# Information-Geometric First-Passage Monitoring of Distributional Stability in Stochastic Systems

arXiv: https://arxiv.org/abs/2604.24083 · HTML: https://mlsanity.com/paper/2604.24083/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [Testing randomness](https://mlsanity.com/paper/1906.09256/) (2019)
- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [Improving Out-of-Distribution Detection via Dynamic Covariance Calibration](https://mlsanity.com/paper/2506.09399/) (2025)
- [Distributionally Robust LQG control under Distributed Uncertainty](https://mlsanity.com/paper/2306.05227/) (2023)
- [A communication-efficient, online changepoint detection method for monitoring distributed sensor networks](https://mlsanity.com/paper/2403.18549/) (2024)

## Abstract (arXiv)

Runtime monitoring of stochastic systems must distinguish nominal distributional relaxation from regime departure while controlling repeated-test false alarms under explicit validity assumptions. This paper links relative-entropy dissipation, information geometry, and sequential inference in a bounded first-passage monitoring architecture. For reversible Fokker--Planck dynamics, relative entropy to an invariant density is non-increasing; under exogenous forcing, its derivative decomposes into nominal dissipation and an information-space forcing term. The runtime layer uses Gaussian window surrogates, nominal-relative covariance shrinkage, a coordinate-consistent relative precision diagnostic, and randomized conformal ranks aggregated by a mixture power-martingale process. Analytical Ornstein--Uhlenbeck validation gives zero positive nominal Kullback--Leibler increments, forcing-identity residuals below 3.31 x 10^-6, and coordinate-invariance errors at numerical roundoff. On NSL-KDD, the monitor yields 0/100 alarms on internal nominal streams but 63/100 on official test-normal streams; post-change detection is 99.0% for seen and 98.53% for test-only attack types with median one-window delay. On UNSW-NB15, internal-null alarms are 0/100, whereas official test-normal alarms rise to 90/100; post-change detection is 81.33%, with 18.67% pre-change alarms. In these evaluations, calibration transport emerges as a major deployment constraint. No universal benchmark superiority, causal inference, or physical-work interpretation is claimed.