  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.
