Zhiyuan Fan

Tianping Zhang, Zheyu Zhang, Zhiyuan Fan et al.

The goal of automated feature generation is to liberate machine learning experts from the laborious task of manual feature generation, which is crucial for improving the learning performance of tabular data. The major challenge in automated feature generation is to efficiently and accurately identify effective features from a vast pool of candidate features. In this paper, we present OpenFE, an automated feature generation tool that provides competitive results against machine learning experts. OpenFE achieves high efficiency and accuracy with two components: 1) a novel feature boosting method for accurately evaluating the incremental performance of candidate features and 2) a two-stage pruning algorithm that performs feature pruning in a coarse-to-fine manner. Extensive experiments on ten benchmark datasets show that OpenFE outperforms existing baseline methods by a large margin. We further evaluate OpenFE in two Kaggle competitions with thousands of data science teams participating. In the two competitions, features generated by OpenFE with a simple baseline model can beat 99.3% and 99.6% data science teams respectively. In addition to the empirical results, we provide a theoretical perspective to show that feature generation can be beneficial in a simple yet representative setting. The code is available at https://github.com/ZhangTP1996/OpenFE.

Zhiyuan Fan, Jian Li

We consider the sparse moment problem of learning a $k$-spike mixture in high-dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous algorithms either assume certain separation assumptions, use more recovery moments, or run in (super) exponential time. Our algorithm for the one-dimensional problem (also called the sparse Hausdorff moment problem) is a robust version of the classic Prony's method, and our contribution mainly lies in the analysis. We adopt a global and much tighter analysis than previous work (which analyzes the perturbation of the intermediate results of Prony's method). A useful technical ingredient is a connection between the linear system defined by the Vandermonde matrix and the Schur polynomial, which allows us to provide tight perturbation bound independent of the separation and may be useful in other contexts. To tackle the high-dimensional problem, we first solve the two-dimensional problem by extending the one-dimensional algorithm and analysis to complex numbers. Our algorithm for the high-dimensional case determines the coordinates of each spike by aligning a 1d projection of the mixture to a random vector and a set of 2d projections of the mixture. Our results have applications to learning topic models and Gaussian mixtures, implying improved sample complexity results or running time over prior work.

Dadi Guo, Yuejin Xie, Qingyu Liu et al.

As large language models (LLMs) advance their mathematical capabilities toward the IMO level, the scarcity of challenging, high-quality problems for training and evaluation has become a significant bottleneck. Simultaneously, recent code agents have demonstrated sophisticated skills in agentic coding and reasoning, suggesting that code execution can serve as a scalable environment for mathematical experimentation. In this paper, we investigate the potential of code agents to autonomously evolve existing math problems into more complex variations. We introduce a multi-agent framework designed to perform problem evolution while validating the solvability and increased difficulty of the generated problems. Our experiments demonstrate that, given sufficient test-time exploration, code agents can synthesize new, solvable problems that are structurally distinct from and more challenging than the originals. This work provides empirical evidence that code-driven agents can serve as a viable mechanism for synthesizing high-difficulty mathematical reasoning problems within scalable computational environments. Our data is available at https://github.com/TarferSoul/Code2Math.

Weitong Zhang, Jiafan He, Zhiyuan Fan et al.

We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level $ζ>0$. We propose an algorithm based on a novel data selection scheme, which only selects the contextual vectors with large uncertainty for online regression. We show that, when the misspecification level $ζ$ is dominated by $\tilde O (Δ/ \sqrt{d})$ with $Δ$ being the minimal sub-optimality gap and $d$ being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound $\tilde O (d^2/Δ)$ as in the well-specified setting up to logarithmic factors. In addition, we show that an existing algorithm SupLinUCB (Chu et al., 2011) can also achieve a gap-dependent constant regret bound without the knowledge of sub-optimality gap $Δ$. Together with a lower bound adapted from Lattimore et al. (2020), our result suggests an interplay between misspecification level and the sub-optimality gap: (1) the linear contextual bandit model is efficiently learnable when $ζ\leq \tilde O(Δ/ \sqrt{d})$; and (2) it is not efficiently learnable when $ζ\geq \tilde Ω(Δ / {\sqrt{d}})$. Experiments on both synthetic and real-world datasets corroborate our theoretical results.

Zhiyuan Fan, Yumeng Wang, Sandeep Polisetty et al.

Large Vision Language Models (LVLMs) excel in various vision-language tasks. Yet, their robustness to visual variations in position, scale, orientation, and context that objects in natural scenes inevitably exhibit due to changes in viewpoint and environment remains largely underexplored. To bridge this gap, we introduce V$^2$R-Bench, a comprehensive benchmark framework for evaluating Visual Variation Robustness of LVLMs, which encompasses automated evaluation dataset generation and principled metrics for thorough robustness assessment. Through extensive evaluation on 21 LVLMs, we reveal a surprising vulnerability to visual variations, in which even advanced models that excel at complex vision-language tasks significantly underperform on simple tasks such as object recognition. Interestingly, these models exhibit a distinct visual position bias that contradicts theories of effective receptive fields, and demonstrate a human-like visual acuity threshold. To identify the source of these vulnerabilities, we present a systematic framework for component-level analysis, featuring a novel visualization approach for aligned visual features. Results show that these vulnerabilities stem from error accumulation in the pipeline architecture and inadequate multimodal alignment. Complementary experiments with synthetic data further demonstrate that these limitations are fundamentally architectural deficiencies, scoring the need for architectural innovations in future LVLM designs.