The Goldilocks Zone of Z: Balancing Expressivity and Efficiency in JEPA World Models

The Goldilocks Zone of Z: Balancing Expressivity and Efficiency in JEPA World Models Joint-Embedding Predictive Architectures (JEPA) learn world models by predicting future latent states rather than raw pixels. A critical but rarely principled hyperparameter is the dimensionality of the latent space, |Z|. In practice, |Z| is inherited from vision backbone defaults (e. g. , ViT-Tiny's 192 dimensions) and applied uniformly across all environments, ignoring the fundamental trade-off between representational capacity and planning efficiency. This paper formalises a Goldilocks Zone for |Z|: a closed-form two-sided bound d* ≤ |Z| ≤ d* + C_λ ln K where d* is the intrinsic dimensionality of the environment's observation manifold, K is the planner's sample budget, λ is the temperature, and γ is the discount factor. The lower bound prevents underfitting of the dynamics; the upper bound prevents exponential collapse of planning efficiency under MPPI and CEM. The Effective Sample Size ratio (ESS/K) quantifies this collapse: each spurious dimension above d* degrades planning efficiency exponentially over the full discounted horizon. Two lightweight diagnostic tools operationalise the bound: (1) the Two-NN intrinsic dimensionality estimator, applied to trajectory data before training to measure d*; and (2) the PCA utilisation ratio, applied after training to verify that |Z| was not oversized. Both tools require no modification to the training procedure. Empirical validation on TwoRoom-v1 across six models (|Z| ∈ 2, 4, 8, 16, 32, 192) confirms that PCA utilisation, Two-NN d*, and predicted ESS/K all converge on the same optimal zone (|Z|* ≈ 4–8, d* ≈ 1. 7). The benchmark default of |Z| = 192 — 115× the intrinsic dimensionality — collapses to near-zero planning efficiency. An interactive implementation of the Goldilocks formula is available at: https: //huggingface. co/spaces/robomotic/goldillock-jepa Code: https: //github. com/robomotic/stable-worldmodel/tree/goldilocks A companion paper surveys seven Z-sizing methods and provides a full environment complexity taxonomy (Zenodo preprint, 2025).