Predictive Coding Networks Enhanced with Hierarchical Gaussian Filters
A recent study published on arXiv (2605.20293) introduces closed-form predictive coding utilizing hierarchical Gaussian filters (HGFs). Traditional predictive coding frameworks often set the precision matrix to the identity, neglecting the precision-weighted prediction errors essential for efficient, localized, and Bayesian learning. By modeling networks as deep HGFs and reinstating precision-weighted message passing, this technique provides dynamic uncertainty assessments and Hebbian-compatible update mechanisms at each layer. The networks simultaneously learn activations, weights, and precisions through a unified free-energy objective, eliminating the need for global error signals and bypassing iterations or automatic differentiation. This method tackles the decline in performance seen in deep networks and presents a biologically inspired alternative to backpropagation.
Key facts
- Paper arXiv:2605.20293 proposes closed-form predictive coding via hierarchical Gaussian filters.
- Current PC networks fix precision matrix to identity, discarding precision-weighted prediction errors.
- New method expresses PC networks as deep hierarchical Gaussian filters (HGFs).
- Restores precision-weighted message passing for dynamic uncertainty estimates.
- Produces Hebbian-compatible update rules at every layer.
- Networks learn activations, weights, and precisions under a single free-energy objective.
- No global error signal required; resolves inference without iterations or automatic differentiation.
- Addresses slower training and performance degradation in deep networks.
Entities
Institutions
- arXiv