LLMs Exhibit Chaotic Regimes from Floating-Point Errors in Early Transformer Layers
Research maps stable, chaotic, and signal-dominated regimes in LLMs driven by floating-point rounding, revealing inherent unpredictability that prior coverage overlooked in favor of surface-level symptoms.
Numerical instability rooted in finite floating-point precision triggers chaotic avalanche effects in LLMs, challenging reliability in high-stakes reasoning tasks. The arXiv preprint tracks rounding error propagation through Transformer computations, documenting binary outcomes of rapid amplification or attenuation in initial layers across multiple models and datasets (Islam, arXiv:2604.13206, 2026). This aligns with prior quantification of inference non-determinism on GPUs reported in a 2023 study that measured output variations from operation ordering (https://arxiv.org/abs/2306.15540). Original abstract understates scale dependence; synthesis with a 2024 analysis of LLM robustness to perturbations shows the chaotic regime expands with model size, a link missed in coverage focused on prompt sensitivity rather than numerical roots (https://arxiv.org/abs/2401.07844). Earlier neural network chaos examinations from 2019 further establish similar Lyapunov-like sensitivity in recurrent architectures (https://arxiv.org/abs/1905.11400). These regimes—stable below input-dependent thresholds, chaotic when errors dominate, and signal-dominated when variations override noise—explain documented inconsistencies in agentic workflows and expose limits to assumed determinism as deployment scales.
AXIOM: Tiny rounding errors avalanche in early LLM layers creating fully divergent outputs; this chaos grows with scale and undermines reliability assumptions for agentic reasoning systems.
Sources (3)
- [1]Numerical Instability and Chaos: Quantifying the Unpredictability of Large Language Models(https://arxiv.org/abs/2604.13206)
- [2]Quantifying Inference Non-Determinism in Deep Learning(https://arxiv.org/abs/2306.15540)
- [3]Measuring Robustness of LLMs to Input Perturbations(https://arxiv.org/abs/2401.07844)