Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

By Lars Buesing, Johannes Bill, Bernhard Nessler, Wolfgang Maass. 2011

441 citations recorded by the source corpus.

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.

Subfields: Cognitive Neuroscience, Electrical and Electronic Engineering

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Citations in the corpus

Toward an Integration of Deep Learning and Neuroscience (2016, background): “…in which a fraction of hidden units is stochastically set to zero during each round of training: such a procedure may correspond to the noisiness of neural spike trains, although other theories interpret spikes as sampling in probabilistic inference (Buesing et al., 2011), or in many other ways.”
Probabilistic Inference in General Graphical Models through Sampling in Stochastic Networks of Spiking Neurons (2011, methodology): “Before the first use of this strategy in networks of spiking neurons in [1], MCMC sampling had already been studied in the context of artificial neural networks, so-called Boltzmann machines [15].”
Bayesian Computation Emerges in Generic Cortical Microcircuits through Spike-Timing-Dependent Plasticity (2013, background): “In particular, [24,25] have recently shown how recurrently connected neurons can be designed to perform neural sampling, an approach in which time-independent probability distributions can be represented through spiking activity in recurrent neural networks.”
Advancing Neuromorphic Computing With Loihi: A Survey of Results and Outlook (2021, background): “Buesing et al. [75] had shown that the stochastic dynamics of such networks converge exponentially fast to a probability distribution p ∝ exp( − E/η ) , where η parameterizes the degree of stochasticity.”
Event-driven contrastive divergence for spiking neuromorphic systems (2013, methodology): “The neural RBM’s network architecture consisted of two layers, as illustrated in Figure 5.”
Integration of nanoscale memristor synapses in neuromorphic computing architectures (2013, methodology): “through MCMC sampling can be implemented by networks of stochastically spiking neurons [79, 80].”
Reservoir Computing Trends (2012, background): “Recently he and his group have added reinforcement learning [27] and Bayesian inferencing [4] to the picture of microcir-”
Neurons as Monte Carlo Samplers: Bayesian Inference and Learning in Spiking Networks (2014, background): “The model thus provides a concrete neural implementation of sampling ideas previously suggested in [16, 17, 18, 19, 20].”
Loihi: A Neuromorphic Manycore Processor with On-Chip Learning (2018, methodology): “This provides support for algorithms such as Neural Sampling, 9 which can solve probabilistic inference and constraint satisfaction problems using stochastic dynamics and a form of Markov chain Monte Carlo sampling.”
Representation of uncertainty in deep neural networks through sampling (2016, background): “Restricted Boltzmann machines (RBMs) (Hinton, 2010) and spiking neural networks with binary stochastic units that perform Bayesian inference have been proposed as models (Buesing et al., 2011; Habenschuss et al., 2013).”
Cognitive computational neuroscience (2018, background): “As theories of brain computation, approximate inference algorithms like sampling may explain cortical feedback signals and activity correlations.(144,164,165,166,167) Moreover, the corners cut by the brain for computational efficiency, the approximations, may explain human deviations from statistica”
Deep Learning in Spiking Neural Networks (2018, methodology): “employed in sequential data processing [99] and Markov chain Monte Carlo sampling interpreted by stochastic firing activity of spiking neurons [100].”
Noise as a Resource for Computation and Learning in Networks of Spiking Neurons (2014, background): “Positive results are provided by the neural sampling theory of [12].”