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文章背景与核心概要

联合嵌入预测架构（JEPA）近年来在自监督学习领域取得了巨大成功，但其底层的理论机理与经典统计学习模型的关系仍有待系统性阐明。本文深入探讨了JEPA与隐马尔可夫模型（HMM）之间的深层理论联系，证明了全时序索引的预测信息瓶颈VJEPA（PIB-VJEPA）本质上映射了HMM的计算机制，涵盖信念推理、马尔可夫转移传播以及向观测空间的发射过程。

为了弥合预测学习与经典状态空间模型之间的鸿沟，作者正式提出了“马尔可夫链JEPA（MCJEPA）”，并建立了多层级的形式化对应关系。该研究不仅为时序JEPA奠定了严谨的概率框架，还通过受控实验验证了转移组合、滤波解释以及预测马尔可夫化，为理解现代自监督表征学习提供了全新的状态空间视角。

Your Probabilistic JEPA Is Secretly a Hidden Markov Model: A State-Space Interpretation of Joint-Embedding Predictive Learning

arXiv: 2608.13621 [cs.AI]
Authors: Yongchao Huang
Submitted: August 13, 2026 (69 pages)
Primary Subject: Artificial Intelligence (cs.AI)

Executive Summary

This paper investigates the deep theoretical connection between Joint-Embedding Predictive Architectures (JEPAs) and Hidden Markov Models (HMMs). The author demonstrates that full, time-indexed Predictive Information Bottleneck VJEPA (PIB-VJEPA) inherently mirrors the computational mechanics of an HMM—specifically handling belief inference, Markov transition propagation, and emission back into observation space.

本文研究了联合嵌入预测架构（JEPA）与隐马尔可夫模型（HMM）之间的深层理论联系。作者证明了全时序索引的预测信息瓶颈VJEPA（PIB-VJEPA）本质上映射了HMM的计算机制——具体处理信念推理、马尔可夫转移传播以及向观测空间的发射。

To bridge the gap between predictive learning and classical state-space models, the paper introduces the Markov-Chain JEPA (MCJEPA) and explores various levels of formal correspondence, establishing a principled probabilistic framework for temporal JEPA.

为了弥合预测学习与经典状态空间模型之间的鸿沟，本文引入了马尔可夫链JEPA（MCJEPA），并探讨了不同层级的形式化对应关系，为时序JEPA建立了一个有原则的概率框架。

Key Contributions & Core Concepts

  • The HMM Triad in JEPA: The work maps components of PIB-VJEPA directly to classical HMM functions:
  • Stochastic Context Encoder \(\rightarrow\) Amortized filtering distribution.
  • Probabilistic Predictor \(\rightarrow\) Latent-state dynamics.
  • Decoder / Inverse Target Encoder \(\rightarrow\) Emission direction.
  • JEPA中的HMM三元组： 该工作将PIB-VJEPA的组件直接映射到经典的HMM功能：
  • 随机上下文编码器（Stochastic Context Encoder） \(\rightarrow\) 分摊滤波分布（Amortized filtering distribution）。
  • 概率预测器（Probabilistic Predictor） \(\rightarrow\) 潜在状态动力学。
  • 解码器 / 逆目标编码器（Decoder / Inverse Target Encoder） \(\rightarrow\) 发射方向。
  • Levels of Correspondence: The paper outlines four progressively stronger levels of theoretical correspondence, culminating in sufficient conditions for exact sequence-level HMM equivalence.
  • 对应层级： 论文概述了四个渐进增强的理论对应层级，最终得出了实现精确序列级HMM等价的充分条件。
  • Markov-Chain JEPA (MCJEPA): To solidify the connection, MCJEPA replaces the latent predictor with a learned transition matrix. In finite time-homogeneous settings, matrix powers guarantee exact multi-horizon Chapman–Kolmogorov consistency.
  • 马尔可夫链JEPA（MCJEPA）： 为了巩固这一联系，MCJEPA用学习得到的转移矩阵替代了潜在预测器。在有限的时间齐次设定下，矩阵幂保证了精确的多步查普曼-柯尔莫哥洛夫（Chapman–Kolmogorov）一致性。
  • Generalizations & Degenerate Cases: The formulation expands to conditioned discrete-state transitions, continuous-state Markov kernels, and continuous-time dynamics. Deterministic temporal JEPA is shown to emerge as a degenerate Dirac-kernel special case.
  • 泛化与退化情况： 该公式扩展到了条件离散状态转移、连续状态马尔可夫核以及连续时间动力学。研究表明，确定性时序JEPA可以作为狄拉克核（Dirac-kernel）的退化特例出现。
  • Information-Bottleneck Interpretation: Predictive information-bottleneck learning is framed as a search for compact predictive states, where data compression promotes minimality, and residual predictability tests sufficiency.
  • 信息瓶颈解释： 预测信息瓶颈学习被构想为对紧凑预测状态的搜索，其中数据压缩促进了极小性（minimality），而残余可预测性则检验了充分性（sufficiency）。

Experimental Highlights

Controlled empirical experiments validate: 1. Transition composition and filtering interpretations. 2. Predictive Markovization within a known synthetic process. 3. The functional distinction between traditional JEPA latent prediction and HMM-style sequence learning.

受控的实证实验验证了以下内容： 1. 转移组合与滤波解释。 2. 在已知合成过程中的预测马尔可夫化。 3. 传统JEPA潜在预测与HMM风格序列学习之间的功能区别。

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