Generalizing Numerical Reasoning in Table Data through Operation Sketches and Self-Supervised Learning

Table Question Answering (TableQA) aims to reason over tables to answer user queries. Existing research treats all questions uniformly and evaluates solely through overall accuracy, obscuring a critical reality that LLMs excel at simple lookups yet struggle with complex operations like aggregation and arithmetic. To reveal this disparity, we introduce a novel \emph{Operation-wise TableQA} task with a fine-grained question taxonomy and release two datasets named WikiTQ-ow and TabFact-ow for evaluation. As for modeling bottlenecks, existing methods flatten tables into linearized texts, disrupting inherent structures and inducing the ``lost-in-the-middle'' issue, which poses a primary barrier to complex cross-row reasoning. Moreover, they typically reason from scratch, neglecting reusable patterns shared across similar operations. To address these limitations, we propose a Skill-augmented Table Graph Reasoning (SkillTGR) framework for self-evolving structured reasoning. Specifically, SkillTGR represents tables as attributed graphs with explicit row-column-cell structures, where LLMs plan and execute dynamic chains to retrieve evidence subgraphs for graph traversal reasoning. Based on this, SkillTGR builds a hierarchical SkillBank to distill reason trajectories into abstract skills under cognitive heuristics, then hybrid retrieves both successful and failed skills for contrastive augmented table graph reasoning, thereby enabling the continual self-evolution. Extensive experiments demonstrate that SkillTGR achieves superior performance with an average of 5.91% overall and 5.06% operation-wise improvement, also reducing 19.76% token consumption and 27.64% inference latency. Our codes and data will be released upon publication.

Financial question answering over hybrid tabular and textual data may require multi-source reasoning and precise numerical computation. While large language models (LLMs) can generate intermediate reasoning steps, natural-language rationales remain prone to arithmetic errors, making them an unreliable supervision source for distillation. Building on programmatic distillation, we develop an approach that transfers reliable numerical reasoning from a large teacher model to a compact student using execution-verified Python programs instead of free-form textual rationales. It leverages gold derivations to guide teacher-side program synthesis and retains only programs that execute correctly and produce the gold answer, ensuring high-quality supervision. We further introduce an iterative recovery stage that revisits teacher-failed examples, enabling the student to recover and incorporate newly verified programs into training. Experiments on TAT-QA show that our framework is highly effective for hybrid financial reasoning. Our best 7B student achieves 87.00 EM / 87.18 F1 on the test set, substantially outperforming the 72B teacher (78.46 EM) as well as traditional and strong LLM-based baselines, including TAGOP and TAT-LLM. These results demonstrate that execution-verified programmatic distillation provides an effective and extensible framework for training smaller models to perform reliable numerical reasoning.

Tabular foundation models have advanced deep learning for tabular data by delivering strong default performance across many small and medium tasks. Yet in niche domains, where data is scarce, high-dimensional, and shifted from the pretraining distribution, they may still fail to outperform carefully designed domain-specific methods. Many such domains also provide curated relational knowledge in the form of knowledge graphs and knowledge banks, but how to use this knowledge to improve and steer \textit{small} specialist tabular foundation models remains unclear. We address this problem through \textbf{Know}ledge-informed fine-tuning of \textbf{s}mall \textbf{T}abular \textbf{F}oundation \textbf{M}odels (\modelname). Specifically, we study nanoscale TabPFN- and TabICL-style variants, pretrained under controlled synthetic prior families and adapted using two complementary mechanisms: structural attention priors derived from knowledge graphs and parameter-efficient low-rank updates. We show that injecting domain-specific structural knowledge during fine-tuning yields meaningful gains over vanilla variants in specialist settings, whereas gains on general-domain tasks are marginal. We further observe that continual fine-tuning of frontier models can trigger collapse of pretrained knowledge and mechanisms.