Despite exceptional performance on static benchmarks, Large Language Models (LLMs) exhibit significant brittleness when evaluated on perturbed variants of the original questions. Current extrinsic interventions, prompt engineering or supervised fine-tuning, overlook an important intrinsic factor underlying this degradation: the distributional shifts in layer activations between original and perturbed questions. To address this, this work formulates the reasoning robustness challenge as an Unsupervised Domain Adaptation (UDA) problem and proposes the Elastic Domain Adaptation (EDA) method. Unlike rigid strategies that enforce a uniform alignment constraint, EDA dynamically aligns layer activations based on the specific layers and perturbation types. Specifically, EDA incorporates an Adaptive Layer Selection (ALS) to identify pivotal layers and employs an Elastic Shift Module (ESM) to selectively pull or push layer representations depending on the perturbation types. Extensive experiments across six LLMs and 15 perturbation types demonstrate that EDA achieves state-of-the-art performance on most perturbed benchmarks while preserving reasoning capability on original benchmarks.

Large Language Models (LLMs) have achieved remarkable performance across a wide range of mathematical benchmarks. However, concerns remain as to whether these successes reflect genuine reasoning or superficial pattern recognition. Existing evaluation methods, which typically focus either on the final answer or on the intermediate reasoning steps, reduce mathematical reasoning to a shallow input–output mapping, overlooking its inherently multi-stage and multi-dimensional cognitive nature. Inspired by P’olya’s problem-solving theory, we propose SMART, a benchmark that decomposes mathematical problem-solving into four cognitive dimensions: Semantic Understanding, Mathematical Reasoning, Arithmetic Computation, and Reflection RefinemenT, and introduces dimension-specific tasks to measure the corresponding cognitive processes of LLMs. We apply SMART to 22 state-of-the-art open- and closed-source LLMs and uncover substantial discrepancies in their capabilities across dimensions. Our findings reveal genuine weaknesses in current models and motivate a new metric, the All-Pass Score, designed to better capture true problem-solving capability.