Do 3D Medical Foundation Models See Through MRI Artifacts? A Controlled Study of Representation Robustness

Self-supervised 3D medical foundation models are increasingly used as general-purpose feature extractors, yet their sensitivity to MRI artifacts remains poorly understood. We present a controlled evaluation of representation robustness across five pretrained 3D encoders spanning different architectures, objectives, pretraining domains, and dataset scales. Using BraTS-Africa cases with four MRI sequences, we generate seven frequency- and image-domain artifacts at five predefined corruption settings. Robustness is assessed using linear centered kernel alignment (CKA), RankMe, and UMAP, complemented by an independent segmentation-consistency analysis. We find that robustness is strongly model- and artifact-dependent. 3DINO exhibits the most consistently stable representations, while BrainIAC is highly sensitive to several corruptions; NeuroVFM, BrainFM, and Neuro-SimCLR show intermediate but distinct artifact-specific profiles. Across many conditions, CKA decreases substantially while RankMe remains comparatively stable, indicating that artifacts often distort representation geometry without causing dimensional collapse. Segmentation consistency also degrades under corruption, particularly for ghosting and Rician noise, but aligns only partially with representation-level robustness. These findings show that larger-scale or domain-specific pretraining alone does not guarantee artifact invariance and motivate explicit robustness evaluation before deploying 3D foundation models in heterogeneous MRI settings.

TREAT: Evaluating Access to Formal Knowledge across Equivalent Mathematical Representations

AI systems increasingly operate between flexible input representations and formal objects used by downstream tools. A key challenge is recognizing when an unfamiliar formulation denotes a known formal object. We study this challenge through theorem recognition: given an equivalence-preserving transformation of a theorem condition, a model must recover the theorem identity associated with the standard statement. We introduce TREAT, a benchmark for evaluating whether large language models can recover known theorem identities from equivalence-preserving formula-level transformations. Rather than paraphrasing theorem text, TREAT changes the mathematical form of theorem conditions themselves, expressing known results through residual equations, witness statements, optimization identities, set relations, operator forms, and proof-intermediate characterizations. Starting from scraped theorem pages, we filter for entries with usable mathematical expression forms, extract canonical theorem conditions, and generate transformed variants with recorded assumptions and inverse mappings. The final corpus contains 737 theorem identities and 29,480 transformed rows. On a test panel, the best model retrieves the correct theorem identity in only 60.73% of cases. Other systems reveal different failure modes, including abstention, wrong detection, and malformed outputs. These suggest that theorem knowledge can be fragile under equivalent changes in representation. TREAT therefore provides a controlled testbed for evaluating representation-robust access to formal knowledge, with broader relevance to domains that require stable target objects, explicit equivalence relations, validation procedures, and auditable scoring.

Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving

Large language models (LLMs) are increasingly evaluated on mathematical problem solving, yet prior work often treats representationally equivalent formulations as interchangeable and conflates reasoning errors with interface failures. This paper investigates representation robustness in LLM-based mathematical problem solving by systematically varying surface representations of the same underlying problems, including story problems, word-equations, symbolic equations, and isomorphic paraphrases. Using a curated dataset of mathematically equivalent problems, we evaluate five contemporary LLMs under a direct answer generation condition. We find substantial representational sensitivity: models frequently change correctness across equivalent formulations, with nontrivial flip rates across story, symbolic, and word-equation variants. We also observe systematic regressions under isomorphic reformulations, showing that even subtle paraphrase-level changes can degrade performance despite preserved mathematical structure. We then evaluate a code-augmented condition in which models externalize reasoning as executable Python code that is run locally for validation. This interface reveals strong latent reasoning capability in some models that perform poorly under direct prompting, but it does not uniformly improve robustness. Instead, failures shift across interaction layers, from opaque reasoning errors to protocol violations and execution failures. Even when executable reasoning succeeds, representation sensitivity often persists. Overall, our results show that reasoning scaffolds do not eliminate representational brittleness, but expose new tradeoffs among correctness, reliability, latency, and cost. We argue that representation should be treated as a first-class interface design variable in LLM evaluation and deployment, especially for AI-assisted problem-solving systems.