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.
Intraday market manipulation is hard to detect because its footprint is brief, buried in millions of quotes, and statistically similar to ordinary volatility. Detectors reach high recall only by flagging so many other days that measured precision collapses, producing alerts no regulator can act on. We show that this manipulation leaves a distinctive dynamic signature: a pump-and-crash pattern visible in the velocity of market state, rather than its level. We build a minute-level detection pipeline, strictly partitioned in time, based on smoothed state velocity: option-Delta velocity for index options and price velocity for equities. We explain every alert with SHAP attribution. We hold the test period strictly out-of-sample and fix all thresholds before evaluation. On the locked Indian BANKNIFTY index-options test, the plain autoencoder recovers 10 of 10 regulator-identified manipulation days. Conditioning detection on market regimes inferred by a hidden Markov model yields an instructive negative result. The regimes are descriptively distinct, but using them trades recall for precision. Under the closed-world assumption that unlabeled days are normal, precision remains near 25%. The same dynamic appears in thinly traded U.S. equities (SEC v. Patel). The shape of the signature survives the transfer; its velocity magnitude does not. A pump-reversal shape score ranks the complaint's alleged manipulation days with AUC 0.91 (ARQQ) and 0.81 (ACY). On the ARQQ worked example, the score peaks inside the complaint's documented minute window. Finally, exact SHAP attribution over every alert shows that unconfirmed alerts share the regulator-identified days' attribution profile (cosine similarity 0.99). The precision ceiling is consistent with incomplete enforcement labels rather than detector failure. What transfers across markets and instrument types is the dynamic signature itself.
Gaussian Processes (GPs) are a powerful tool for Bayesian time-series modeling, yet their cubic computational cost remains a severe barrier for application to long, high-cadence datasets in astronomy. While specialized scalable solvers like Celerite elegantly reduce this scaling to linear time, repeatedly evaluating the exact likelihood during iterative Bayesian sampling is a bottleneck for developing more complex models, like hierarchical or additive models in which Celerite is only one component. To make this inference computationally tractable, we introduce a generative surrogate framework. By utilizing a Variational Autoencoder (VAE) to learn a compressed representation of the Celerite prior, we map highly correlated stochastic dependencies into a low-dimensional, isotropic manifold. This transition completely bypasses exact covariance operations, shifting the computational burden to a rapid neural network forward pass. Through an extensive simulation study, we show that the generative surrogate accurately reproduces the structural fidelity of exact physical kernels like Celerite. Finally, we demonstrate embedding our VAE approximation into an additive model that combines Celerite and a hidden Markov model (HMM) for stellar flare detection in time series data of stars. We evaluate the joint VAE+HMM architecture against the exact Celerite+HMM framework on empirical astrophysical time series and demonstrate that the proposed methodology achieves significant reductions in computational time, enabling the rigorous, large-scale characterization of stellar flares across massive data archives.