SJEPA: Learning Elegant Latent Dynamics with Hybrid Symbolic-Neural Predictors

• URL: http://arxiv.org/abs/2608.04060v1
• Date: Tue, 04 Aug 2026 13:08:07 GMT
• Title: SJEPA: Learning Elegant Latent Dynamics with Hybrid Symbolic-Neural Predictors
• Abstract summary: We introduce SJEPA, a reconstruction-free JEPA framework that learns predictive representations whose induced dynamics admit compact symbolic descriptions.<n>We formalise this principle through induced-dynamics complexity, analyse predictive-coordinate non-identifiability, and show that unconstrained operator compression creates a direct shortcut to representation collapse.<n>The results expose a controllable trade-off among predictive fidelity, representation quality, symbolic parsimony, and symbolic-neural allocation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Joint-embedding predictive architectures learn abstract states by predicting target embeddings from context embeddings, but their transition models are typically opaque neural maps. We introduce SJEPA, a reconstruction-free JEPA framework that learns predictive representations whose induced dynamics admit compact symbolic descriptions. Its hybrid transition combines a symbolic law with a regularised neural correction for dynamics outside the selected grammar. The central principle is to learn the simplest adequate dynamics: representation constraints preserve informative, non-collapsed predictive coordinates, while operator compression favours low-complexity symbolic-neural transitions that remain predictively adequate. We formalise this principle through induced-dynamics complexity, analyse predictive-coordinate non-identifiability, and show that unconstrained operator compression creates a direct shortcut to representation collapse. The framework supports both alternating representation-equation learning and symbolic dynamics fitted to fixed representations. In controlled pendulum experiments, joint learning discovers substantially simpler symbolic dynamics with lower long-horizon rollout error and divergence than post-hoc fitting, while an unconstrained one-step diagnostic realises the predicted collapse shortcut. Under grammar misspecification, correction regularisation preserves the representable symbolic mechanism and directs the neural component towards residual dynamics. The results expose a controllable trade-off among predictive fidelity, representation quality, symbolic parsimony, and symbolic-neural allocation.

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