Fragile Reasoning: A Mechanistic Analysis of LLM Sensitivity to Meaning-Preserving Perturbations

TL;DR

This paper investigates why large language models are fragile to meaning-preserving perturbations, introduces diagnostic tools to analyze failure mechanisms, and proposes a taxonomy and repair strategies for these failures.

Contribution

It presents the Mechanistic Perturbation Diagnostics framework and a failure taxonomy, advancing understanding of LLM fragility and potential repair methods.

Findings

Number paraphrasing causes more disruption than name swaps.

CAI metric predicts failures better than divergence layer.

Activation patching can recover some localized failures.

Abstract

Large language models demonstrate strong performance on mathematical reasoning benchmarks, yet remain surprisingly fragile to meaning-preserving surface perturbations. We systematically evaluate three open-weight LLMs, Mistral-7B, Llama-3-8B, and Qwen2.5-7B, on 677 GSM8K problems paired with semantically equivalent variants generated through name substitution and number format paraphrasing. All three models exhibit substantial answer-flip rates (28.8%-45.1%), with number paraphrasing consistently more disruptive than name swaps. To trace the mechanistic basis of these failures, we introduce the Mechanistic Perturbation Diagnostics (MPD) framework, combining logit lens analysis, activation patching, component ablation, and the Cascading Amplification Index (CAI) into a unified diagnostic pipeline. CAI, a novel metric quantifying layer-wise divergence amplification, outperforms first divergence layer as a failure predictor for two of three architectures (AUC up to 0.679). Logit lens reveals that flipped samples diverge from correct predictions at significantly earlier layers than stable samples. Activation patching reveals a stark architectural divide in failure localizability: Llama-3 failures are recoverable by patching at specific layers (43/60 samples), while Mistral and Qwen failures are broadly distributed (3/60 and 0/60). Based on these diagnostic signals, we propose a mechanistic failure taxonomy (localized, distributed, and entangled) and validate it through targeted repair experiments: steering vectors and layer fine-tuning recover 12.2% of localized failures (Llama-3) but only 7.2% of entangled (Qwen) and 5.2% of distributed (Mistral) failures.