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

Dimensions overall score 7.0

• Quantifies numerical instability in LLMs, identifying a chaotic 'avalanche effect' and three distinct regimes of unpredictability based on floating-point precision. While recent studies have demonstrated the significant downstream effects of these instabilities, the root causes and underlying mechanisms remain poorly understood.problem 35%
  Evidencepartial

  Quantifies numerical instability in LLMs, identifying a chaotic 'avalanche effect' and three distinct regimes of unpredictability based on floating-point precision. While recent studies have demonstrated the significant downstream effects of these instabilities, the root causes and underlying mechanisms remain poorly understood.

  Implicationpartial

  Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.

  Verificationpartial

  partial

• 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.method 35%
  Evidencepartial

  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.

  Implicationpartial

  Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.

  Verificationpartial

  partial

• ScienceToStartup currently rates this 7.0/10 on the public viability pass. 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. Code availability is flagged in the production record; the public repository link still needs proof alignment.result 35%
  Evidencepartial

  ScienceToStartup currently rates this 7.0/10 on the public viability pass. 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. Code availability is flagged in the production record; the public repository link still needs proof alignment.

  Implicationpartial

  Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.

  Verificationpartial

  partial

• LLM Reliability moved forward this cycle; last verified April 2026. Public score 7.0/10. Production flags indicate code availability.why now 35%
  Evidencepartial

  LLM Reliability moved forward this cycle; last verified April 2026. Public score 7.0/10. Production flags indicate code availability.

  Implicationpartial

  Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.

  Verificationpartial

  partial

Competitive landscape

Quantifies numerical instability in LLMs, identifying a chaotic 'avalanche effect' and three distinct regimes of unpredictability based on floating-point precision.