TabularMath: Evaluating Computational Extrapolation in Tabular Learning via Program-Verified Synthesis

• URL: http://arxiv.org/abs/2602.02523v1
• Date: Sun, 25 Jan 2026 23:44:03 GMT
• Title: TabularMath: Evaluating Computational Extrapolation in Tabular Learning via Program-Verified Synthesis
• Authors: Zerui Cheng, Jiashuo Liu, Jianzhu Yao, Pramod Viswanath, Ge Zhang, Wenhao Huang,
• Abstract summary: We propose TabularMath, a diagnostic benchmark of 114 deterministic problems (233,472 rows) generated from verified programs based on 8K and AIME.<n>On standard regression metrics, TabPFN v2.5 performs remarkably well, achieving R2=0.998 in-distribution and maintaining positive R2 even under distribution shift.<n>When we measure rounded consistency (exact integer accuracy), a different picture emerges: TabPFN v2.5 drops below 10% on out-of-distribution data, while ICL maintains around 40%.
• Score: 22.883505574924303
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Standard tabular benchmarks mainly focus on the evaluation of a model's capability to interpolate values inside a data manifold, where models good at performing local statistical smoothing are rewarded. However, there exists a very large category of high-value tabular data, including financial modeling and physical simulations, which are generated based upon deterministic computational processes, as opposed to stochastic and noisy relationships. Therefore, we investigate if tabular models can provide an extension from statistical interpolation to computational extrapolation. We propose TabularMath, a diagnostic benchmark of 114 deterministic problems (233,472 rows) generated from verified programs based on GSM8K and AIME. We evaluate 9 tabular architectures and in-context learning (ICL) with GPT-OSS-120B. On standard regression metrics, TabPFN v2.5 performs remarkably well, achieving R^2=0.998 in-distribution and maintaining positive R^2 even under distribution shift, which is unique among the tabular models we tested. When we measure rounded consistency (exact integer match), a different picture emerges: TabPFN v2.5 drops below 10% on out-of-distribution data, while ICL maintains around 40%. This gap between R^2 and exact-match accuracy suggests that tabular models learn smooth function approximations but struggle to recover precise computational outputs under extrapolation. The two paradigms appear complementary: TabPFN scales efficiently with data; ICL achieves exact computation from few examples. We release all code and data to support further investigation.

Related papers

• TabPFN: One Model to Rule Them All? [21.658323618943697]
  We provide a tailored explanation of how TabPFN works for a statistics audience.<n>We show that an out-of-the-box application of TabPFN vastly outperforms specialized state-of-the-art methods.
  arXiv  Detail & Related papers  (2025-05-26T13:55:29Z)
• TabICL: A Tabular Foundation Model for In-Context Learning on Large Data [15.08819125687632]
  We introduce TabICL, a tabular foundation model for classification, pretrained on synthetic datasets with up to 60K samples.<n>Across 200 classification datasets from the TALENT benchmark, TabICL is on par with TabPFNv2 while being systematically faster (up to 10 times)<n>On 53 datasets with over 10K samples, TabICL surpasses both TabPFNv2 and CatBoost, demonstrating the potential of ICL for large data.
  arXiv  Detail & Related papers  (2025-02-08T13:25:04Z)
• Drift-Resilient TabPFN: In-Context Learning Temporal Distribution Shifts on Tabular Data [39.40116554523575]
  We present Drift-Resilient TabPFN, a fresh approach based on In-Context Learning with a Prior-Data Fitted Network. It learns to approximate Bayesian inference on synthetic datasets drawn from a prior. It improves accuracy from 0.688 to 0.744 and ROC AUC from 0.786 to 0.832 while maintaining stronger calibration.
  arXiv  Detail & Related papers  (2024-11-15T23:49:23Z)
• TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation [91.50296404732902]
  We introduce TabDiff, a joint diffusion framework that models all mixed-type distributions of tabular data in one model.<n>Our key innovation is the development of a joint continuous-time diffusion process for numerical and categorical data.<n>TabDiff achieves superior average performance over existing competitive baselines, with up to $22.5%$ improvement over the state-of-the-art model on pair-wise column correlation estimations.
  arXiv  Detail & Related papers  (2024-10-27T22:58:47Z)
• TabDPT: Scaling Tabular Foundation Models on Real Data [20.00390825519329]
  We propose an approach to combine ICL-based retrieval with self supervised learning to train foundation models.<n>We show that incorporating real data during the pre-training phase can lead to significantly faster training and better generalization to unseen data.<n>Our resulting model, TabDPT, achieves top performance on both regression (CTR23) and classification (CC18) benchmarks.
  arXiv  Detail & Related papers  (2024-10-23T18:00:00Z)
• Large Scale Transfer Learning for Tabular Data via Language Modeling [30.44823668480631]
  We present TabuLa-8B, a language model for tabular prediction. We use a dataset of over 2.1B rows from over 4M unique tables. We find that TabuLa-8B has zero-shot accuracy on unseen tables that is over 15 percentage points (pp) higher than random guessing.
  arXiv  Detail & Related papers  (2024-06-17T18:58:20Z)
• Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data [6.550684951976902]
  We show how iterative methods can be used to reduce computational costs in calculating likelihoods, gradients, and predictive distributions with full-scale approximations (FSAs)<n>We introduce a novel preconditioner and show theoretically and empirically that it accelerates the conjugate gradient method's convergence speed and mitigates its sensitivity with respect to the FSA parameters.<n>In our experiments, it outperforms existing state-of-the-art preconditioners for Vecchia approximations.
  arXiv  Detail & Related papers  (2024-05-23T12:25:22Z)
• Computational-Statistical Gaps in Gaussian Single-Index Models [77.1473134227844]
  Single-Index Models are high-dimensional regression problems with planted structure. We show that computationally efficient algorithms, both within the Statistical Query (SQ) and the Low-Degree Polynomial (LDP) framework, necessarily require $Omega(dkstar/2)$ samples.
  arXiv  Detail & Related papers  (2024-03-08T18:50:19Z)
• On the Performance of Empirical Risk Minimization with Smoothed Data [59.3428024282545]
  Empirical Risk Minimization (ERM) is able to achieve sublinear error whenever a class is learnable with iid data. We show that ERM is able to achieve sublinear error whenever a class is learnable with iid data.
  arXiv  Detail & Related papers  (2024-02-22T21:55:41Z)
• The Languini Kitchen: Enabling Language Modelling Research at Different Scales of Compute [66.84421705029624]
  We introduce an experimental protocol that enables model comparisons based on equivalent compute, measured in accelerator hours. We pre-process an existing large, diverse, and high-quality dataset of books that surpasses existing academic benchmarks in quality, diversity, and document length. This work also provides two baseline models: a feed-forward model derived from the GPT-2 architecture and a recurrent model in the form of a novel LSTM with ten-fold throughput.
  arXiv  Detail & Related papers  (2023-09-20T10:31:17Z)
• Learning Summary Statistics for Bayesian Inference with Autoencoders [58.720142291102135]
  We use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information that has been used to generate the training data.
  arXiv  Detail & Related papers  (2022-01-28T12:00:31Z)
• Scaling Structured Inference with Randomization [64.18063627155128]
  We propose a family of dynamic programming (RDP) randomized for scaling structured models to tens of thousands of latent states. Our method is widely applicable to classical DP-based inference. It is also compatible with automatic differentiation so can be integrated with neural networks seamlessly.
  arXiv  Detail & Related papers  (2021-12-07T11:26:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.