# Threshold Crossings as Tail Events for Catastrophic AI Risk

arXiv: https://arxiv.org/abs/2503.18979 · HTML: https://mlsanity.com/paper/2503.18979/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 23 Mar 2025.

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

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [An Overview of Catastrophic AI Risks](https://mlsanity.com/paper/2306.12001/) (2023)
- [Revisiting Neural Scaling Laws in Language and Vision](https://mlsanity.com/paper/2209.06640/) (2022)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [Introduction to AI Safety, Ethics, and Society](https://mlsanity.com/paper/2411.01042/) (2024)
- [Superintelligence Strategy: Expert Version](https://mlsanity.com/paper/2503.05628/) (2025)
- [Where AI Assurance Might Go Wrong: Initial lessons from engineering of critical systems](https://mlsanity.com/paper/2502.03467/) (2025)
- [Statistical Scenario Modelling and Lookalike Distributions for Multi-Variate AI Risk](https://mlsanity.com/paper/2502.14491/) (2025)

## Abstract (arXiv)

We analyse circumstances in which bifurcation-driven jumps in AI systems are associated with emergent heavy-tailed outcome distributions. By analysing how a control parameter's random fluctuations near a catastrophic threshold generate extreme outcomes, we demonstrate in what circumstances the probability of a sudden, large-scale, transition aligns closely with the tail probability of the resulting damage distribution. Our results contribute to research in monitoring, mitigation and control of AI systems when seeking to manage potentially catastrophic AI risk.