Bayesian Brain — Predictive Coding

Walk into your own dark bedroom and you don't grope around — you already know roughly where the bed is, so you barely glance. Your brain runs on expectations: it predicts what the world will throw at it, then mostly just checks whether the prediction was right. You usually "see" what you expect, and you really only notice the moments when reality disagrees — a chair someone moved, a step that wasn't there. Perception is less like a camera and more like a constantly-corrected guess.

Two ingredients decide what you perceive: a prior (what you expected, from past experience) and the likelihood (what your senses report right now). Bayes' rule blends them, $p(\text{cause}\mid\text{obs})\propto p(\text{obs}\mid\text{cause})\,p(\text{cause})$, and the trick is that the more reliable source gets more say — this is called precision weighting. Worked number: your memory says a sound is 10° to your left and you're fairly sure (spread ±5°); your ears say 20°, but they are noisy (±15°). The brain doesn't pick one or simply average them — it weights each by 1/variance, so the tight prior counts about nine times as much as the noisy ears, landing near 11°: it hugs the trustworthy prior while still nudging toward what you heard.

Predictive coding makes this dynamic and hierarchical. Each cortical level sends a prediction $\hat{y}$ down to the level below; that level computes a prediction error $\epsilon=y-\hat{y}$ and passes only the surprising part back up. The optimal running version is the Kalman filter, $\hat{x}_{t}=\hat{x}_{t\mid t-1}+K_t\,(y_t-H\hat{x}_{t\mid t-1})$, where the gain $K_t$ sets how far you move toward fresh data: high gain means "trust the senses" (attention turned up), low gain means "trust the model." Friston's free-energy principle frames the whole cortex as minimising this surprise. In the sim, Parameter 1 stands for prior precision, Parameter 2 for sensory (likelihood) precision, and Input I for the incoming observation.

Push Parameter 2 (sensory precision) to its maximum and change Input I: the estimate snaps straight to the input — "believe your eyes." Now drop Parameter 2 low and raise Parameter 1 (prior precision): the estimate barely budges when the input moves — a strong prior, like recognising a friend in a blurry photo. Finally sweep Input I and watch the prediction error jump and then settle as the model catches up — a miniature version of repetition suppression and the mismatch negativity (MMN).

Rao & Ballard (1999): each cortical level predicts the level below (top-down) and sends prediction errors up (bottom-up). Representation units minimise prediction error. V1 error units fire when retinal input ≠ V2 prediction. Explains: repetition suppression, mismatch negativity (MMN), end-stopping, extra-classical RF suppression.

Friston (2005): all cortical processing minimises variational free energy F = KL[q||p] - log p(o). Simultaneously: makes posterior q accurate AND drives action to match expected sensory states. Subsumes Bayesian perception, motor control, and RL under one framework. Applications: autism (excess precision of sensory input), psychosis (abnormal prior beliefs).

Kalman gain K_t balances prior vs likelihood (precision weighting). Neural implementation: K_t = attention (high attention = high likelihood weighting). Cerebellum implements forward model (Kalman predictor) for motor commands. Disrupting precision → attenuation of self-generated sensations (why you can't tickle yourself).