发表机构
Université Paris-Saclay, CEA, List; Computer Vision Center Barcelona（巴黎萨克雷大学，法国国家科学研究中心，List研究所; 巴塞罗那计算机视觉中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究JEPA世界模型，通过将四个正则化器组织成层次结构，证明选择抗坍缩正则化器决定训练目标是否为有效AIF变分自由能，在特定条件下SIGReg有优势，还扩展对应关系并确定未计算的AIF项。
AI 中文摘要
联合嵌入预测架构（JEPA）是潜在世界模型的主要设计，但通常以经验性能而非规范原则为依据。我们表明，抗坍缩正则化器的选择决定了JEPA的训练目标（预测损失加权嵌入正则化器）是否是有效的主动推理（AIF）变分自由能。我们将四个非对比正则化器（VICReg、LogDet、PairDist和SIGReg）组织成一个由先验错误校准差距索引的熵估计层次结构，并表明该差距的符号（估计器是从上方还是下方限制潜在熵）决定了AIF意外边界是否存在：VICReg和LogDet是不安全的上界，PairDist是安全的下界，SIGReg消除了差距。然后我们证明了一个对应定理：在标准恒定噪声编码器模型和成功的SIGReg实施（各向同性高斯嵌入）下，差距消失，目标成为精确的信息瓶颈，意外边界得以保留，潜在目标成本成为AIF实用价值的精确代理，而VICReg留下不可约的二阶各向异性项。我们将对应关系扩展到多步预期自由能、整体认知价值和学习策略机制，并确定了当前JEPA世界模型未计算的一个AIF项：状态认知价值，一个未来状态覆盖信号。预测在种类上而非程度上有所不同，在此作为理论结果留待单独工作中的实证检验；完整证明在附录A中，每个结果的代数核心在Lean 4中经过机器验证（附录D）。
英文摘要
Joint-Embedding Predictive Architectures (JEPAs) are the dominant design for latent world models, yet they are usually justified by empirical performance rather than a normative principle. We show that the choice of anti-collapse regulariser determines whether a JEPA's training objective, a prediction loss plus a weighted embedding regulariser, is a valid Active Inference (AIF) variational free energy. We organise four non-contrastive regularisers (VICReg, LogDet, PairDist, and SIGReg) into an entropy-estimator hierarchy indexed by a prior-miscalibration gap, and show that the gap's sign, whether the estimator bounds the latent entropy from above or below, decides whether the AIF surprise bound survives: VICReg and LogDet are unsafe upper bounds, PairDist a safe lower bound, and SIGReg eliminates the gap. We then prove a correspondence theorem: under the standard constant-noise encoder model and successful SIGReg enforcement (isotropic-Gaussian embeddings), the gap vanishes, the objective becomes an exact information bottleneck, the surprise bound is preserved, and the latent goal cost becomes an exact proxy for AIF pragmatic value, whereas VICReg leaves an irreducible second-order anisotropy term. We extend the correspondence to multi-step expected free energy, ensemble epistemic value, and a learned-policy regime, and we identify the one AIF term no current JEPA world model computes: the state-epistemic value, a future-state coverage signal. The predictions differ in kind, not degree, and are stated here as theoretical consequences left for empirical test in separate work; full proofs are in Appendix A, and the algebraic core of every result is machine-verified in Lean 4 (Appendix D).
CommentsTheoretical paper; empirical validation of the stated predictions is left to separate work. 28 pages, 4 figures, 4 tables
