified by name to be read do file_enable layer name The only other aspect to be considered is that if there are modules which originally computed those layers they should be disabled from processing To close the file execute the following command close file_name where file_name is the name of the file to be close If the command is executed without a file name then the current open file is closed 6 4 Simulation Management One important aspect of the system is the ability to record automatically any interaction done by the user so it can be reproduced at any time in the future 28 6 5 Numerical Methods NSL current release provides two different numerical methods for integration 22 set To choose the appropriate numerical method NSL provides with the following command set integration type where type may be EULER or INTERPOLATION For example to use the didday model with the EULER method which is also the default one write set integration EULER 6 6 Other Other commands are included in section 10 28 Simulation management is under current development and will be available with the next system release 29 Future releases will extend upon the number and types of numerical methods available Yet the user may include new numerical methods with any NSL model Alfredo Weitzenfeld NSL 2 1 46 7 NSL Window Interface The window interface compris
61. ies the name to be used for the display frame frame_width specifies the width of the display frame frame_height specifies the height of the display frame frame_X0 specifies the left pixel location of the display frame where the coordinate is zero on the left of the screen and increments towards the right until the monitor s maximum width is reached frame_Y0 specifies the top pixel location of the display frame where the coordinate is zero on the top of the screen and increments towards the bottom until the monitor s maximum height is reached frame_rows specifies the number of rows of display windows to be included inside the display frame graphs are assigned row wise frame_cols specifies the number of columns of display windows to be included inside the display frame create The create command creates a new display frame according to the specified setting update The update command updates an existing display frame according to the specified settings 7 1 3 display window A display window is a non visual object containing two types of of visual objects a display_canvas where all graphics takes place and a display_panel a special window used for controlling the display canvas The display window also contains an internal database storing all the window parameters In the the sample frame of Figure 12 two display windows are created with the following commands set window_name WN11 Alfredo Weitzenf
62. ing C from Stroustrup 1989 or any other C textbook 5 2 Model Creation Writing a simulation in NSL consists of several steps The first step is to describe the model as a set of NSL equations stored into the model file c file The second step consists of writing a simulation environment and stored into simulation files as many as needed nsl files Simulation files contain input and parameter assignments which may vary during different simulation runs They also include any graphical set ups 5 3 Model Object Classes NSL basic network objects are of three types NETWORK MODULE and LAYER These classes serve as super classes utilizing C terminology for other derived classes meaning that any other classes inherit their respective characteristics These names define macros which get translated into internal NSL object class declaration as will be explained in the advanced programming section in further detail In what follows characters shown in bold letters are meant to be typed exactly as they appear and should not be used as variable names words appearing in italics are user supplied strings either names or values 5 3 1 Network A model is described by a NETWORK object which points to a list of LAYERs and processing MODULEs Figure 8 shows the network structure Alfredo Weitzenfeld NSL 2 1 21 LAYER list NETWORK Figure 8 NETWORK class The declaration of the network object should always prec
63. input_matrix char int int nsl_input_matrix int get_stim_total Ie 9 2 Adding NSL Language Functions New NSL language functions can be written by following C syntax Any NSL data structure can be used inside functions and as arguments to the function The only restriction is that no NSL macros may be Alfredo Weitzenfeld NSL 2 1 66 declared DATA VECTOR MATRIX etc only the raw nsl structures nsl_ data nsl_ vector nsl_matrix etc It is also important that any nsl structures be declared by specifying its size and not the optional name thus making it unknown from the global nsl structures34 For example to write a function that takes two nsl_matrix arguments and checks if both matrix arguments are of the same size declares a new matrix m of equal size assigns to the corresponding elements of the new matrix either 1 if both argument matrices have an equal corresponding element value or 0 otherwise the newly created matrix containing the result is then returned nsl_matrix function nsl_matrix m1 nsl_matrix amp m2 int rows m1 get_rows int cols m1 get_cols nsl_matrix m rows cols initializes the matrix with 0 if rows m2 get_rows cols m2 get_cols cmd_error Bad matrix sizes in function else for int i 0 i lt rows i index go from 0 to rows 1 for intj 0 j lt cols j j index goes from 0 to cols 1 if m1 elem ij
64. instantiation variable name is used the name to be stored internally for linking the compiled code with the run time interpreted environment The module class definition is as follows class nsl_module char name NAME SIZE module name int index module index number public nsl_module nsl_module char get_name return module name int get_index return module index number y 9 1 3 layers The layer class which is the super class for the derived data vector and matrix classes definition is as follows Alfredo Weitzenfeld NSL 2 1 62 class nsl_layer char name NAME SIZE int index int layer_type 1 nsl_data 2 nsl_vector 3 nsl_matrix public nsl_layer int nsl_layer char int void set_name char void set_index int void set_layer_type int char get_name int get_index int get_layer_type 9 1 3 1 data The macro declaration DATA name translates to nsl_data name name where nsl_data is the name of the object class and name is the name of the instantiation variable name is used for linking the compiled code with the run time interpreted environment The data structure is as follows class nsl_data public nsl_layer num_type v public nsl_data nsl_data nsl_data amp nsl_data nsl_model amp char nsl_data nsl_model char nsl_data char nsl_data num_type amp get_data num_type amp elem
65. int value 3D graph z reference point value 3D graph x scale value 3D graph y scale value 3D graph z scale print status information for object type type option description window_interface display_frame name index display_window name index display_canvas name index display_panel name index window_item name index canvas_item name index panel_item name index interface status information frame status information display frame status by name display frame status by index window status information display window status by name display window status by index canvas status information display canvas status by name display canvas status by index panel status information display panel status by name display panel status by index window item status information window item status by name window item status by index canvas item status information canvas item status by name canvas item status by index panel item status information panel item status by name panel item status by index name is either a string name or ALL index is an integer Alfredo Weitzenfeld NSL 2 1 79 11 9 update The update command updates current display information update type type description window_interface update all display frames and display windows display_frame update display frame display_window update display window display_canvas update display canv
66. lass function are basically functions applied to a particular layer while layer library functions are routines taking any number of layer arguments not all arguments have to be of layer type The following sections describe the most relevant layer class functions 5 5 1 Transformations While there are three basic types of layers it is important to be able to do transformations among them Figure 10 shows row and column transformations among vectors and matrices Figure 10 Vector and Matrix Transformations Transforming from vectors into matrices either as a row or column vector expansion 7 matrix row_vector expand_row n matrix col_vector expand_col n From Figure 10 B A expand_row n 17 Previously know as NSLcol_vec_to_mat and NSLrow_vec_to_mat Alfredo Weitzenfeld NSL 2 1 28 B ij AG B C expand_col n Bij Cli Transforming from matrices into vectors either as a row or column vector reduction 8 row_vector matrix reduce_row col_vector matrix reduce_col From Figure 10 A B reduce_row Ajj Y BG j i C B reduce_col Ci BG j j Since vectors may be row wise or col wise it is important to have a transformation from one to the other 9 To transpose row vectors and columns vectors 0 To set a vector as a row vector do row_vector vector transpose_row To set a vector as a column vector do col_vector vector transpose_col To switch a vector from its
67. matically resized when the frame itself is resized For this purpose ff set frame_auto_resize is ON which is the default then every time a frame is resized all the windows will be automatically resized according to the number of rows and columns that have been specified for the particular frame If the option is OFF no internal window resizing will take place even though the frame will change its size 7 2 2 Drawing Canvas The following are different types of interactive commands which may be activated through the help of the mouse while inside a display canvas Obtaining a Window Dump A Window Dump a display picture snapshot may be obtained from any display frame at any time A window dump can be saved into a raster file ras a postscript file ps or directly be sent to a printer The menu containing these options is found by moving the mouse over the desired frame and pressing the mouse s right button which will show a menu with three entries WinDump UpdateGraph and ControlPanel Drag the mouse to the right of the WinDump menu entry while still holding down the right button a new menu will appear with the following choices WindowDump gt Printer Send the window dump directly to the printer without having to store it first in a file Alfredo Weitzenfeld NSL 2 1 54 WindowDump gt RasterFile Save the window dump into a rasterfile ras specified by the dump_file variable
68. modifier option description layer current layer name layer by name index layer by index data_value name all_data_value name elem_i index elem_j index elem_data_value name input layer set modifier option modifier option layer name followed by all values layer name followed by single data value for whole layer layer row element index layer col element index layer name followed by elem data value used in conjunction with elem_i and elem_j description input_layer name index input_xz index input_yz index input_dx value current input layer input layer by name input layer by index zero coordinate x layer element default is 0 zero coordinate y layer element default is 0 distance between adjacent x layer elements Alfredo Weitzenfeld NSL 2 1 73 default is 1 0 input_dy value distance between adjacent y layer elements default is 1 0 input_stim set modifier option modifier option description input_stim current stim index stim by index stim_index index stim index stim_dx value stim x size width default is 1 0 stim_dy value stim y size height default is 1 0 stim_xc value stim x center initial location default is 0 0 stim_yc value stim y center initial location default is 0 0 stim_x0 value stim x left initial location default is 0 0 stim_y0 value stim y top initial location default is 0 0 stim_spec type CENTER
69. n this simulation In this case we hold the input constant throughout the run All values of the S array are 0 except for 1 0 in the fourth entry arrays start at the zeroth entry and 0 5 in the sixth entry set data_value S 000010005000 4 2 3 Graphics Finally we specify the windows to be used in displaying the input S and the membrane potential u MIN OO wi Max 2 00 ts 0 00 11 39 mM 3 00 WY MAX 00 ts 0 00 imax 10 t00 00 t1 20 00 Figure 6 The Didday model window set up We specify that both displays will be contained in a frame called FW1 which will have two rows graphics create window_interface set frame_name FW1 set frame_X0 250 set frame_YO 100 set frame_width 510 set frame_height 335 set frame_rows 2 create display_frame The first row contains a window WN11 which displays the vector S with each element shown as an area level graph while the second row contains a window WN12 which displays the vector u with each element shown as a temporal graph Alfredo Weitzenfeld NSL 2 1 19 set window_name WN11 set window_layer S set window_graph area_level_graph set window_wymin 0 set window_wymax 2 create display_window set window_name WN12 set window_layer u set window_graph temporal_graph set window_wymin 3 set window_wymax 3 set window_tl 20 create display_window 4 2 4 Running the Simulation The previous commands could have been loaded interactively into NSL s comman
70. ntaining all the graphics descriptions data assignments and any other run time specifications l NSL has been developed on a SUN workstation platform 2 The simulator may be run independent from a graphical interface in that case the X server is not required The X windows system has been developed utilizing the XVIEW library 3 NSL advanced programming section includes explanations directed to more advanced users with some basic knowledge of C and C 4 C and C supporting code may be stored in separate files to be linked together with the model file 5 Several command files may be assigned to a single model file Alfredo Weitzenfeld NSL 2 1 8 The Window Interface is composed of the Graphical Displays where all window and graphics interaction takes places the Graphics Libraries containing all display functions and object libraries Window Interface Graphical Graphics Displays Libraries Simulator Model Language Libraries Processing Module Model Language Compiler Commands Interpreter Figure 1 NSL Simulation System One of the key consideration when designing these modules has been that of extensibility where new functions and objects may be added into any of these libraries as will be described in later sections 3 Neural Network Simulation In general neural network simulation can be divided into two distinct categories biological neural networks designed to model the
71. o regular layer expressions VECTOR MATRIX INPUT_DAT INPUT_VEC INPUT_MAT Figure 21 NSL input layer classes The following are the different classes of input layers Data layer INPUT_DAT layer_name e g INPUT_DAT S a data layer Vector layer INPUT_VEC layer_name size e g INPUT_VEC INP 10 a 10 unit vector layer Matrix layer INPUT_MAT layer_name rows columns e g INPUT_MAT A 10 8 a 10x8 layer where layer_name specifies the name of the layer size specifies the length of the vector rows specifies the number of rows of a matrix layer and columns represent the number of columns of a matrix layer Alfredo Weitzenfeld NSL 2 1 5 8 1 2 processing Processing of any stimuli specifications done from the nsl file is achieved by including the following line inside a RUN MODULE input_layer run where layer_name specifies the name of the layer and run is the function which will process any existing stimuli specification 8 2 Simulation Commands Once an input layer has been declared in the model file it is necessary to give the input object specifications in the command file For example the object shown in Figure 19 was created with the following script set input_layer IN set input_xz 0 set input_yz 16 set input_dx 1 set input_dy 1 reset stim_list set stim_val 1 5 set stim_x0 4 set stim_y0 0 set stim_dx 8 set stim_dy 4 create block_stim The object shown in Figure 20 was created
72. of Southern California Wang D Hsu C 1990 SLONN A Simulation Language for modeling of Neural Networks Simulation pp 69 83 Weitzenfeld A 1989 NSL Neural Simulation Language Version 1 0 TR 89 02 Center for Neural Engineering University of Southern California Weitzenfeld A 1990 NSL Neural Simulation Language Version 2 0 TR 90 01 Center for Neural Engineering University of Southern California Wilson M A Bhalla U S Uhley J D Bower J M 1989 GENESIS A System for Simulating Neural Networks Advances in Neural Network Information Processing System Morgan Kauffman 13 Appendices The following appendices give have been added to the manual to give further explanations Alfredo Weitzenfeld NSL 2 1 80 13 1 NSL Environment To start an NSL session one including graphics make sure you have initialized the appropriate windowing environment Due to the fact that NSL s current window interface release runs under the X window environment The regular xstart or xinit can be used to enter the environment In a Sun there is also the option to run the openwinodws environment by executing openwin nsl can be run from any c shell window or any xterm If this is the first time you are going to run a model in NSL execute first the nsl_init command to create default settings and copy the sample models from the NSL directories 13 2 NSL Library Functions The following is a list of the differ
73. of the object class and name is the name of the instantiation variable name is used the name to be stored internally for linking the compiled code with the run time interpreted environment The network class definition is as follows class nsl_network char name NAME SIZE model name float DELTA time step float CURRENT_TIME current time float END_TIME end time int layer_total total number of layers int module_total total number of modules Alfredo Weitzenfeld NSL 2 1 61 public nsl_network char nsl_network float get_delta get delta time step float get_time get current simulation time float get_end_time get simulation end time void set_delta float set time step void set_time float set current simulation time void set_end_time float set simulation end time void reset_time reset time to 0 int get_layer_total total number of layers nsl_layer get_layer char name search nsl_layer get_layer int index search int get_module_total total number of modules void print_status print model information i For example to get the value for the delta do and having a network called DIDDAY float dt DIDDAY get_delta 9 1 2 modules The macro declaration of MODULE name translates to a C declaration of nsl_module name name where nsl_module is the name of the object class and name is the name of the
74. or CORNER stim_type type BLOCK or ICON stim_val value stim value used for BLOCK type default is 1 0 stim_mat matrix stim icon matrix used for ICON type stim_vx value stim velocity positive going right stim_vy value stim velocity positive going up stim_t0 value beginning of stim time interval stim_t1 value end of stim time interval 10 11 shell cmd option execute a unix shell command cmd option description cd dir_name change the model directory to dir_name csh cmd_line execute a csh cmd_line sh emd_line execute a sh cmd_line 10 12 status status type option print status information for object type type option description system list all linked models files list all active data files current current system status network status on current model Alfredo Weitzenfeld NSL 2 1 74 name status on a model by name index status on a model by index module status on current module name status on a module by name index status on a module by index layer status on current layer name status on a layer by name index status on a layer by index data_value current layer data values name current layer data values by name index current layer data values by index input_layer status on current input_layer name status on an input_layer by name index status on an input_layer by index input_stim print all input layer stimuli name print stimuli of an inpu
75. otely run nsl as follows nsl display hostname 0 where hostname is the name of the machine physically displaying the graphics 10 A single nsl_main c is required even if multiple model files are compiled together Alfredo Weitzenfeld NSL 2 1 17 nsl The NSL prompt will appear nsl gt Although we could set up the simulation environment interactively it is more convenient to have it stored in a batch file a nsl file 4 2 didday nsl The simulation set up is provided in the form of simulation parameters model parameters including network input and graphics 4 2 1 Simulation Parameters In the first part of didday nsl we tell the compiler to set up the network DIDDAY i e it should link the DIDDAY network stored in didday c to the material that follows to use the EULER integration method and to run the model from time 0 to time 20 0 using a time step delta of 0 1 thus making a total of 200 iterations of the model didday nsl simulation set up set network DIDDAY network set integration EULER set delta 0 1 set end_time 20 0 4 2 2 Model Parameters We also tell it to set those network parameters whose values were not specified in didday c set data_value tu 1 0 set data_value tv 1 0 set data_value k 0 1 set data_ value wl 1 0 set data value w2 1 0 set data_value h1 0 1 set data_value h2 0 5 Alfredo Weitzenfeld NSL 2 1 18 Next we specify the input to be used i
76. p nsl_data amp nsl_vector operator nsl_data z nsl_vector z nsl_matrix operator nsl_matrix amp nsl_matrix operator nsl_matrix amp nsl_matrix amp nsl_matrix operator nsl_matrix amp nsl_data amp nsl_matrix operator nsl_data amp nsl_matrix amp Alfredo Weitzenfeld NSL 2 1 81 nsl_matrix nsl_matrix operator nsl_matrix amp num_type operator num_type nsl_matrix z pointwise multiplication nsl_vector nsl_vector nsl_vector nsl_vector nsl_vector nsl_matrix nsl_matrix nsl_matrix nsl_matrix nsl_matrix operator nsl_vector amp nsl_vector amp operator nsl_vector amp num_type operator num_type nsl_vector amp 5 operator nsl_vector z nsl_data z operator nsl_data amp nsl_vector amp operator nsl_matrix amp nsl_matrix operator nsl_matrix nsl_datad operator nsl_data amp nsl_matrix amp operator nsl_matrix amp num_type operator num_type nsl_matrix amp pointwise division nsl_data nsl_data nsl_data nsl_vector nsl_vector nsl_vector nsl_vector nsl_vector nsl_matrix nsl_matrix nsl_matrix nsl_matrix nsl_matrix convolution operator nsl_data amp nsl_data amp operator nsl_data amp num_type operator num_type nsl_data amp operator nsl_vector amp nsl_vector amp operator nsl_vector amp num_type operator num_type nsl_vector amp operator nsl_vector z nsl_data z operator nsl_data amp nsl_vecto
77. py M X As can be seen when comparing the results and as the name implies the differences are shown on the edges the further away from the edges the less the importance of edge effects 5 6 6 Threshold Figure 11 shows the available threshold functions These functions are applied to every element in the layer independently The return layer type is similar to the first argument given in the function where B indicates the returning value while A indicates the input value The function may be overloaded i e its arguments may be of different types The different argument types are given in Appendix 13 2 step NSLstep layer0 For example B NSLstep A corresponds to an iteration over all i j for if Ali j lt 0 Bfi j 0 else if A i j 0 Bfi j 1 NSLramp layer0 For example B NSLramp A corresponds to an iteration over all i j for if Ali j lt 0 Bfi j 0 else if Ali j 0 Bii j AL saturation NSLsaturation layer0 For example B NSLsaturation A corresponds to an iteration over all ij for if Ali j lt 0 ij else if 0 lt A ij lt 1 ij Alij ww Alfredo Weitzenfeld NSL 2 1 35 else if Ali j 1 Bij 1 sigmoid NSLsigmoid layer0 For example B NSLsigmoid A corresponds to an iteration over all i j for if Ali j lt 0 Bli j 0 else if 0 lt Ali j lt 1 Bli j Alij 2 2Ali else if Aij gt 1 Bij 1 B B 1 0 10 gt gt 1 0 NSLstep NSLramp B B 1
78. r amp operator nsl_matrix amp nsl_matrix amp operator nsl_matrix amp nsl_data amp operator nsl_data amp nsl_matrix amp operator nsl_matrix num_type operator num_type nsl_matrix amp nsl_data operator nsl_data amp nsl_data amp nsl_data operator nsl_data amp num_type nsi_ data operator num_type nsl_data amp nsl_vector operator nsl_vector amp nsl_vector amp nsl_matrix operator nsl_vector amp nsl_matrix amp nsl_vector operator nsl_vector amp nsl_data amp nsl_vector operator nsl_data amp nsl_vector amp nsl_vector operator nsl_vector amp num_type nsl_vector operator num_type nsl_vector z nsl_matrix operator nsl_matrix amp nsl_matrix amp nsl_matrix operator nsl_vector amp nsl_matrix amp row vector convolution nsl_matrix operator nsl_matrix amp nsl_vector amp column vector convolution nsl_matrix operator nsl_matrix amp nsl_data amp nsl_matrix operator nsl_data amp nsl_matrix amp nsl_matrix operator nsl_matrix amp num_type nsl_matrix operator num_type nsl_matrix z threshold functions NSLmax num_type NSLmax nsl_vector amp num_type NSLmax nsl_matrix amp nsi_ data NSLmax nsl_ data amp nsl_data amp Alfredo Weitzenfeld NSL 2 1 nsl_data nsl_vector nsl_vector nsl_vector nsl_matrix nsl_matrix nsl_matrix NSLmin num_type num_type nsl_data nsl_data nsl_vector nsl_vector nsl_vector nsl_matrix nsl_matrix
79. r functions include the max and min between to layers of the same size max Function returning a layer containing the pointwise maxima where both function arguments have to be of the same size NSLmax layer1 layer2 For example B NSLmax A1 A2 corresponds to an iteration over all i j of B ij max A1fi j A2fi j min Functions returning a layer containing the pointwise minima where both function arguments have to be of the same size NSLmin layer1 layer2 For example Alfredo Weitzenfeld NSL 2 1 38 B NSLmin A1 A2 corresponds to an iteration over all i j of Bli j min A1 i j A2 i j 5 7 Numerical Methods NSL provides a library of numerical methods for integration of differential equations The syntax for a differential equation is as follows DIFF eq u tm f u which translates to tm du dt f u NSL will then apply the appropriate numerical method euler etc at run time as specified by the user For example in the case of the leaky integrator model we would write DIFF eq u tm u S for f u u S where S is the input to the neuron layer While different numerical methods may be used to solve a particular neuron model the neural network architecture and connection weights should not have to change depending on this For this reason we treat numerical methods as orthogonal object classes totally independent from network specification A numerical method is instantiated only after
80. rent display panel name disable display panel by name index disable display panel by index canvas_item disable current canvas item index disable canvas item by index panel_item disable current panel item index disable panel item by index name is either a string name or ALL index is an integer 11 4 enable enable type l option enable window object type type option description Alfredo Weitzenfeld NSL 2 1 16 display_panel enable current display panel name enable display panel by name index enable display panel by index canvas_item enable current canvas item index enable canvas item by index panel_item enable current panel item index enable panel item by index name is either a string name or ALL index is an integer 11 5 print A window dump may also be generated from the command interpreter as follows cmd option cmd option description win_dump do a window dump on the current frame_name frame_name do a window dump on the specified frame_name print_dump print the current dump_file dump_file print the specified dump_file The win_dump command may be instructed to generate automatic file names by using the following commands set modifier option modifier option description dump_file name name of file used for window dumps dump_type PRINTER output will be sent directly to printer RASTER output will be saved as raster ras
81. s Figure 20 shows a temporal graph of an input layer INPUT_DAT made of a single element containing an object appearing at two different time intervals w emini 1 50 wymas 1 50 ts 5 00 t000 00 t1 5 00 Figure 20 NSL input stim objects These and many other object specifications may be done with the help of NSL s input facility as will be shown in the following sections 8 1 Model Language In this section we will describe the input layer class declarations and expressions included in NSL model language c file 8 1 1 input_layer The input_layer classes are derived from the basic layer classes data vector and matrix giving rise to INPUT_DAT INPUT_VEC and INPUT_MAT classes These three classes vary according to the number of dimensions they contain Figure 21 shows the layer class hierarchy Alfredo Weitzenfeld NSL 2 1 56 Since the input_layer is derived from the regular layer it includes all the basic functionality of the layer extended with its own private functionality Thus for example an input layer may be added with regular layers and so on What s characteristic to the input layer is its ability to be map external objects into itself These objects or stimuli have special characteristics such as movement and may be assigned time intervals on when to appear This facility thus provides a means for assigning external object specifications into a layer which at any moment may be incorporated int
82. s a low level C C variable structure such as float diff is a differential type of equation which will be further described in the numerical method section 5 expression is defined as follows expression gt expression expression gt expression operator expression expression gt term operator is defined as follows operator gt 1 1 1 1 where is the layer addition operator is the layer subtraction operator is the layer convolution operator is the pointwise layer multiplication operator 15 Both sides of the equality should return compatible value types in particular if the left hand side is of var type the right hand side should also return a var type 16 Due to its current implementation the has the lowest precedence requiring parenthesis around the partial expression Alfredo Weitzenfeld NSL 2 1 26 is the pointwise layer division operator term is defined as any of the following term gt layer term gt var term gt val term gt function where layer gt data vector matrix var is a variable returning a float type val is a float number function gt function_name par1 par2 parN where parj 1 lt j lt N can be any layer type data vector or matrix or a number value depending on the function argument specification All operators have a corresponding function performing the same operation In the C implementation operators are overlo
83. s connectivity among the different layers Alfredo Weitzenfeld NSL 2 1 13 Figure 5 Layers and interconnections as defined by the sample network The model represents an array of 10 cells with membrane potential u and firing rate U connected to a single inhibitory cell with firing rate V and membrane potential v The circuit is driven by an input array S The mathematical description of the model is dui t u gp it w1 flu wa glv hy sj 1sisn dv a Ty a V h i 1 where 1 u gt 0 w o He 0 and g S lo S lt 0 The model has the parameters w1 w2 h1 h2 with the restriction that 0 lt hl and 0 lt s h2 lt 1 and n 10 see Arbib 1989 Sec 4 4 for a full exposition 4 1 didday c Let s take the previously described Didday model as our sample model As in C comments are preceded by either and take effect until the end of the line or as in both C and C they start with until a is used to close the comments marks the end of the expression Alfredo Weitzenfeld NSL 2 1 14 4 1 1 Declarations We start by providing comments to name the program a line to tell the compiler that it should use the library nsl_include h and a line to name the program declaring that it is a network and that its name is DIDDAY In NSL we use two layers of elements to represent one layer of neurons The first layer holds the membrane potentials while the second layer holds
84. s the differential equation by m t At 1 a m t aa Sm t Tm Tm while the interpolation method replaces the differential equation by m t At p m t 1 p Sm t where p e Atit 3 4 Learning Methods An important part of neural network modelling is to be able to introduce learning in a model There are many different learning algorithms commonly utilized in neural network simulation among the most popular being back propagation Rumelhart et al 1986 This learning algorithm is not biological and thus differentiates biological modelling which is primarily concerned with modelling the brain in a faithful way from the study of artificial neural networks otherwise known as connectionism or neural engineering where the main concern is in applying neural network computing techniques to varied technological applications Artificial neural networks take advantage of newly developed neural learning algorithms to approach problem domains where traditional programming approaches may not have been very successful Biological learning can be exemplified by Hebbian learning Hebb 1949 4 Amari Arbib Maximum Selector Didday Model In this section we present the Maximum Selector model Amari and Arbib 1977 based on the Didday model for prey selection Didday 1976 This model uses a competition mechanism to obtain a single winner in the network and will serve as sample network to be simulated in NSL Figure 5 shows the network
85. second generation NSL language NSL 2 0 Weitzenfeld 1990 has been widely used in varied simulation applications giving rise to an accompanying document with sample neural network models simulated in NSL These second generation versions are direct successors to the original NSL 1 0 Weitzenfeld 1989 which has also been extensively used in our research lab and by students taking brain theory course given at USC 2 NSL System Overview This section gives an overview of NSL in terms of the requirements for its use and an overview of the overall system design Alfredo Weitzenfeld NSL 2 1 7 2 1 System Requirements NSL 2 1 like NSL 2 0 is implemented in C Stroustrup 1987 while NSL 1 0 was implemented in C Kernighan and Ritchie 1978 The current system requires an AT amp T C 2 0 compiler an X X11R4 server 2 2 User Expertise There are two levels of user expertise when developing NSL models the basic level requires familiarity with NSL high level language as described in the manual s next sections and there is no need to know either C or C the advanced level requires some basic understanding of C and C allowing great flexibility on they type of models which can be described as well as permitting communication with other software tools 2 3 System Design The system is composed of several modules whose functionality is basically the same in the different NSL versions differing most importantl
86. sl_input_data public nsl_data int stim_total print layer data sector print layer information Alfredo Weitzenfeld NSL 2 1 65 nsl_stim_list stim_list public nsl_input_data char nsl_input_data int get_stim_total p 9 1 4 2 input_vector The macro INPUT_VEC name size translates to nsl_input_vector name name size where nsl_input_vector is the name of the object class and name is the name of instantiation variable name is utilized for linking the compiled code with the run time interpreted environment size is simply the size of the vector which get also passed as argument to the nsl_vector class constructor The vector structure is as follows class nsl_input_vector public nsl_vector int stim_total nsl_stim_list stim_list public nsl_input_vector char int nsl_input_vector int get_stim_total le 9 1 4 3 input_matrix The macro INPUT_MAT name rows columns translates to nsl_input_matrix name name rows columns where nsl_input_matrix is the name of the object class and name is the name of instantiation variable name is utilized for linking the compiled code with the run time interpreted environment rows and columns simply the size of the matrix which get also passed as arguments to the nsl_matrix class constructor The matrix structure is as follows class nsl_input_matrix public nsl_matrix int stim_total nsl_stim_list stim_list public nsl_
87. sse teats east hails fo sro ek iss deena fhe nn OO er 72 ON 72 109 RS SPOSC E E A tet cations niet amuaeeasenaneten cee 72 LOTO O 72 LOL li a A at ie 74 10 12 estatuas aba 75 1019 Update ito daa 75 O A A Es tea Seka totes te et 75 Alfredo Weitzenfeld NSL 2 1 11 NSL Window Interface Command Summary ss 76 Tits ARG ptt sade RE RER RSS SR RE saa oped cele 76 11 2 Create usine nn Marennes rl dents dd lue aaa iaaa aai aiia til tete ete Oe 76 T3 disabl ss ssssiissthas assume a vts 76 TVA Enable osea 77 LUS TN 77 11 6 a nn inside ten d die lente den dde SAS 78 VAT St radas uth ese hice ee bd bude eas A 78 TL8 status i scccisdin sense eme lens ca casa uen retraite hod cakseaehnetdans Terrase deduce boxe 79 11 9 FUP OO 80 12 R ferences 3 tienne eme dolia Messed bids 80 LS A PPENGICeS ads tas 81 13 1 NSL Environment iii es 81 13 2 NSL o ss re ins ar EE Eer EEE e A 81 Alfredo Weitzenfeld NSL 2 1 6 1 Introduction NSL pronounced Nissl Neural network Simulation Language is a powerful yet easy to use simulation language and development system The simulator is designed and implemented following an object oriented paradigm and includes NSL s high level language for describing neural networks an interactive command interpreter and powerful visualization tools for analyzing models in different ways The goal of NSL is to facilitate the description of models in r
88. t layer by name index print stimuli of an input layer by index name is either a string name or ALL index is an integer 10 13 update The update command is utilized for updating model class objects The syntax is as follows update type type description block_stim update block type stim object icon_stim update icon type stim object time_stim update time interval for existing stim object 10 14 user user cmd user written command 11 NSL Window Interface Command Summary There are several types of display class commands including the creation of objects and the modification of object parameters 11 1 help help command command option NSL help on window interface commands command description Alfredo Weitzenfeld NSL 2 1 75 help this command create create model objects disable disable objects enable enable objects print printing commands print_ dump print a screen dump win_dump get a screen dump reset reset options set set options status status information on display objects update update display objects 11 2 create The create command is utilized for creating display class objects The syntax is as follows create type type description display_frame create display frame display_window create display window 11 3 disable disable type l option disable window object type type option description display_panel disable cur
89. uctions da iii 6 2 UNSL System OVervie Witt alada 6 2 1 System Requirements tissue it edo alii stas 7 2 2 User Expertises hist ainia lada ainia di eee 7 2 3 a ee ee EN ns desde ent 7 3 Neural Network Simulati n sirvio depa dea adas ad 9 3 1 Neurons dk iii ad 9 3 2 Layers and Mask cited nine toronto las 10 Bios Ni merical Methods conato ia osito 12 sd sario Methods li 12 4 Amari Arbib Maximum Selector Didday Model 13 4 1 didday is di tia 13 4 1 1 D clarations LA ALLA 14 4 1 2 INT MODULE tia dial 15 4 1 3 RUN MODULES join poli 15 4 1 4 Compila Ho Meis erata rer a DoS sda neem ata ala 16 4 2 Cidday Asler iresi Meads dE ne de PR Nr Reset diese nds te me ee A 17 4 2 1 Simulation Param t rs s sss sisi issus 17 4 2 2 Model Parameters 28 is ur din o ases 17 4 2 3 CPAP TCS RS RSS Re Gat cakes 18 4 2 4 Running the SAMOA a asias 19 S t ONSE Model dang ua ge ovaladas oil iaa 20 5 1 Object Oriented Programming ss 20 5 2 Model Cr ations ea di ne di 20 5 3 Model Object Classes sieste case anotan nr ntm rendent attire ceo ten 20 5 3 1 Networks caidas aia 20 5 3 2 AS de 21 5 3 3 Modules ist di ito isis 23 5 4 EXPLOSION lA te CA E A tn ne 25 5 5 Layer Class Functions ss 27 5 5 1 Transformations seen ceevdoa vests ccusaoad a tarte 27 5 5 2 SOCLOLS e dise rend re nn on is a tes nd a en nn lon ia ane sidi a 29 5 53 ORME Pessina ds ii OS de 29 5 6 Layer Library Function mesh
90. wing is a list of values separated by spaces with the list size matching the number of elements in the layer In the case of a data layer only one value would be entered in the case of a vector a list of values matching the number of elements in the vector would be entered and in the case of a matrix a list of values row wise and starting with row 0 followed by row 1 and son on would be entered until all the elements have been assigned 26 For example for the didday model one can assign the following values to its variables set data_value tu 1 0 set data_value tv 1 0 set data_value k 0 1 set data_value w1 1 0 set data_value w2 1 0 set data_value h1 0 1 set data_value h2 0 5 set data_value S 0000100 5000 assigning 1 0 to S 4 and 5 to S 6 Layers can be assigned a single data value for the complete layer by using set all_data_value name value For example set all_data_value S 1 26 NSL 2 2 will include assignment operators at the interpreter level so the same operation would be written as name value for data name value for vectors and name value for matrices Alfredo Weitzenfeld NSL 2 1 42 is equivalent to set data_value S 1111111111 Layers can be assigned single element data values by set elem_i index set elem_j index set elem_data_value name value elem_i specifies the vector element index or the matrix row index while elem_j specifies the matrix column in
91. y mainly in the object oriented emphasis given to the second generation system which includes the evolution from C into C as the system s implementation language Two aspects of the simulator have been greatly enhanced by the objectization of the system first the internal design now follows a very natural object oriented design and implementation and second the development of neural networks models is enhanced by the incorporation of special object classes into the simulation language The structure of the simulator is shown in Figure 1 The system is divided into two independent sub systems the Simulator where model interaction and processing takes place the Window Interface where all graphics interaction takes place The Simulator is composed of the Processing Module where the network is fully processed the Model Language Compiler which together with the Model Language Libraries translates and links the user s Model File loading it into the Processing Module the Commands Interpreter executing the user s Command Files for setting up and controlling the simulation The development of a simulation is then done in two separate steps by the creation of two different types of files Model File The user describes the network model a c file to be compiled which may include any C or C code4 Command Files The user describes the simulation environment a nsl file to be interpreted co
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