The brain as a predictive system

For Karl Friston (Friston, 2005, 2010), the predictive coding hypothesis is part of a much broader theoretical framework, the principle of free energy minimization. In its author's own words, this is a "mathematical formulation of how biological agents resist the natural tendency to disorder": they "maintain their state in a changing environment". The organism's states must therefore be of low entropy: "biological agents must minimize the long-term average of surprise". Free energy is a mathematical equation that gives an upper bound on surprise: "if agents minimize free energy, they implicitly minimize surprise". In the field of perception, the principle leads to the optimization of perceptual inferences. "The agent implicitly infers or represents the causes of its sensory inputs according to the principles of optimal Bayesian inference".

Free energy can be maximized by the EM(Expectation-Maximization) algorithm, an iterative procedure which, by repeatedly alternating two steps (E and M), finds the maximum likelihood or maximum a posteriori of the parameters of a probabilistic model. Friston proposes that the brain uses an EM algorithm. If the generating model is Gaussian, he shows that this amounts to propagating prediction errors. Each area of the cortex would perform a specific causal inference, and the passage of error messages between areas would enable them to be updated. The layered architecture of the cortex would correspond to a natural distribution of computation. Top-down connections would implement theforward model, i.e. the prediction of signals at level n, based on representations inferred at level n+1. Conversely, the ascending connections, originating in the upper layers of the cortex, would transmit the prediction error, i.e. the difference between the input received and its prediction. The error signal is used to update the higher-level model, to prevent the error from recurring in the future.

Although the precise model proposed by Friston has not received definitive validation, and has been criticized for its ambiguity (Spratling, 2008), the more general idea of a two-way exchange of predictions and error signals accounts for an exceptionally large body of electro-physiological observations. Indeed, many brain responses are evoked by stimuli that are unexpected or violate a previously inferred rule. For example, the presentation of repeated sounds, followed by a new sound, elicits a wave(mismatch response [MMR] or mismatch negativity [MMN]) that can easily be measured on the surface of the scalp, at any age. Other similar waves index surprise in other sensory modalities or at a higher level: semantic representation of words or images (N400), syntactic anomalies (ELAN), awareness of the need to update working memory (P3b).

Although some have attempted to explain these responses by a simple synaptic habituation/recovery process (May & Tiitinen, 2010), much recent evidence supports the predictive coding hypothesis. In the case of the MMN wave, the response continues to be observed when stimuli alternate (ABAB...) or are presented in pairs (AB), and it is therefore repetition (AA) that constitutes a novel stimulus (Horvath & Winkler, 2004). Analyzing a paradigm of this type at the neuronal level in the visual modality, Meyer and Olson (2011) clearly show that the decrease in neuronal discharges at the second element of the AB pair can only be explained by a predictive signal. The surprise observed when an unexpected pair is presented (AC) results in such an early neuronal discharge that it implies the violation of a perceptual expectation.

The predictive model assumes that our brain generates sensory expectations at every moment. Even before receiving a stimulus, a top-down signal attempts to cancel out its sensory consequences. Only the error, i.e. the difference between prediction and observation, is represented in the neuronal discharges transmitted. This leads to a simple prediction: if the expected input is suppressed, a neuronal response should be evoked by the absence of an expected sound. This prediction has been verified (Joutsiniemi & Hari, 1989). The paradigm of unexpected omission of an expected stimulus offers a simple way of isolating a predictive signal and studying its hierarchical organization properties (Wacongne et al., 2011).

Friston's model accounts for these observations, but is confined to the level of a phenomenological mathematical description. Catherine Wacongne, Jean-Pierre Changeux and I have proposed a neuro-realistic model of predictive coding, which captures the vast majority of observations on mismatch negativity (Wacongne, Changeux & Dehaene, 2012).

Conclusion

The "Bayesian brain" hypothesis is proving remarkably productive in many fields of cognitive neuroscience. Animal and human behavior suggests that adults and children possess a vast capacity for statistical inference at multiple levels (perception, action, language...). The very architecture of the cortex could be explained by the replication, at several hierarchical levels, of the same Bayesian neural circuit. In the 2012-2013 lecture, we'll be looking at how the Bayesian hypothesis applies to early learning, when children learn to adjust their internal models according to the environment around them and the education they receive.