Stable Unsupervised Continual Chunking with Sheaf SyncMap
TL;DR
This work proposes sheaf regularization to reduce local inconsistencies in Decentralized SyncMap, a self-organizing system, and thereby stabilize its chunking dynamics, and introduces a radial sheaf structure that penalizes distance-dependent radial motion between pairs of variables.
Abstract
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.
