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Neural responses in the cortex change over time both systematically, due toongoing plasticity and learning, and seemingly randomly, due to various sourcesof noise and variability. Most previous work considered each of theseprocesses, learning and variability, in isolation -- here we study neuralnetworks exhibiting both and show that their interaction leads to the emergenceof powerful computational properties. We trained neural networks on classicalunsupervised learning tasks, in which the objective was to represent theirinputs in an efficient, easily decodable form, with an additional cost forneural reliability which we derived from basic biophysical considerations. Thiscost on reliability introduced a tradeoff between energetically cheap butinaccurate representations and energetically costly but accurate ones. Despitethe learning tasks being non-probabilistic, the networks solved this tradeoffby developing a probabilistic representation: neural variability representedsamples from statistically appropriate posterior distributions that wouldresult from performing probabilistic inference over their inputs. We provide ananalytical understanding of this result by revealing a connection between thecost of reliability, and the objective for a state-of-the-art Bayesianinference strategy: variational autoencoders. We show that the same cost leadsto the emergence of increasingly accurate probabilistic representations asnetworks become more complex, from single-layer feed-forward, throughmulti-layer feed-forward, to recurrent architectures. Our results provideinsights into why neural responses in sensory areas show signatures ofsampling-based probabilistic representations, and may inform future deeplearning algorithms and their implementation in stochastic low-precisioncomputing systems.

Sampling-based probabilistic inference emerges from learning in neural circuits with a cost on reliability