Stochastic computations in cortical microcircuit models
S. Habenschuss, Z. Jonke, and W. Maass
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.
Reference: S. Habenschuss, Z. Jonke, and W. Maass.
Stochastic computations in cortical microcircuit models.
PLOS Computational Biology, 9(11):e1003311, 2013.