Predictive Coding with Bayesian Priors via Proximal Gradients
We recast predictive coding as continuous-time proximal gradient descent applied to a regularized maximum-a-posteriori (MAP) objective. We study first a single-level problem and then a multi-level hierarchy. For the single-level problem, we show that proximal gradient descent is precisely a leaky firing-rate network: the membrane leak, the effective recurrent matrix, the local synaptic drive, and the static nonlinearity all follow from one optimization principle, and the resulting circuit is the one proposed by Rao and Ballard. The prior selects the nonlinearity through its proximal operator, and the likelihood precision sets the gain on the observation. For the hierarchy, we show that a ...
| Authors | Francesco Bullo |
|---|---|
| Primary category | eess.SY |
| Published | 6 June 2026 |
| Last updated at source | 6 June 2026 |
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