Module 3
Predictive Coding in the Cortex
Predictive coding proposes that cortical hierarchies implement variational Bayesian inference. Deep layers send top-down predictions; superficial layers compute prediction errors that feed forward. Rao & Ballard 1999 showed the framework explains V1 extra-classical receptive-field properties; Friston 2005 generalised to the full cortex.
1. Rao & Ballard 1999
Rao & Ballard trained a two-layer hierarchical generative model with sparse priors on natural-image patches. Units in the first layer acquired receptive fields resembling V1 simple cells: oriented, spatially localised, bandpass. Just as importantly, the model reproduced V1’s extra-classicalproperties — reduced response when a stimulus extended beyond the classical receptive field — because top-down predictions explained away the context.
2. Mumford 1992 & Hierarchical Inference
Mumford 1992 proposed that the two-way cortical connectivity between deep and superficial layers implements top-down predictions (deep) and bottom-up residuals (superficial). The hierarchical arrangement recursively invokes the same rule: each level’s predictions are the priors for the level below, each level’s residuals propagate up to the level above.
\[ \epsilon_l \;=\; x_l - f_l\bigl(\mu_{l+1}\bigr),\qquad \mu_{l+1}\ \text{updates to minimise}\ \sum_l \epsilon_l^T \Pi_l \epsilon_l \]
Simulation: Gabor Receptive Fields
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Code will be executed with Python 3 on the server
3. Empirical Tests
Direct neural signatures of predictive coding include: reduced V1 responses to expected vs. unexpected stimuli (Alink 2010), mismatch-negativity (MMN) ERP attributed to a prediction-error response in auditory cortex (Wacongne 2012), feedforward/feedback asymmetries in oscillatory bands (Bastos 2012, M6), and fMRI suppression effects during repetition.
Key References
• Rao, R. P. N. & Ballard, D. H. (1999). “Predictive coding in the visual cortex.” Nat. Neurosci., 2, 79–87.
• Mumford, D. (1992). “On the computational architecture of the neocortex. II. The role of cortico-cortical loops.” Biol. Cybern., 66, 241–251.
• Alink, A. et al. (2010). “Stimulus predictability reduces responses in primary visual cortex.” J. Neurosci., 30, 2960–2966.
• Wacongne, C. et al. (2012). “A neuronal model of predictive coding accounting for the mismatch negativity.” J. Neurosci., 32, 3665–3678.
• Friston, K. J. (2005). “A theory of cortical responses.” Phil. Trans. R. Soc. B, 360, 815–836.