On the Demand-Supply Geometry of Representation Collapse

Preventing representation collapse remains a central challenge in Joint-Embedding Predictive Architectures (JEPAs). Endpoint-only constraints cannot fully prevent or repair collapse when intermediate representations lose sample distinctions. We introduce SADL (Supply And Demand Loss), an adaptive one-sided bridge that matches endpoint demand to the available capacity of the representation path. SADL compares demand from the output objective and realized endpoint geometry with the weaker of encoder excitation and cross-endpoint transmission capacity, applying a correction only when demand exceeds supply. It works with different output regularization functions without auxiliary networks, learned gates, or a separate schedule. In single-task and jointly trained four-task LeWorldModel (LeWM) and INTACT experiments, the collapse rate falls from 50% to 0% in a ten-seed collapse test. After only 1 epoch of training with SADL, encoder effective rank increases by 3.4–6.4× and latent prediction error decreases by 20–303× relative to the corresponding endpoint-only baselines. Under multiple regularization functions, INTACT also achieves over 95% mean search-free control success. Across four image datasets, each with multiple paired seeds, SADL delivers consistent seed-wise improvements in accuracy and stability at representative checkpoints, with its largest gains emerging early in training. These findings indicate that demand–supply matching along the representation path is a general principle for faster and more stable representation learning across control and image classification.