Some AI hallucinations are caused by chaotic 'avalanche effects' in floating-point rounding, not just bad training data.
April 16, 2026
Original Paper
Numerical Instability and Chaos: Quantifying the Unpredictability of Large Language Models
arXiv · 2604.13206
The Takeaway
This paper proves that LLM unpredictability is rooted in fundamental numerical instability where tiny decimal rounding errors in early layers can explode into totally different outputs. It's a 'butterfly effect' for neural networks. This means even with a perfect dataset, models might still be inconsistent due to how hardware handles math. This shifts the blame for some hallucinations from the model's 'knowledge' to the model's 'arithmetic.' For developers building deterministic systems, this highlights the need for better quantification of chaotic noise in high-depth models. It suggests that scaling alone can't fix reliability if the underlying compute remains numerically unstable.
From the abstract
As Large Language Models (LLMs) are increasingly integrated into agentic workflows, their unpredictability stemming from numerical instability has emerged as a critical reliability issue. While recent studies have demonstrated the significant downstream effects of these instabilities, the root causes and underlying mechanisms remain poorly understood. In this paper, we present a rigorous analysis of how unpredictability is rooted in the finite numerical precision of floating-point representation