PredProp: Bidirectional Stochastic Optimization with Precision Weighted Predictive Coding

TL;DR

PredProp introduces a novel stochastic optimization method for predictive coding networks that adaptively weights updates using error precision, effectively implementing approximate Natural Gradient Descent and outperforming Adam on image benchmarks.

Contribution

It proposes PredProp, a new optimization approach for PCNs that leverages error precision for adaptive weighting and extends to deep neural network layers within PCNs.

Findings

PredProp outperforms Adam in dense decoder networks on image benchmarks.

Using error precision improves optimization of hierarchical predictive coding layers.

PredProp effectively implements approximate Natural Gradient Descent in PCNs.

Abstract

We present PredProp, a method for optimization of weights and states in predictive coding networks (PCNs) based on the precision of propagated errors and neural activity. PredProp jointly addresses inference and learning via stochastic gradient descent and adaptively weights parameter updates by approximate curvature. Due to the relation between propagated error covariance and the Fisher information matrix, PredProp implements approximate Natural Gradient Descent. We demonstrate PredProp's effectiveness in the context of dense decoder networks and simple image benchmark datasets. We found that PredProp performs favorably over Adam, a widely used adaptive learning rate optimizer in the tested configurations. Furthermore, available optimization methods for weight parameters benefit from using PredProp's error precision during inference. Since hierarchical predictive coding layers are optimised individually using local errors, the required precisions factorize over hierarchical layers. Extending beyond classical PCNs with a single set of decoder layers per hierarchical layer, we also generalize PredProp to deep neural networks in each PCN layer by additionally factorizing over the weights in each PCN layer.