# The Boiling Frog Threshold: Criticality and Blindness in World Model-Based Anomaly Detection Under Gradual Drift

arXiv: https://arxiv.org/abs/2603.08455 · HTML: https://mlsanity.com/paper/2603.08455/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Latent dynamics models and model-based RL, one of 11 directions in World models.
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Placed in

- World models / [Latent dynamics models and model-based RL](https://mlsanity.com/wm/latent-dynamics-models-and-model-based-rl/)

## Builds on (most cited first, 7 of 7)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [World Models for Anomaly Detection during Model-Based Reinforcement Learning Inference](https://mlsanity.com/paper/2503.02552/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Price of Self-Calibration: Exact Evidence Budgets and Manufactured Blind Sets in Adaptive Monitoring](https://mlsanity.com/paper/2609.23254/) (2026)

## Abstract (arXiv)

When an RL agent's observations are gradually corrupted, at what drift rate does it "wake up" -- and what determines this boundary? We study world model-based self-monitoring under continuous observation drift across four MuJoCo environments, three detector families (z-score, variance, percentile), and three model capacities. We find that (1) a sharp detection threshold varepsilon^* exists universally: below it, drift is absorbed as normal variation; above it, detection occurs rapidly. The threshold's existence and sigmoid shape are invariant across all detector families and model capacities, though its position depends on the interaction between detector sensitivity, noise floor structure, and environment dynamics. (2) Sinusoidal drift is completely undetectable by all detector families -- including variance and percentile detectors with no temporal smoothing -- establishing this as a world model property rather than a detector artifact. (3) Within each environment, varepsilon^* follows a power law in detector parameters (R2 = 0.89-0.97), but cross-environment prediction fails (R2 = 0.45), revealing that the missing variable is environment-specific dynamics structure partial PE/partialvarepsilon. (4) In fragile environments, agents collapse before any detector can fire ("collapse before awareness"), creating a fundamentally unmonitorable failure mode. Our results reframe varepsilon^* from an emergent world model property to a three-way interaction between noise floor, detector, and environment dynamics, providing a more defensible and empirically grounded account of self-monitoring boundaries in RL agents.