Hybrid Inference Accelerates Hierarchical Sparse Predictive Coding Models.

Hierarchical predictive coding offers an interpretable framework for understanding perception as an error-driven inference process within multi-layer generative models. When combined with sparse coding, which enforces parsimonious latent representations, these models exhibit appealing computational and neuroscientific properties. However, their practical application is often hindered by the high computational cost of iterative latent inference, especially as the model hierarchy deepens. Each input can demand numerous recurrent refinement steps to obtain a useful sparse representation, creating a significant bottleneck. This study investigates this bottleneck by comparing different inference procedures while keeping the underlying hierarchical sparse energy model fixed. Four schemes were evaluated: classical iterative inference (ISTA), an accelerated variant (MFISTA), a structurally informed amortized inference using a LISTA-style bottom-up encoder, and a novel hybrid method. The hybrid approach combines the speed of amortized initialization with a small number of corrective energy-based refinement steps. The results, measured on static image benchmarks, show that this hybrid method significantly improves reconstruction quality and sparsity compared to pure amortization. Crucially, it remains substantially faster than traditional long iterative inference. This demonstrates that a shallow LISTA-style initializer followed by brief corrective recurrence offers a superior balance of speed and accuracy for hierarchical sparse predictive coding models.