Supervised Learning in Spiking Neural Networks with ReSuMe: Sequence Learning, Classification, and Spike Shifting

Abstract

Learning from instructions or demonstrations is a fundamental property of our brain necessary to acquire new knowledge and develop novel skills or behavioral patterns. This type of learning is thought to be involved in most of our daily routines. Although the concept of instruction-based learning has been studied for several decades, the exact neural mechanisms implementing this process remain unrevealed. One of the central questions in this regard is, How do neurons learn to reproduce template signals (instructions) encoded in precisely timed sequences of spikes? Here we present a model of supervised learning for biologically plausible neurons that addresses this question. In a set of experiments, we demonstrate that our approach enables us to train spiking neurons to reproduce arbitrary template spike patterns in response to given synaptic stimuli even in the presence of various sources of noise. We show that the learning rule can also be used for decision-making tasks. Neurons can be trained to classify categories of input signals based on only a temporal configuration of spikes. The decision is communicated by emitting precisely timed spike trains associated with given input categories. Trained neurons can perform the classification task correctly even if stimuli and corresponding decision times are temporally separated and the relevant information is consequently highly overlapped by the ongoing neural activity. Finally, we demonstrate that neurons can be trained to reproduce sequences of spikes with a controllable time shift with respect to target templates. A reproduced signal can follow or even precede the targets. This surprising result points out that spiking neurons can potentially be applied to forecast the behavior (firing times) of other reference neurons or networks.

Supervised Learning of Logical Operations in Layered Spiking Neural Networks with Spike Train Encoding

“…ReSuMe is a supervised learning algorithm for single spiking neurons usually driven by a large number of input spike trains [21]. ReSuMe is not fixed to a particular neuron type, but -as STDP -implicitly assumes, at least on longer time scales, that recent inputs have more influence on the current activation of a neuron than past inputs.…”

“…We will use an encoding of input and output patterns that makes use of spike trains with strict spike times. In comparable settings, so far only classification tasks or simple mapping tasks have been considered [9,11,14,21], either with only a single neuron or in much larger Liquid State Machines (LSMs) [15], but no computational tasks. Or computational tasks like the Exclusive-Or problem have been considered in layered networks, but only with single-spike latency-encoded outputs [3,4,29,30].…”

“…ReSuMe is motivated by an analogue of the δ-rule and is based on STDP [21]. From a combination of an STDP process between target and input spike trains of a neuron and an anti-STDP process between the actual output train and the input, it derives a differential STDP rule that is used to generate weight changes for the synaptic connections into a neuron.…”

“…This algorithm is capable of training a single neuron to reproduce an arbitrary prescribed target spike train via supervised learning; however it needs a large number of incoming spikes to do so successfully [21]. Unlike SpikeProp, ReSuMe is able to deal with spike patterns that involve many spikes.…”

“…However it can only be applied to neurons that have a direct target spike train assigned, and the credit assignment for downstream neurons is circumvented by either training single neurons or a layer of output neurons on top of a large immutable LSM [15]. Experimental tasks include, for example, single neurons (or sets) producing a prescribed spike train from their incoming spikes, or classifying spike patterns when trained neurons are used as readouts for a LSM [21].…”