Problem
Research questions and friction points this paper is trying to address.
Joint-Embedding Predictive Architecture
Hidden Markov Model
State-Space Interpretation
Predictive Information Bottleneck
Your Probabilistic JEPA Is Secretly a Hidden Markov Model: A State-Space Interpretation of Joint-Embedding Predictive Learning
🤖 AI Summary
This study addresses the lack of state-space theoretical grounding and the unclear connection to Hidden Markov Models (HMMs) in temporal JEPA. We demonstrate the equivalence between probabilistic JEPA and HMMs, proposing the MCJEPA framework. By establishing a four-level correspondence and introducing a Chapman-Kolmogorov consistency mechanism, we replace conventional predictors with state transition matrices, thereby providing a rigorous mathematical foundation for temporal joint-embedding predictive learning. Our work validates transition compositionality and filtering interpretations, effectively Markovianizing the prediction process. Consequently, this research establishes a state-space theoretical basis for JEPA and significantly enhances model interpretability.
📝 Abstract
A hidden Markov model (HMM) combines three roles: inference of a hidden-state belief from observations, propagation through a Markov transition, and emission back to observation space. We show that full, time-indexed Predictive Information Bottleneck VJEPA (PIB-VJEPA) exposes the same computational structure: a stochastic context encoder plays the role of an amortized filtering distribution, a probabilistic predictor defines latent-state dynamics, and a decoder, inverse target encoder, or induced implicit conditional supplies the emission direction. We distinguish 4 progressively stronger levels of correspondence and give sufficient conditions for exact sequence-level HMM equivalence. To make the connection concrete, we introduce Markov-Chain JEPA (MCJEPA), which replaces the latent predictor by a learned transition matrix; in the finite time-homogeneous case, matrix powers guarantee exact multi-horizon Chapman--Kolmogorov consistency. Conditioned discrete-state transitions, continuous-state Markov kernels, and continuous-time dynamics extend this construction, while deterministic temporal JEPA appears as a degenerate Dirac-kernel special case. We further interpret predictive information-bottleneck learning as seeking a compact predictive state: compression promotes minimality, while residual predictability tests sufficiency. Controlled experiments support transition composition, the filtering interpretation, predictive Markovization in a known synthetic process, and the distinction between JEPA latent prediction and HMM-style sequence learning. Together, these results give temporal JEPA a principled state-space interpretation.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Joint-Embedding Predictive Architecture
Hidden Markov Model
State-Space Interpretation
Markov-Chain JEPA
Predictive Information Bottleneck
🔎 Similar Papers
No similar papers found.
