Predictive perception via simultaneous learning and inference
Perception has been proposed to involve an inferential process that combines noisy sensory evidence with prior expectations to estimate the latent states of the environment. Exact Bayesian inference is intractable in the continuous, high-dimensional state spaces of the natural world. Variational schemes address this by restricting the form of the posterior, whereas sampling schemes represent the posterior with a finite set of samples. In both cases the approximation concerns the posterior rather than the state space over which it is defined. Here we place the approximation elsewhere. Rather than restricting the form of the posterior, we restrict the state space, modeling environmental states as discrete and thereby making Bayesian filtering exact. Beliefs are then unconstrained in shape and what has to be learned can be reduced to a transition matrix updated online by a local rule. The cost is that the states, rather than the distribution, must be specified in advance. The Simultaneous Learning and Inference Model (SLIM) combines this exact filtering with a gated Hebbian rule that learns transitions from inferred rather than observed states. In simulations SLIM recovers environmental dynamics under sensory noise and adapts when those dynamics change, with error growing only once the sensor becomes uninformative. A hierarchical instantiation reproduces local and global prediction error effects. Applied to two auditory decision-making experiments under noise, SLIM reproduces behavioral signatures of expectation and supplies trial-level measures of expectation and surprise. Exact inference over a small discrete state space with a single local Hebbian rule is therefore sufficient to account for these phenomena, without an explicit optimization objective and without a parametric approximation to the posterior.