Error Optimization: Overcoming Exponential Signal Decay in Deep Predictive Coding Networks
Journal:
arXiv
Published Date:
May 26, 2025
Abstract
Predictive Coding (PC) offers a biologically plausible alternative to
backpropagation for neural network training, yet struggles with deeper
architectures. This paper identifies the root cause: an inherent signal decay
problem where gradients attenuate exponentially with depth, becoming
computationally negligible due to numerical precision constraints. To address
this fundamental limitation, we introduce Error Optimization (EO), a novel
reparameterization that preserves PC's theoretical properties while eliminating
signal decay. By optimizing over prediction errors rather than states, EO
enables signals to reach all layers simultaneously and without attenuation,
converging orders of magnitude faster than standard PC. Experiments across
multiple architectures and datasets demonstrate that EO matches
backpropagation's performance even for deeper models where conventional PC
struggles. Besides practical improvements, our work provides theoretical
insight into PC dynamics and establishes a foundation for scaling
biologically-inspired learning to deeper architectures on digital hardware and
beyond.
