Predictive coding equals proximal gradient descent on MAP problems, with priors setting nonlinearities via proximal operators and yielding leaky firing-rate networks plus hierarchical MRFs.
An approximation of the error backpropagation algorithm in a predictive coding network with local Hebbian synaptic plasticity
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PC-ALM uses dual ascent on an augmented Lagrangian to achieve exact backpropagation gradients via layer-local updates in linear networks and matching performance in nonlinear networks up to depth 128.
Adding temporal memory via LIF, precision-weighted gating, and anticipatory prediction to MoE routers recovers effective expert selection at distribution transitions, with ablation confirming a super-additive beta-ant interaction.
Backpropagated gradients from vision models predict higher visual cortex signals but diverge from brain hierarchies in spatial and temporal organization.
Predictive coding is recast as deep hierarchical Gaussian filters to restore precision-weighted message passing, yielding closed-form inference and online precision learning that matches backpropagation speed on FashionMNIST while outperforming on online and concept-drift tasks.
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Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts
Adding temporal memory via LIF, precision-weighted gating, and anticipatory prediction to MoE routers recovers effective expert selection at distribution transitions, with ablation confirming a super-additive beta-ant interaction.