Bio-inspired feedback-circuit implementation of discrete, free energy optimizing, winner-take-all computations

Abstract

Bayesian inference and bounded rational decision-making require the accumulation of evidence or utility, respectively, to transform a prior belief or strategy into a posterior probability distribution over hypotheses or actions. 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. 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. We discuss in how far neural circuits could implement these operations that might provide a generic competitive principle underlying both perception and action.

On the simplicity of simple heuristics

“…However, it has been long since the rule-based models had their own corner on the market. The alternatives include network (Glo¨ckner et al, 2014) and circuit models Genewein and Braun (2016). For such models circuit complexity analysis would probably be more suitable (Wegener, 1987).…”

On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning

“…From a game theory and reinforcement learning perspective, the softmax function maps the raw payoff or the score (or Q-value) associated with a payoff to a mixed strategy [1], [2], [4], whereas from the perspective of multi-class logistic regression, the softmax function maps a vector of logits (or feature variables) to a posterior probability distribution [5], [6]. The broader engineering applications involving the softmax function are numerous; interesting examples can be found in the fields of VLSI and neuromorphic computing, see [35], [36], [37], [39].…”