Supervised Learning in Multilayer Spiking Neural Networks

We introduce a supervised learning algorithm for multilayer spiking neural networks. The algorithm overcomes a limitation of existing learning algorithms: it can be applied to neurons firing multiple spikes in artificial neural networks with hidden layers. It can also, in principle, be used with any linearizable neuron model and allows different coding schemes of spike train patterns. The algorithm is applied successfully to classic linearly nonseparable benchmarks such as the XOR problem and the Iris data set, as well as to more complex classification and mapping problems. The algorithm has been successfully tested in the presence of noise, requires smaller networks than reservoir computing, and results in faster convergence than existing algorithms for similar tasks such as SpikeProp.

[1]  W. Gerstner,et al.  Chapter 12 A framework for spiking neuron models: The spike response model , 2001 .

[2]  Sander M. Bohte,et al.  Error-Backpropagation in Networks of Fractionally Predictive Spiking Neurons , 2011, ICANN.

[3]  R. Johansson,et al.  First spikes in ensembles of human tactile afferents code complex spatial fingertip events , 2004, Nature Neuroscience.

[4]  Jing Wu,et al.  Arc/Arg3.1 Mediates Homeostatic Synaptic Scaling of AMPA Receptors , 2006, Neuron.

[5]  R. Fisher THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[6]  André Grüning,et al.  Reference time in SpikeProp , 2011, The 2011 International Joint Conference on Neural Networks.

[7]  Peter Tiño,et al.  Learning Beyond Finite Memory in Recurrent Networks of Spiking Neurons , 2005, Neural Computation.

[8]  G. Laurent,et al.  Odour encoding by temporal sequences of firing in oscillating neural assemblies , 1996, Nature.

[9]  Peter Tiño,et al.  Learning Beyond Finite Memory in Recurrent Networks of Spiking Neurons , 2005, ICNC.

[10]  H. Sompolinsky,et al.  The tempotron: a neuron that learns spike timing–based decisions , 2006, Nature Neuroscience.

[11]  Wulfram Gerstner,et al.  Intrinsic Stabilization of Output Rates by Spike-Based Hebbian Learning , 2001, Neural Computation.

[12]  Okyay Kaynak,et al.  Variable-structure-systems based approach for online learning of spiking neural networks and its experimental evaluation , 2014, J. Frankl. Inst..

[13]  Sander M. Bohte,et al.  Fractionally Predictive Spiking Neurons , 2010, NIPS.

[14]  V. Sánchez Connectionism in perspective , 1991 .

[15]  Benjamin Schrauwen,et al.  Improving SpikeProp: Enhancements to An Error-Backpropagation Rule for Spiking Neural Networks , 2004 .

[16]  Simon J. Thorpe,et al.  BIOLOGICAL CONSTRAINTS ON CONNECTIONIST MODELLING , 2015 .

[17]  Christopher J. Bishop,et al.  Pulsed Neural Networks , 1998 .

[18]  W. Singer,et al.  Long-range synchronization of oscillatory light responses in the cat retina and lateral geniculate nucleus , 1996, Nature.

[19]  M. Poo,et al.  Propagation of activity-dependent synaptic depression in simple neural networks , 1997, Nature.

[20]  Mark C. W. van Rossum,et al.  A Novel Spike Distance , 2001, Neural Computation.

[21]  Hieu Tat Nguyen,et al.  A gradient descent rule for spiking neurons emitting multiple spikes , 2005, Inf. Process. Lett..

[22]  D. Buonomano,et al.  The neural basis of temporal processing. , 2004, Annual review of neuroscience.

[23]  Bruno Cessac,et al.  Reverse-engineering in spiking neural networks parameters: exact deterministic parameters estimation , 2010 .

[24]  Haim Sompolinsky,et al.  Learning Input Correlations through Nonlinear Temporally Asymmetric Hebbian Plasticity , 2003, The Journal of Neuroscience.

[25]  Wolfgang Maass,et al.  Fast Sigmoidal Networks via Spiking Neurons , 1997, Neural Computation.

[26]  F. Ponulak ReSuMe-Proof of convergence , 2006 .

[27]  Andrzej J. Kasinski,et al.  Supervised Learning in Spiking Neural Networks with ReSuMe: Sequence Learning, Classification, and Spike Shifting , 2010, Neural Computation.

[28]  David P. M. Northmore,et al.  Building silicon nervous systems with dendritic tree neuromorphs , 1999 .

[29]  E. Knudsen Instructed learning in the auditory localization pathway of the barn owl , 2002, Nature.

[30]  Robert A. Legenstein,et al.  What Can a Neuron Learn with Spike-Timing-Dependent Plasticity? , 2005, Neural Computation.

[31]  Linda Bushnell,et al.  Spike-Timing Error Backpropagation in Theta Neuron Networks , 2009, Neural Computation.

[32]  Shahnorbanun Sahran,et al.  Time Window, Spike Time and Threshold Boundary for Spiking Neural Network Applications , 2014 .

[33]  Robert Gütig,et al.  To spike, or when to spike? , 2014, Current Opinion in Neurobiology.

[34]  Terumine Hayashi,et al.  Obstacle to training SpikeProp networks — Cause of surges in training process — , 2009, 2009 International Joint Conference on Neural Networks.

[35]  Liam McDaid,et al.  SWAT: A Spiking Neural Network Training Algorithm for Classification Problems , 2010, IEEE Transactions on Neural Networks.

[36]  Jianguo Xin,et al.  Supervised learning with spiking neural networks , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[37]  André Grüning,et al.  Supervised Learning of Logical Operations in Layered Spiking Neural Networks with Spike Train Encoding , 2012, Neural Processing Letters.

[38]  Niraj S. Desai,et al.  Homeostatic Plasticity and STDP: Keeping a Neuron's Cool in a Fluctuating World , 2010, Front. Syn. Neurosci..

[39]  R. Christopher deCharms,et al.  Primary cortical representation of sounds by the coordination of action-potential timing , 1996, Nature.

[40]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[41]  Wofgang Maas,et al.  Networks of spiking neurons: the third generation of neural network models , 1997 .

[42]  E. Knudsen Supervised learning in the brain , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[43]  Li I. Zhang,et al.  Selective Presynaptic Propagation of Long-Term Potentiation in Defined Neural Networks , 2000, The Journal of Neuroscience.

[44]  K. Hidehiko,et al.  Shape of error surfaces in SpikeProp , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

[45]  W. Senn,et al.  Reinforcement learning in populations of spiking neurons , 2008, Nature Neuroscience.

[46]  Michael Schmitt,et al.  Learning Temporally Encoded Patterns in Networks of Spiking Neurons , 2004, Neural Processing Letters.

[47]  Raúl Rojas,et al.  Neural Networks - A Systematic Introduction , 1996 .

[48]  Hojjat Adeli,et al.  A new supervised learning algorithm for multiple spiking neural networks with application in epilepsy and seizure detection , 2009, Neural Networks.

[49]  Sander M. Bohte,et al.  Error-backpropagation in temporally encoded networks of spiking neurons , 2000, Neurocomputing.

[50]  Wulfram Gerstner,et al.  SPIKING NEURON MODELS Single Neurons , Populations , Plasticity , 2002 .

[51]  K. Harris Stability of the fittest: organizing learning through retroaxonal signals , 2008, Trends in Neurosciences.

[52]  Cornelius Glackin,et al.  Receptive field optimisation and supervision of a fuzzy spiking neural network , 2011, Neural Networks.

[53]  Wolfgang Maass,et al.  Networks of Spiking Neurons: The Third Generation of Neural Network Models , 1996, Electron. Colloquium Comput. Complex..

[54]  Wulfram Gerstner,et al.  Spiking Neuron Models: An Introduction , 2002 .

[55]  Pieter R. Roelfsema,et al.  Attention-Gated Reinforcement Learning of Internal Representations for Classification , 2005, Neural Computation.

[56]  Filip Ponulak,et al.  Analysis of the ReSuMe Learning Process For Spiking Neural Networks , 2008, Int. J. Appl. Math. Comput. Sci..

[57]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[58]  E. Capaldi,et al.  The organization of behavior. , 1992, Journal of applied behavior analysis.

[59]  Terumine Hayashi,et al.  Shape of error surfaces in SpikeProp , 2008, IJCNN.

[60]  André Grüning,et al.  Elman Backpropagation as Reinforcement for Simple Recurrent Networks , 2007, Neural Computation.