Predictive coding under the free-energy principle

Abstract

This paper considers prediction and perceptual categorization as an inference problem that is solved by the brain. We assume that the brain models the world as a hierarchy or cascade of dynamical systems that encode causal structure in the sensorium. Perception is equated with the optimization or inversion of these internal models, to explain sensory data. Given a model of how sensory data are generated, we can invoke a generic approach to model inversion, based on a free energy bound on the model's evidence. The ensuing free-energy formulation furnishes equations that prescribe the process of recognition, i.e. the dynamics of neuronal activity that represent the causes of sensory input. Here, we focus on a very general model, whose hierarchical and dynamical structure enables simulated brains to recognize and predict trajectories or sequences of sensory states. We first review hierarchical dynamical models and their inversion. We then show that the brain has the necessary infrastructure to implement this inversion and illustrate this point using synthetic birds that can recognize and categorize birdsongs.Keywords: generative models; predictive coding; hierarchical; birdsong INTRODUCTIONThis paper reviews generic models of our sensorium and a Bayesian scheme for their inversion. We then show that the brain has the necessary anatomical and physiological equipment to invert these models, given sensory data. Critically, the scheme lends itself to a relatively simple neural network implementation that shares many features with real cortical hierarchies in the brain. The basic idea that the brain tries to infer the causes of sensations dates back to Helmholtz (e.g. Helmholtz 1860/1962Barlow 1961;Neisser 1967;Ballard et al. 1983;Mumford 1992;Kawato et al. 1993;Dayan et al. 1995;Rao & Ballard 1998), with a recent emphasis on hierarchical inference and empirical Bayes (Friston 2003(Friston , 2005Friston et al. 2006). Here, we generalize this idea to cover dynamics in the world and consider how neural networks could be configured to invert hierarchical dynamical models and deconvolve sensory causes from sensory input. This paper comprises four sections. In §1, we introduce hierarchical dynamical models and their inversion. These models cover most of the models encountered in the statistical literature. An important aspect of these models is their formulation in generalized coordinates of motion, which lends them a hierarchal form in both structure and dynamics. These hierarchies induce empirical priors that provide structural and dynamical constraints, which can be exploited during inversion. In §2, we show how inversion can be formulated as a simple gradient ascent using neuronal networks; in §3, we consider how evoked brain responses might be understood in terms of inference under hierarchical dynamical models of sensory input. 1

Repetition probability effects for inverted faces

“…It postulates that vision is a hierarchical process in which higher order areas shape and predict the tuning properties of lower level areas via strong feedback connections (Friston, 2005). This is achieved by suppressing the repeated or predicted, and hence redundant, neural responses in lower level areas that are consistent with the higher level expectations, resulting in a suppressed response of these neuronal populations and in an efficient encoding mechanism (Friston and Kiebel, 2009). …”

“…This discrepancy or residual prediction error signal (ε) is then forwarded to higher areas to re-estimate and update the predictions. The more closely a top-down prediction matches the incoming sensory input, the smaller the feed-forward ε is, which maximizes the "efficiency" of the CNS in the sense that the neural activity evoked by predicted stimuli is less than that evoked by novel and hence unexpected stimuli (Friston and Kiebel, 2009). According to PC accounts RS reflects the reduction of ε during subsequent bottom-up/top-down processing iterations within a hierarchical system (Kveraga et al, 2007): repeating a stimulus (or adapting to it) leads to its increased expectation and recalibrates the predictions such that the adapted stimulus evokes reduced ε, which leads to RS in an area.…”

The contribution of surprise to the prediction based modulation of fMRI responses

“…To re-estimate and update predictions, ɛ is forwarded from lower to higher areas of the processing system. Consequently, surprising/incorrectly predicted events generate higher neural activity in comparison with correctly predicted events, maximizing the efficiency of neuronal processing (Friston, 2005(Friston, , 2010Friston & Kiebel, 2009). Summerfield et al, 2008 interpreted the enhanced magnitude of RS for expected stimuli as the reduced neuronal activity induced by a smaller ɛ (following Henson, 2003 claim of a link between RS and ɛ).…”

Evidence for embodied predictive coding: the anterior insula coordinates cortical processing of tactile deviancy

“…These findings together suggest that the AIC coordinates the global cortical processing of surprising bodily stimuli by linking lower-level sensory regions to more attention and salience-related areas in the prefrontal and cingulate cortex during the processing of unexpected tactile changes. As discussed above, an interesting possible interpretation is that the AIC supports the emergence of a global workspace by directly monitoring and modulating the precision of these top-down and bottom-up inputs (Friston and Kiebel 2009;Bastos et al 2012). Future studies will benefit from directly manipulating tactile precision and deviancy in conjunction with computational modelling to address this question.…”