Local learning methods offer an alternative to end-to-end backpropagation, but their unstructured local objectives can produce weak feature learning in deep networks. We study whether the order of hidden-state optimization can address this limitation. We propose a boundary-first inference schedule that partitions a model into chunks, first coordinates hidden states at chunk boundaries, and then refines representations within each chunk. We instantiate this schedule in predictive coding networks (PCNs), a local-learning framework in which hidden activities and prediction errors are explicitly exposed during inference. On CIFAR-10, the resulting boundary-first predictive-coding instantiation improves accuracy over standard predictive coding by $9.77\%$ under a standard parametrization and by $5.51\%$ under a $μ$-parametrization. Diagnostic analyses further show more non-trivial early-layer updates, lower initial-to-final CKA, and more diverse layerwise gradients, consistent with stronger feature learning. These results support boundary-first, chunk-based inference as a practical design principle for predictive-coding training and motivate its study in broader local-learning systems.
Unsupervised Continual chunking is a fundamental problem in machine learning and neuroscience, where the goal is to identify groups of states that frequently co-occur in temporal sequences. A key challenge is to form accurate chunks while maintaining their stability over time. In this work, we propose sheaf regularization to reduce local inconsistencies in Decentralized SyncMap, a self-organizing system, and thereby stabilize its chunking dynamics. We introduce a radial sheaf structure that penalizes distance-dependent radial motion between pairs of variables. Experimental results show that the proposed method achieves the highest normalized mutual information (NMI) among the evaluated SyncMap variants on 12 of 18 probabilistic Continual General Chunking Problem (CGCP) graphs with two-state memory and on 17 of 18 graphs with dynamic memory. In the sequential adaptation experiment, Sheaf SyncMap also achieves high NMI after shifts in the input distribution, indicating that it can adapt to new knowledge while avoiding the negative transfer commonly observed in modern machine learning systems such as neural networks.