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Multi-Horizon Consistency as Geometry: When Latent Dynamics Contract, and When They Do Not

Summary

This study uses the multi-step latent consistency weight λ as a diagnostic tool to explore its effect on the geometry of latent dynamics in video predictors and world models. On Moving-MNIST, increasing λ significantly reduces latent expansion and prediction error, but not in action-conditioned environments, indicating domain-limited applicability. A stochastic forcing law unifies curves across domains.

SourcearXiv Machine LearningAuthor: Kavya Bhand, Aadi Joshi
Multi-Horizon Consistency as Geometry: When Latent Dynamics Contract, and When They Do Not
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[Submitted on 21 Jul 2026]

Title:Multi-Horizon Consistency as Geometry: When Latent Dynamics Contract, and When They Do Not

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Abstract:Multi-horizon latent consistency is a common training knob in video predictors and world models, but practitioners rarely know what it does to transition geometry. We treat lambda, the weight on multi-step latent agreement, as a diagnostic control and measure an empirical expansion proxy L20,q95 together with horizon-20 prediction error E20. On Moving-MNIST (n=6 seeds at the critical pair), raising lambda from 0 to 0.8 cuts L20 from 4.96 +/- 2.01 to 1.01 +/- 0.06 (paired t p=0.005, Wilcoxon p=0.031) and halves E20 (0.365 to 0.177, paired t p=1.1e-13). Four of six seeds cross L

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Key points and analysis

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Key points

  • Raising λ from 0 to 0.8 on Moving-MNIST reduces latent expansion L20 from 4.96 to 1.01 and halves prediction error E20.
  • The same loss does not produce contraction (L<1) on action-conditioned tasks (Pendulum-v1, CartPole-v1) or KTH video.
  • Mediation analysis indicates λ indirectly reduces error through contraction (r-hat=0.94).
  • A stochastic forcing law L20 ~ 1.23 + 1.82η describes behavior at λ=0.8, with consistent slopes across different λ.

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