Stochastic Computations in Cortical Microcircuit Models

Experimental data from neuroscience suggest that a substantial amount of knowledge is stored in the brain in the form of probability distributions over network states and trajectories of network states. We provide a theoretical foundation for this hypothesis by showing that even very detailed models for cortical microcircuits, with data-based diverse nonlinear neurons and synapses, have a stationary distribution of network states and trajectories of network states to which they converge exponentially fast from any initial state. We demonstrate that this convergence holds in spite of the non-reversibility of the stochastic dynamics of cortical microcircuits. We further show that, in the presence of background network oscillations, separate stationary distributions emerge for different phases of the oscillation, in accordance with experimentally reported phase-specific codes. We complement these theoretical results by computer simulations that investigate resulting computation times for typical probabilistic inference tasks on these internally stored distributions, such as marginalization or marginal maximum-a-posteriori estimation. Furthermore, we show that the inherent stochastic dynamics of generic cortical microcircuits enables them to quickly generate approximate solutions to difficult constraint satisfaction problems, where stored knowledge and current inputs jointly constrain possible solutions. This provides a powerful new computing paradigm for networks of spiking neurons, that also throws new light on how networks of neurons in the brain could carry out complex computational tasks such as prediction, imagination, memory recall and problem solving.Author Summary: The brain has not only the capability to process sensory input, but it can also produce predictions, imaginations, and solve problems that combine learned knowledge with information about a new scenario. But although these more complex information processing capabilities lie at the heart of human intelligence, we still do not know how they are organized and implemented in the brain. Numerous studies in cognitive science and neuroscience conclude that many of these processes involve probabilistic inference. This suggests that neuronal circuits in the brain process information in the form of probability distributions, but we are missing insight into how complex distributions could be represented and stored in large and diverse networks of neurons in the brain. We prove in this article that realistic cortical microcircuit models can store complex probabilistic knowledge by embodying probability distributions in their inherent stochastic dynamics – yielding a knowledge representation in which typical probabilistic inference problems such as marginalization become straightforward readout tasks. We show that in cortical microcircuit models such computations can be performed satisfactorily within a few . Furthermore, we demonstrate how internally stored distributions can be programmed in a simple manner to endow a neural circuit with powerful problem solving capabilities.