Learning-Tool - Neural Micro circuits
Contents
1. A novel strategy for real time computing on time series Special Issue on Foundations of Information Processing of TELEMATIK 8 1 39 43 Natschlager et al 2002b Natschlager T Markram H and Maass W 2002b Computer models and analysis tools for neural microcircuits In K tter R editor A Practical Guide to Neuroscience Databases and Associated Tools chapter 9 Kluver Academic Publishers Boston in press Svahn 2001 Svahn E 2001 Parallel matlab toolbox User documentation Master s thesis Chalmers University of Technology Sweden To get a copy of the toolbox contact E Svahn email ersva igb polymtl ca d96svahn dtek chalmers se or get it via ftp ftp at e technik uni rostock de pub pm2. State of the Microcircuit The transformed smoothed response output of the neural microcircuit in this examples this corresponds to a low pass filtered 30 ms version of the spike trains This transformation can also be dropped if one can cope directly with the spike response Sample Time Points Since we can only handle finite sets of training examples we must define time points at which we want to sample the state of the microcircuit in this example we will sample the states every 25 ms Readout Function A parameterized function device which gets as input the circuit states or in some cases directly the circuit response an computes the outputs of the system n this example a threshold gate Target Function Filter A function which defines for each input time series the target output time series of a readout function In mathematical terms this should be a target filter since we are talking about computations on time series Supervised Learning Algorithm By means of such algorithm the paramters of the read out and only the readout are adjusted such that the actual output of the readout matches as close as possible the target output Training Set Set of inputs used to determine the parameter of the readout Test Set Set of inputs different to the training set which is used to asses the performance of the trained readout As we will see each of this terms has its corresponding element within Learning Tool 2 3 Implement
3. This mimics the effect of spike transmission through a synapse to its postsynaptic neuron This transformation can also be dropped if one can cope directly with the spike response 4 Apply a supervised learning algorithm to a set of training examples of the form state x target value y to train a readout function f a threshold gate in the case of this example such that the actual outputs f x are as close as possible to the target values y given by the target function 5 Evaluate the performance of the trained readout i e the threshold gate on an inde pendent set of test inputs which are usually drawn from the same distribution as the training inputs 2 2 Basic Concepts The above description of the basic algorithm Sec 2 1 implicitly introduced all the basic concepts we need to know to understand how Learning Tool works Input Distribution The distribution from which the training and test inputs are drawn In our example the input distributio is defined byt the following simple procedure for fixed templates 0 and 1 1 Randomly choose template 0 or 1 2 Add noise jitter to each spike in the template Neural Microcircuit The circuit which receives the input and whos response is recorded and analysed in our example this a network of 135 leaky integrate and fire neurons Response of the Microcircuit The response output of the neural microcircuit in our example the 135 spike trains produced by the microcircuit model
4. for setting up to train the threshold gate is rather short readout i external_readout gt description with linear classification gt targetFunction segment_classification algorithm linear_classification Do the training of the threshold gate After everyting is set up properly we just need to start the training Note that in the code below the function function train_readouts Sec also measures the performance on the tes set trained_readouts perf_train perf_test train_readouts readout train_states train_stimuli test_states test_stimuli Evaluation of the performance After training we want to see how the network performs on indinivual test inputs plot_readouts trained_readouts test_states test_stimuli 3 Function reference References Gerstner and Kistler 2002 Gerstner W and Kistler W 2002 Spiking Neuron Models Cambridge University Press See also http diwww epf1l ch gerstner BUCH html Hertz et al 1991 Hertz J Krogh A and Palmer R G 1991 Introduction to the Theory of Neural Computation Addison Wesley Maass et al 2002 Maass W Natschlager T and Markram H 2002 Real time comput ing without stable states A new framework for neural computation based on perturbations Neural Computation 14 11 2531 2560 Natschl ger et al 2002a Natschl ger T Maass W and Markram H 2002a The liq uid computer
5. Learning Tool Analysing the Computational Power of neural microcircuits Version 1 0 User Manual 2002 The IGI LSM Group www lsm tugraz at June 11 2006 This document is part of Learning Tool Version 1 0 Copyright 2002 The IGI LSM group Learning Tool is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 or at your option any later version Learning Tool is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details To get a copy of the GNU General Public License point your browser to http www gnu org copyleft gpl html The IGI LSM group Institute for Theoretical Computer Science Graz University of Technology Inffeldgasse 16 b A 8010 Graz AUSTRIA lsm igi tu graz ac at www 1lsm tugraz at Contents 1 Introduction 1 1 What is Learning Tool 1 2 About this manual 1 3 Features of the current version 1 4 Getting and Installing Learning Tool 2 An Introductory example 2 1 Algorithm for offline training of the 2 2 Basic Concepts 2 3 Implementation with Learning Tool 3 Function reference threshold gate 0 4 w v v uov Ww a ow A 1 Introduction 1 1 What is Learning Tool Learning Tool
6. ation with Learning Tool The full Matlab code is contained in 1lsm learning demos spike train_classification spike_class m Defining the input distribution Several input distributions are readly imlemented as Matlab objects The class jittered_templates Sec provides the kind of input we need for our task The fol lowin code line generates a jittered_templates object which produces single spike trains from 2 patterns with a jitter of 4 ms InputDist jittered_templates nChannels 1 nTemplates 2 Tstim 0 5 jitter 4e 3 Creating the neural microcircuit model The following code generates a sparsely connected network of leaky integrate and fire neurons The details of the network creation are the topic of the Circuit Tool User Manual and thus not described here init the model mmc neural_microcircuit add a pool of 135 leaky integrate and fire neurons Inmc p1 add nmc Pool origin 1 1 1 size 3 3 15 nmc pin add nmc Pool origin 0 0 0 size 1 1 1 gt type SpikingInputNeuron frac_EXC 1 connect the input to the pools pools nmc add nmc Conn dest p1 src pin Cscale 0 9 gt type StaticSpikingSynapse rescale 0 Wscale 0 15 lambda Inf add recurrent connections within the pools nmc add nmc Conn dest p1 src pl lambda 2 define the
7. is a set of Matlab scripts that allows to asses the the real time computing capa bility of neural microcircuit models Learning Tool is based on a new theoretical framework for analysing real time computations in neural microcircuits the Liquid State Machine Sec To get a thorough understandig of Learning Tool it is a good idea to read the paper describing the basic ideas Maass et al 2002 as well as the paper which describes on a higher level this software package Natschlager et al 2002a 1 2 About this manual This manual is intended to describe how to use the Matlab scripts provided by Learning Tool to perform computer experiments within the LSM framework We assume that the reader has Matlab programming knowledge Although a short introtuction into the basic concept of the LSM Sec is given we strongly recommend to read Maass et al 2002 Natschlager et al 2002b This manual is also available in HTML format either online via http www 1sm tugraz at learning usermanual or locally at your computer as file lt somepath gt 1sm learning documentation usermanual index html if you have installed unzipped Learning Tool in the directory lt somepath gt 1 3 Features of the current version Matlab interface Learning Tool is mainly written in Matlab and hence Runs under Unix Linux and Windows Object oriented design All the Learning Algorithms Sec target functions Sec and readouts Sec are impleme
8. nted as Matlab classes Parallel Processing Usually the training of a readout Sec involves many simulations of the same microcircuit with different inputs and training of several readouts This can easily be run in parallel Learning Tool provides means to do this in a convinient way by employing the Parallel Matlab Toolbox Svahn 2001 1 4 Getting and Installing Learning Tool Learning Tool is distributed under the GNU General Public License and can be downloaded from http www igi tugraz at learning To install Learning Tool perform the following steps 1 Donwload Learning Tool from http www igi tugraz at learning microcircuit gt i S threshold gate A gt input spike train L A HOK Figure 1 Architecture used to classify a spike train The microcircuit is modeled as a network of leaky integrate and fire neurons 2 Unzip the file learning tool VER zip where VER stands for the version you have down loaded This will create a subdirectory 1sm and 1sm learning 3 Start Matlab and change into the directory 1sm 4 Run the Matlab script install m 5 Add the path 1sm to the Matlab search path e g e addpath home jack 1sm or e addpath C Work Neuroscience lsm 6 Change into the directory 1sm learning demos and play around with them Have fun using Learning Tool 2 An Introductory example In this section we will introduce Learning Tool by means of an introductory example In
9. respones i e what to record nmc record nmc Pool p1 Field spikes Creating the Training and Test inputs Since we have defined the circuit model and the input distribution we can now simulate the circuit with inuts drawn from this distribution an collect a training and test set After the simulations the spike responses are lowpass fitered and the states are samples every 25 ms collect stimulus response pairs for training train_response train_stimuli collect_sr_data nmc InputDist 500 apply low pass filter to spikes train_states response2states train_response 0 0 025 Tmax collect stimulus response pairs for testing test_response test_stimuli collect_sr_data nmc InputDist 200 apply low pass filter to spikes test_states response2states test_response 0 0 025 Tmax Setting up to train the threshold gate Everything which has to do with the training of a readout is encapsulated in the class external_readout Sec This object allows you to specify the target function tar get filter and the training algorithm and several options for preprocessing In our example we use pseudo invers methode implemented in the class linear_classification Sec to determine the parameters of the threshold gate The target function which outputs 0 1 for all sample times see definition of the task Sec 2 is implemented in the class segment_classification Sec Hence the code
10. this simple example we will train a readout neuron modeled as a threshold gate see Hertz et al 1991 to classify a spike train This readout neuron will receive its input from a neural microcircuit modeled as a network of leaky integrate and fire neurons see Gerstner and Kistler 2002 which is stimulated by the input spike train which should be classified The setup is shown in Figure 1 2 0 1 Precise definition of the classification task Two Poisson spike trains freqency 20 Hz length 0 5 sec are generated and fixed as templates 0 and 1 The actual input spike train is generated as jittered versions of a template by varying each spike by a random drawn amount Gaussion distribuion with zero mean and a given STD this STD is called jitter default jitter 4ms The task of the threshold gate is to output 4 the number 0 or 1 of the random choosen template from which the input spike train was generated 2 1 Algorithm for offline training of the threshold gate Here we just outline the main body of the procedure which we will use to train the readout This will be discussed in more detail in Section 1 Define the neural microcircuit to be analyzed 2 Record spike responses of the neural microcircuit caused by different training inputs drawn from an appropriate input distribution 3 Convert the spike responses into states x t at various sample time points tg by some low pass filtering to get a somewhat smoothed signal
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