ABSTRACT: 

Backpropagation underpins modern deep learning but relies on point-estimate optimisation, providing no principled representation of epistemic uncertainty and limiting robustness and interpretability, while remaining vulnerable to distribution shift. Bayesian neural networks address some of these limitations but are difficult to scale, while predictive coding offers biologically grounded inference learning with explicit uncertainty at the cost of expensive iterative inference.
 

This PhD proposes a hybrid Bayesian learning framework that integrates predictive coding and backpropagation via a decoupled neural interface. A predictive coding network performs variational inference and generates oracle gradients corrected by a path–integral over inference dynamics, which are then amortised into a conventional backpropagation network. This yields an explicit variational free energy defined over backpropagation-trained models, enabling principled uncertainty
estimation, causal structure learning, and free-energy–based pruning while preserving computational efficiency.
 

The project will develop the theoretical foundations of this framework, implement and evaluate it on benchmark datasets, and explore extensions to neuromorphic hardware and active inference.