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This paper investigates the sensitivity of Mistral-7B, Llama-3-8B, and Qwen2.5-7B to meaning-preserving perturbations in GSM8K math problems, finding significant answer-flip rates. They introduce Mechanistic Perturbation Diagnostics (MPD), a framework combining logit lens, activation patching, component ablation, and a novel Cascading Amplification Index (CAI) to trace the mechanistic basis of these failures. Their analysis reveals an architectural divide in failure localizability and proposes a mechanistic failure taxonomy, validated through targeted repair experiments using steering vectors and layer fine-tuning.
Even meaning-preserving changes to math problems can cause LLMs to fail, but the *type* of failure (localized, distributed, entangled) varies dramatically across architectures like Llama-3, Mistral, and Qwen.
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.