Fragility Is Not Reducible to Hardness: Conditional Causal Difficulty for LLMs

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.

As large language models (LLMs) are increasingly deployed to perform tasks with minimal human oversight, it is crucial that these models operate robustly. In particular, a model that can solve a given problem should not fail simply because certain entities$\unicode{x2013}$such as names, numbers, or other contextual details$\unicode{x2013}$have changed while the underlying problem logic remains the same. Prior work suggests that current LLMs still struggle with this form of robustness: they often succeed on some variations of a problem but fail on others. However, existing evaluations often lack a systematic way to identify which logic-preserving variations are most likely to induce failure. Instead, they typically test a random subset of allowable variations, which can overstate robustness. To address this gap, we introduce logic-preserving difficulty scaling (LPDS), a framework that (i) quantifies the difficulty of a problem variation and (ii) systematically searches the space of allowable variations to find those that maximize difficulty and expose failures. We show that as difficulty increases, performance declines and errors in the models' reasoning chains become more pronounced. We further demonstrate that LPDS efficiently finds difficult problem variations for a model, resulting in performance drops up to 5 times larger compared to random sampling. Finally, we show that fine-tuning on more difficult variations leads to more consistent robustness gains than training on easier ones.

Predicting human item difficulty is central to educational assessment, where reliable estimates support fairness and effective test construction. Existing methods often depend on costly human calibration or item-level textual representations, providing limited evidence about the cognitive processes that make items difficult. We argue that difficulty should be viewed not only as a property of item text, but also as an observable consequence of the problem-solving burden an item induces. Large Reasoning Models (LRMs) offer scalable process evidence through reasoning traces, but such evidence must be structured to support interpretable modeling. To this end, we introduce Epi2Diff (Episode to Difficulty), a framework that maps LRM reasoning traces into cognitively grounded episode sequences. These episodes group trace segments into functional problem-solving states, enabling difficulty to be modeled through reasoning scale, effort allocation, and state transitions. Epi2Diff extracts compact episode-dynamic features and combines them with semantic item representations for human difficulty prediction. Experiments on four real-world human difficulty datasets show that Epi2Diff consistently outperforms strong baselines, including fine-tuned small language models, LLM in-context learning, and supervised LLM adaptation. On SAT-derived classification benchmarks, Epi2Diff achieves an 8.1% average relative gain over supervised LLM fine-tuning baselines. Further analyses show that harder items induce more effortful, iterative, and implementation-centered episode dynamics, rather than merely longer responses. These results demonstrate that cognitive episodes in LRM reasoning traces provide a predictive and interpretable process representation for human item difficulty, offering a new lens for educational measurement with reasoning models.