H Dong

Yurong Liu, Yeye He, Haoyu Dong et al.

Predicting missing cell values in tabular data is a fundamental problem in data cleaning. While state-of-the-art reasoning models show great promise in predicting missing values in tables, by reasoning holistically across rows and columns, they are costly to deploy at scale and tend to be overconfident, often generating hallucinated or false-positive predictions. In this paper, we observe that achieving high-precision missing-value prediction in tables requires a distinct combination of three capabilities: (1) world knowledge, (2) text-based reasoning, and (3) code-based reasoning. We systematically explore design choices for combining these capabilities, and propose an Auto-Fill approach that post-trains three specialist small language models (SLMs), each optimized for one capability. We develop a calibrated ensemble mechanism that either dynamically selects the most confident specialist or abstains, ensuring high accuracy. Extensive experiments on 11 benchmarks with 2200 real tables drawn from diverse domains show that Auto-Fill achieves superior accuracy compared to state-of-the-art reasoning models (e.g., o3-pro, Gemini 3 Pro, and DeepSeek R1), while operating at a fraction (less than 1%) of the cost of these frontier models. Our results highlight the effectiveness of specialization and calibrated abstention in the important domain of tabular data. Auto-Fill is publicly available at https://github.com/lyrain2001/auto-fill.

Jiale Linghu, Hao Dong, Yangshuai Wang

Random-feature methods reduce high-dimensional elliptic PDE collocation to linear coefficient problems, but full-dimensional trial spaces overlook lower-dimensional structure. We introduce the Hierarchical Analysis-of-Variance Random Feature Method (HA-RFM), which selects coordinate blocks using closed Sobol indices of the PDE residual, identifies oblique low-rank features from fitted-predictor gradients, and couples all retained features in one regularized least-squares solve. Under structural and stability hypotheses, we establish an $L^2$ error bound that links solution and residual truncation to finite-width approximation and regularized finite-sample fitting, and we derive guarantees for width and structure recovery. The resulting width is polynomial in the dimension at fixed interaction order, with dimension-independent higher-order contributions under uniform structural control. Residual screening achieves exact recovery of the prescribed three-pair support, while fitted-predictor gradients recover oblique directions through dimension $50$. In random-ridge tests, less than $1\%$ additional width reduces errors by factors of $14$-$39$ over coordinate blocks and $34$-$100$ over equal-width full-dimensional RFM. Semilinear computations extend HA-RFM through dimension $100$, while dense and distributed interactions delineate the coordinate families required for broader structure.