Is the reconstruction loss culprit? An attempt to outperform JEPA

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.

In joint-embedding predictive architectures (JEPA), an encoder and a predictor are trained together to produce a representation that minimizes the error in predicting the representation of the next observation. Because the representations of both the current and the next observation are learned, it is unclear which features they will include. Earlier characterizations describe the features JEPA selects in terms of their individual predictability, raising the concern that unpredictable features, like a traffic light, will not be encoded into the representation. However, the prediction error is also affected by the relationships between features, e.g., the light's color helps predict whether the traffic will stop. We propose the predictive closure characterization, which accounts for these relationships. Based on a reformulation of the JEPA training objective, we show that selection depends on properties of feature sets. This view agrees with earlier works when features evolve independently, but makes new predictions when they do not, for instance that a feature like the traffic light can still be retained. We test this characterization in controlled experiments, which show that unpredictable features can become better represented when they help predict other features, and that changing one feature's predictive relationships can affect how well others are represented. We also demonstrate implications for steering feature selection: targeting one feature with an auxiliary objective, or supplying it to the predictor as side information, can strengthen the representation of another feature whose future values it helps predict, so steering can be indirect.

Joint-Embedding Predictive Architectures (JEPAs) are prone to representation collapse, typically mitigated through empirical heuristics. We develop an early-training stability theory that unifies these heuristics. Linearising the coupled JEPA gradient flow around the trivial fixed point reveals two competing effects: a driving force ($γ$) and a decay effect ($σ$). Under approximate spectral decoupling, a per-mode stability ratio $μ_i = γ_i / σ_i$ factorises into independent data-side and predictor-side terms and the count of unstable modes tracks the rank of representations that can emerge. The framework predicts a phase boundary, which we confirm empirically across more than 800 Tabular-JEPA configurations. It also unifies predictor scaling, masking ratio, and EMA as distinct mechanisms for shifting $μ$. Guided by this analysis, we introduce ResidualPred, a transformer predictor whose attention is biased toward the identity at initialisation; it improves both effective rank and downstream accuracy on tabular benchmarks and in I-JEPA pretraining on CIFAR-10, CIFAR-100, STL-10, and ImageNet. Our framework connects empirical collapse-avoidance heuristics to an explicit dynamical picture, yielding theory-driven stabilizers. Code is available at https://github.com/jose-melo/drive-vs-decay.