AGENTIC-SYSTEMSApril 17, 20261 min read14 views

Numerical Instability and Chaos: Quantifying the Unpredictability of Large Language Models

This paper analyzes how finite numerical precision in floating-point representations leads to unpredictability in LLMs through rounding error propagation, identifying an 'avalanche effect' and three distinct behavioral regimes.

Computer Science > Artificial Intelligence

Title: Numerical Instability and Chaos: Quantifying the Unpredictability of Large Language Models

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 representations, tracking how rounding errors propagate, amplify, or dissipate through Transformer computation layers.

Specifically, we identify a chaotic "avalanche effect" in the early layers, where minor perturbations trigger binary outcomes: either rapid amplification or complete attenuation. Beyond specific error instances, we demonstrate that LLMs exhibit universal, scale-dependent chaotic behaviors characterized by three distinct regimes:

A stable regime, where perturbations fall below an input-dependent threshold and vanish, resulting in constant outputs;
A chaotic regime, where rounding errors dominate and drive output divergence; and
A signal-dominated regime, where true input variations override numerical noise.

We validate these findings extensively across multiple datasets and model architectures.

Source: arXiv cs.AI Recent

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