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

• URL: http://arxiv.org/abs/2604.13206v1
• Date: Tue, 14 Apr 2026 18:26:38 GMT
• Title: Numerical Instability and Chaos: Quantifying the Unpredictability of Large Language Models
• Abstract summary: Large Language Models (LLMs) are increasingly integrated into agentic computation.<n>Their unpredictability stemming from numerical instability has emerged as a critical reliability issue.<n>We present a rigorous analysis of how unpredictability is rooted in the finite numerical precision of floating-point representations.
• Score: 1.4234197455380129
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• NICE: Scale-Stable Perturbations for Graph Neural Network Explanations via Noise Corruption [67.57304101271096]
  Element-wise Masking (EM) suppresses edge-induced messages toward zero.<n>Noise Corruption (NC) perturbs each message through matched-norm random-direction corruption.<n>NICE, a Noise Corruption-based explanation framework, learns a Restoration Boundary (SRB) under NC-induced uncertainty.
  arXiv  Detail & Related papers  (2026-08-17T03:08:14Z)
• Emergent Latent-State Computation under Stochastic Volatility [3.8881341075549947]
  We study how models internally represent latent dynamics under noisy, partially observed observations.<n>Across architectures, losses, and output heads, we find evidence for a two-stage computation.<n>These results suggest that volatility models provide a useful benchmark for interpretability under noisy latent dynamics and partial observability.
  arXiv  Detail & Related papers  (2026-07-28T08:49:48Z)
• TS-Fault: Benchmarking Time Series Forecasters Against Structural Faults [22.88447833683736]
  Time series forecasting (TSF) underpins consequential decisions in energy, transportation, finance, and healthcare.<n>TSF models are almost universally ranked by a single number on clean held-out data, under the implicit assumption that it predicts deployed reliability.<n>We present TS-Fault, a benchmark that evaluates forecasting models under explicit, parameterized fault scenarios with controllable semantic difficulty.
  arXiv  Detail & Related papers  (2026-06-16T23:15:20Z)
• Mitigating Error Amplification in Fast Adversarial Training [58.74042726356826]
  Fast Adversarial Training (FAT) has proven effective in enhancing model robustness by encouraging networks to learn perturbation-invariant representations.<n>FAT often suffers from catastrophic overfitting (CO), where the model overfits to the training attack and fails to generalize to unseen ones.<n>We propose a Distribution-aware Dynamic Guidance (DDG) strategy that dynamically adjusts both the perturbation budget and supervision signal.
  arXiv  Detail & Related papers  (2026-04-27T11:23:18Z)
• Causally-Constrained Probabilistic Forecasting for Time-Series Anomaly Detection [1.8995711908407733]
  This study introduces a causally-constrained probabilistic forecasting framework for anomaly detection.<n>It integrates an explicit time-lagged causal graph prior with deep sequence modeling.<n>Experiments indicate that the proposed method achieves state-of-the-art detection performance.
  arXiv  Detail & Related papers  (2026-04-20T09:24:28Z)
• DSO: Dual-Scale Neural Operators for Stable Long-term Fluid Dynamics Forecasting [7.678457910726061]
  We argue that existing neural operators treat local and global information processing uniformly.<n>We propose the Dual-Scale Neural Operator (DSO), which explicitly decouples information processing into two complementary modules.<n>Experiments on turbulent flow benchmarks show that DSO state-of-the-art accuracy while maintaining robust long-term stability, reducing prediction error by over 88% compared to existing neural operators.
  arXiv  Detail & Related papers  (2026-03-26T03:03:12Z)
• OrthoFormer: Instrumental Variable Estimation in Transformer Hidden States via Neural Control Functions [0.0]
  Transformer architectures excel at sequential modeling yet remain fundamentally limited by correlational learning.<n>We propose OrthoFormer, a causally grounded architecture that embeds instrumental variable estimation directly into Transformer blocks via neural control functions.
  arXiv  Detail & Related papers  (2026-03-08T03:05:16Z)
• Gradients Must Earn Their Influence: Unifying SFT with Generalized Entropic Objectives [22.29000001610794]
  Standard negative log-likelihood for Supervised Fine-Tuning (SFT) applies uniform token-level weighting.<n>This rigidity creates a two-fold failure mode: (i) overemphasizing low-probability targets can amplify gradients on noisy supervision and disrupt robust priors, and (ii) uniform weighting provides weak sharpening when the model is already confident.<n>Existing methods fail to resolve the resulting plasticity--stability dilemma, often suppressing necessary learning signals alongside harmful ones.<n>We introduce Dynamic Entropy Fine-Tuning (DEFT), a parameter-free objective that modulates the
  arXiv  Detail & Related papers  (2026-02-11T22:56:43Z)
• Generalizing GNNs with Tokenized Mixture of Experts [75.8310720413187]
  We show that improving stability requires reducing reliance on shift-sensitive features, leaving an irreducible worst-case generalization floor.<n>We propose STEM-GNN, a pretrain-then-finetune framework with a mixture-of-experts encoder for diverse computation paths.<n>Across nine node, link, and graph benchmarks, STEM-GNN achieves a stronger three-way balance, improving robustness to degree/homophily shifts and to feature/edge corruptions while remaining competitive on clean graphs.
  arXiv  Detail & Related papers  (2026-02-09T22:48:30Z)
• Same Answer, Different Representations: Hidden instability in VLMs [65.36933543377346]
  We introduce a representation-aware and frequency-aware evaluation framework that measures internal embedding drift, spectral sensitivity, and structural smoothness.<n>We apply this framework to modern Vision Language Models (VLMs) across the SEEDBench, MMMU, and POPE datasets.
  arXiv  Detail & Related papers  (2026-02-06T12:24:26Z)
• Character as a Latent Variable in Large Language Models: A Mechanistic Account of Emergent Misalignment and Conditional Safety Failures [70.48661957773449]
  Emergent Misalignment refers to a failure mode in which fine-tuning large language models on narrowly scoped data induces broadly misaligned behavior.<n>Across multiple domains and model families, we find that fine-tuning models on data exhibiting specific character-level dispositions induces substantially stronger and more transferable misalignment than incorrect-advice fine-tuning.
  arXiv  Detail & Related papers  (2026-01-30T15:28:42Z)
• Revisiting Multivariate Time Series Forecasting with Missing Values [65.30332997607141]
  Missing values are common in real-world time series.<n>Current approaches have developed an imputation-then-prediction framework that uses imputation modules to fill in missing values, followed by forecasting on the imputed data.<n>This framework overlooks a critical issue: there is no ground truth for the missing values, making the imputation process susceptible to errors that can degrade prediction accuracy.<n>We introduce Consistency-Regularized Information Bottleneck (CRIB), a novel framework built on the Information Bottleneck principle.
  arXiv  Detail & Related papers  (2025-09-27T20:57:48Z)
• Causality-Based Multivariate Time Series Anomaly Detection [63.799474860969156]
  We formulate the anomaly detection problem from a causal perspective and view anomalies as instances that do not follow the regular causal mechanism to generate the multivariate data. We then propose a causality-based anomaly detection approach, which first learns the causal structure from data and then infers whether an instance is an anomaly relative to the local causal mechanism. We evaluate our approach with both simulated and public datasets as well as a case study on real-world AIOps applications.
  arXiv  Detail & Related papers  (2022-06-30T06:00:13Z)
• Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding [101.35070661471124]
  We show that unobserved confounding leaves a characteristic footprint in the observed data distribution that allows for disentangling spurious and causal effects. We propose an adjusted score-based causal discovery algorithm that may be implemented with general-purpose solvers and scales to high-dimensional problems.
  arXiv  Detail & Related papers  (2021-03-28T11:07:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.