Genewein T, Braun DA (2016). Bio-inspired feedback-circuit implementation of discrete, free energy optimizing, winner-take-all computations. Biological Cybernetics. doi: 10.1007/s00422-016-0684-8
Our paper on bio-inspired feedback circuits for free-energy optimization was published. In the paper we explore the idea that a free energy minimization (which is the basis of an information theoretic framework for bounded rational inference and decision-making, see the corresponding Research article) can be described by a dynamical system.
Bounded rational decision-making (including Bayesian inference as a special case) requires the accumulation of utility (or evidence), to transform a prior strategy (or belief) into a posterior probability distribution over actions (or hypotheses). Crucially, this process cannot be simply realized by independent integrators, since the different hypotheses and actions also compete with each other. In continuous time, this competitive integration process can be described by a special case of the replicator equation (known from evolutionary biology for describing evolutionary competition between different populations). Here we investigate simple analog electric circuits that implement the underlying differential equation under the constraint that we only permit a limited set of building blocks that we regard as biologically interpretable, such as capacitors, resistors, voltage-dependent conductances and voltage- or current-controlled current and voltage sources. The appeal of these circuits is that they intrinsically perform normalization without requiring an explicit divisive normalization.
However, even in idealized simulations, we find that these circuits are very sensitive to internal noise as they accumulate error over time. In the paper, we discuss in how far neural circuits could implement these operations that might provide a generic competitive principle underlying both perception and action. In short: the problem is that a naive implementation of the replicator equation requires synaptic weights to change on the same time-scale with which the (perceptual) input to the system varies. This cannot be mapped to any of the standard models of neural competitive integration (e.g. pooled-inhibition models). This observation naturally leads to the question of whether signatures of the replicator-dynamics might be evident in other, perhaps more intricate, neural circuitry. While this question is beyond the scope of the paper, the novel point of view on competitive utility (or evidence) integration with dynamical systems as presented in the paper could be very interesting for researchers working on the neurophysiological basis of decision-making.