mlsanityData to 7 Oct 2026

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

arXiv 2604.13206 ↗First posted 14 Apr 2026cs.AI cs.LG cs.NAcited by 0

On the map: LLM agents and tool use → General LLM agent frameworks and benchmarks

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use. Builds on 19 of its 32 references that are in the map. First posted on arXiv 14 Apr 2026.

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19 of 32 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024Large Language Model based Multi-Agents: A Survey of Progress and Challenges21 Jan
  2. 2023The Rise and Potential of Large Language Model Based Agents: A Survey14 Sep
  3. 2023A Survey on Large Language Model based Autonomous Agents22 Aug
  4. 2023AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors21 Aug
  5. 2023MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework1 Aug

Other references · 14

  1. 2023QLoRA: Efficient Finetuning of Quantized LLMscited by 3,355
  2. 2023Universal and Transferable Adversarial Attacks on Aligned Language Modelscited by 2,914
  3. 2023AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversationcited by 1,906
  4. 2022GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformerscited by 1,838
  5. 2022Large Language Models Encode Clinical Knowledgecited by 1,807
  6. 2022SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Modelscited by 1,338
  7. 2019Universal Adversarial Triggers for Attacking and Analyzing NLPcited by 709
  8. 2019Theoretical Limitations of Self-Attention in Neural Sequence Modelscited by 286
  9. 2021Randomness In Neural Network Training: Characterizing The Impact of Toolingcited by 57
  10. 2020Lyapunov spectra of chaotic recurrent neural networkscited by 37
  11. 2024Persona is a Double-edged Sword: Mitigating the Negative Impact of Role-playing Prompts in Zero-shot Reasoning Taskscited by 28
  12. 2024Impacts of floating-point non-associativity on reproducibility for HPC and deep learning applicationscited by 24
2 more
  1. 2018Deterministic Implementations for Reproducibility in Deep Reinforcement Learningcited by 19
  2. 2025Embeddings to Diagnosis: Latent Fragility under Agentic Perturbations in Clinical LLMscited by 1

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