spikelm: a second-order supervised learning algorithm for training spiking neural networks
DESCRIPTION
Yongji Wang Jian Huang Huazhong University of Sci. & Tech. Wuhan, China. SpikeLM: A Second-Order Supervised Learning Algorithm for Training Spiking Neural Networks. Overview. Introduction Preliminaries SpikeLM algorithm Experimental validation Conclusions. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
IJCNN, July 27, 2004 [email protected] 1
SpikeLM: A Second-Order Supervised Learning Algorithm
for Training Spiking Neural Networks
Yongji WangJian Huang
Huazhong University of Sci. & Tech.Wuhan, China
IJCNN, July 27, 2004 [email protected] 2
Overview
● Introduction● Preliminaries● SpikeLM algorithm● Experimental validation● Conclusions
IJCNN, July 27, 2004 [email protected] 3
Introduction
● Spiking neural networks get increased attention:● Biologically more plausible ● Computational power not less than traditional ANN
● Main problem: supervised learning algorithms, it is just in its infancy. ● SpikeProp, a grads-descent supervising learning
algorithm
IJCNN, July 27, 2004 [email protected] 4
Preliminaries
● Model of SNN● Originally introduced by Natschläger and Ruf● Every connection consists of several synaptic connections● Each terminal is associated with a different delay and
weight
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Preliminaries
● Model of SNN (continued)● Notations:
● : the set of spiking neurons for the r-th layer;● : the spike firing time from neuron to● : the weight of the m-th terminal between i and j ;● : the delay of the m-th terminal;● : membrane potential of neuron i ;
IJCNN, July 27, 2004 [email protected] 6
Preliminaries
● Model of SNN (continued)● Spiking Response Model (SRM):
● Where is the unweighted contribution of a single synaptic terminal from j to i.
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SpikeLM algorithm
● Training samples:● Note that all inputs and outputs are firing times.● We use and to describe the actual and
desire firing time respectively. ●
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SpikeLM algorithm
● Dynamics equation of the three-layered SNN:
● Vectorial form:
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SpikeLM algorithm
● The performance index:
● To compute the Jacobian matrix, define
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SpikeLM algorithm
● The representation of Jacobian matrix:
where the k,q,r,m,i,j can be easily obtained given h and l.
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SpikeLM algorithm
● Computation of Jacobian matrix:
Sensitivities in SpikeLM
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SpikeLM algorithm
● Computation of Jacobian matrix:● Sensitivities: (output layer) The same way as SpikeProp did
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SpikeLM algorithm
● Computation of Jacobian matrix:● To form sensitivity matrix: (output layer)
where
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SpikeLM algorithm
● Computation of Jacobian matrix:● Sensitivities: (hidden layer)
As SpikeProp did
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SpikeLM algorithm
● Computation of Jacobian matrix:● To form sensitivity matrix: (hidden layer)
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SpikeLM algorithm
● Computation of Jacobian matrix:● The matrix form of computation:
● Define
and
IJCNN, July 27, 2004 [email protected] 20
SpikeLM algorithm
● Computation of Jacobian matrix:● The matrix form of computation:
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SpikeLM algorithm
● Summarize the SpikeLM algorithm:1) Compute the performance index;2) Compute Jacobian matrix via backpropagation method;3) Solve4) Recompute the performance index using . If
the new index is smaller than that computed in step 1, then reduce by , go to 1). Otherwise, increase by and go back to 3).
5) If the convergent condition is met, then stop.
IJCNN, July 27, 2004 [email protected] 23
Experimental validation
● XOR Problem:● We assume the same setup as Bothe did. a “late”
and “early” firing time substitute 0 and 1.● Both SpikeProp and SpikeLM algorithm are applied
to cope with this problem. The convergent rates are compared to illustrate the merit of the latter algorithm.
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Experimental validation
● 4 output spike time examples during learning
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Experimental validation
● Convergence comparison for SpikeProp and SpikeLM
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Experimental validation
● Nonlinear function approximation:● Select a nonlinear function● the values of F(x) are totally normalized into a
interval from 10 to 22.● The approximation curve was obtained after about
200 epochs of learning.
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Experimental validation
● The function approximation by SpikeLM:
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Conclusion
● A second-order supervising learning rule is derived for feedforward spiking neural networks using temporal-coding scheme.
● This procedure is represented by a fairly concise vectorial form, which can be easily implemented by any softwares.
● Elementary tests show the great potential of this algorithm.