揭示大模型不可预测性源于浮点数精度导致的混沌传播。
Numerical Instability and Chaos: Quantifying the Unpredictability of Large Language Models
- 通过追踪浮点误差在Transformer层中的传播，发现早期层存在混沌级联效应。
- 识别出三种行为模式：稳定、混沌与信号主导，且随模型规模变化。
- 适用于关注大模型可靠性与可重复性的研究人员和工程落地团队。
随着大语言模型（LLMs）越来越多地应用于智能体工作流，其由数值不稳定性引发的不可预测性已成为关键可靠性问题。尽管近期研究已揭示这些不稳定性对下游任务的显著影响，但其根本原因和内在机制仍不清楚。本文系统分析了数值不稳定性如何根植于浮点数表示的有限精度，追踪了舍入误差在Transformer计算层中传播、放大或衰减的过程。特别地，我们发现早期层存在一种混沌‘雪崩效应’，微小扰动会引发二元结果：要么快速放大，要么完全衰减。除具体误差实例外，我们还证明了LLMs表现出普遍的、与规模相关的混沌行为，可分为三种典型状态：1）稳定态，扰动低于输入依赖阈值而消失，输出恒定；2）混沌态，舍入误差主导，导致输出发散；3）信号主导态，真实输入变化压倒数值噪声。我们在多个数据集和模型架构上广泛验证了这些发现。
原文摘要 · Abstract (English)
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: 1) a stable regime, where perturbations fall below an input-dependent threshold and vanish, resulting in constant outputs; 2) a chaotic regime, where rounding errors dominate and drive output divergence; and 3) a signal-dominated regime, where true input variations override numerical noise. We validate these findings extensively across multiple datasets and model architectures.
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