Event-driven contrastive divergence: neural sampling foundations

In a recent Frontiers in Neuroscience paper (Neftci et al., 2014) we contributed an on-line learning rule, driven by spike-events in an Integrate and Fire (IF) neural network, that emulates the learning performance of Contrastive Divergence (CD) in an equivalent Restricted Boltzmann Machine (RBM) amenable to real-time implementation in spike-based neuromorphic systems. The eventdriven CD framework assumes the foundations of neural sampling (Buesing et al., 2011; Maass, 2014) in mapping spike rates of a deterministic IF network onto probabilities of a corresponding stochastic neural network. In Neftci et al. (2014), we used a particular form of neural sampling previously analyzed in Petrovici et al. (2013)1, although this connection was not made sufficiently clear in the published article. The purpose of this letter is to clarify this connection, and to raise the reader’s awareness to the existence of various forms of neural sampling.We highlight the differences as well as strong connections across these various forms, and suggest applications of event-driven CD in a more general setting enabled by the broader interpretations of neural sampling. In the Bayesian view on neural information processing, the cognitive function of the brain arises from its ability to encode and combine probabilities describing its interactions with an uncertain world (Doya et al., 2007). A recent neural sampling hypothesis has shed light on how probabilities may be encoded in neural circuits (Fiser et al., 2010; Berkes et al., 2011). In the neural sampling hypothesis, spikes are viewed as samples of a target probability distribution. From a modeling perspective, a key advantage of this view is that learning in spiking neural networks becomes more tractable than the alternative one, in which neurons encode probabilities, because one can borrow from well-established algorithms in machine learning (Fiser et al., 2010) (see Nessler et al., 2013 for a concrete example). Merolla et al. (2010) demonstrated a Boltzmann machine using IF neurons. In this model, spiking neurons integrate Poisson-distributed spikes during a fixed time window set by a global rhythmic oscillation. A first-passage time analysis shows that the probability that a neuron spikes in the given time window follows a logistic sigmoid function consistent with a Boltzmann distribution. The particular form of rhythmic oscillation ensures that, even when neurons are recurrently