BRo-JEPA: Learning Modular Arithmetic in Latent Space
The paper introduces BRo-JEPA, a latent world model that successfully learns modular arithmetic (like addition modulo 10) by explicitly imposing the circular structure of the problem into the latent space, enabling strong zero-shot generalization.
Abstract
More Like ThisCan neural networks learn abstract algebraic rules, or do they merely memorize training patterns? We investigate this using MNIST digits as states and modular arithmetic operations as actions in a JEPA-style latent world model. Standard supervised baselines and JEPA models with additive operation embeddings fit seen operations but fail to extrapolate reliably to unseen ones. To bridge this gap, we introduce a block-rotation predictor that imposes the circular structure of modulo-10 arithmetic in latent space. This enables strong zero-shot generalization, with the best ResNet-based JEPA block-rotation model achieving 99.46\% zero-shot and 99.46\% rollout accuracy. Our results suggest that latent world models can learn symbolic transformation rules when architecture matches the structure of the problem. Our code can be \href{https://github.com/DL-World-Models/mnist-math}{accessed here}.