Tabular data plays a vital role in various real-world scenarios and finds extensive applications. Although recent deep tabular models have shown remarkable success, they still struggle to handle data distribution shifts, leading to performance degradation when testing distributions change. To remedy this, a robust tabular model must adapt to generalize to unknown distributions during testing. In this paper, we investigate the problem of fully test-time adaptation (FTTA) for tabular data, where the model is adapted using only the testing data. We identify three key challenges: the existence of label and covariate distribution shifts, the lack of effective data augmentation, and the sensitivity of adaptation, which render existing FTTA methods ineffective for tabular data. To this end, we propose the Fully Test-time Adaptation for Tabular data, namely FTAT, which enables FTTA methods to robustly optimize the label distribution of predictions, adapt to shifted covariate distributions, and dynamically adapt the model for various tasks and models. We conduct comprehensive experiments on six benchmark datasets, which are evaluated using three metrics. The experimental results demonstrate that FTAT outperforms state-of-the-art methods by a margin.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning.However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems.To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions (PMC) containing over 5,000 validated ill-defined mathematical problems.Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems.To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language.Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

Tabular data is widely adopted in various machine learning tasks. Current tabular data learning mainly focuses on closed environments, while in real-world applications, open environments are often encountered, where distribution shifts and feature decrements occur, leading to severe performance degradation. Previous studies have primarily focused on addressing distribution shifts, while feature decrements, a unique challenge in tabular data learning, have received relatively little attention. In this paper, we present the first comprehensive study on the problem of Fully Test-Time Adaptation for Feature Decrement in Tabular Data. Through empirical analysis, we identify the suboptimality of existing missing-feature imputation methods and the limited applicability of missing-feature adaptation approaches. To address these challenges, we propose a novel method, LLM-IMPUTE, which leverages Large Language Models (LLMs) to impute missing features without relying on training data. Furthermore, we introduce Augmented-Training LLM (ATLLM), a method designed to enhance the robustness of feature decrements by simulating feature-decrement scenarios during the training phase to address tasks that can not be imputed by LLM-IMPUTE. Extensive experimental results demonstrate that our proposal significantly improves both performance and robustness in missing feature imputation and adaptation scenarios.