Author name cluster

Yang Wang 0020

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6 papers

1 author row

ICLR Conference 2025 Conference Paper

Can LLMs Solve Longer Math Word Problems Better?

Xin Xu 0001
Tong Xiao 0004
Zitong Chao
Zhenya Huang
Can Yang 0002
Yang Wang 0020

Math Word Problems (MWPs) play a vital role in assessing the capabilities of Large Language Models (LLMs), yet current research primarily focuses on questions with concise contexts. The impact of longer contexts on mathematical reasoning remains under-explored. This study pioneers the investigation of Context Length Generalizability (CoLeG), which refers to the ability of LLMs to solve MWPs with extended narratives. We introduce Extended Grade-School Math (E-GSM), a collection of MWPs featuring lengthy narratives, and propose two novel metrics to evaluate the efficacy and resilience of LLMs in tackling these problems. Our analysis of existing zero-shot prompting techniques with proprietary LLMs along with open-source LLMs reveals a general deficiency in CoLeG. To alleviate these issues, we propose tailored approaches for different categories of LLMs. For proprietary LLMs, we introduce a new instructional prompt designed to mitigate the impact of long contexts. For open-source LLMs, we develop a novel auxiliary task for fine-tuning to enhance CoLeG. Our comprehensive results demonstrate the effectiveness of our proposed methods, showing improved performance on E-GSM. Additionally, we conduct an in-depth analysis to differentiate the effects of semantic understanding and reasoning efficacy, showing that our methods improves the latter. We also establish the generalizability of our methods across several other MWP benchmarks. Our findings highlight the limitations of current LLMs and offer practical solutions correspondingly, paving the way for further exploration of model generalizability and training methodologies.

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ICML Conference 2025 Conference Paper

UGPhysics: A Comprehensive Benchmark for Undergraduate Physics Reasoning with Large Language Models

Xin Xu 0001
Qiyun Xu
Tong Xiao 0004
Tianhao Chen
Yuchen Yan
Jiaxin Zhang
Shizhe Diao
Can Yang 0002

Large language models (LLMs) have demonstrated remarkable capabilities in solving complex reasoning tasks, particularly in mathematics. However, the domain of physics reasoning presents unique challenges that have received significantly less attention. Existing benchmarks often fall short in evaluating LLMs’ abilities on the breadth and depth of undergraduate-level physics, underscoring the need for a comprehensive evaluation. To fill this gap, we introduce UGPhysics, a large-scale and diverse benchmark specifically designed to evaluate U nder G raduate-level Physics ( UGPhysics ) reasoning with LLMs. UGPhysics includes 5, 520 undergraduate-level physics problems in both English and Chinese across 13 subjects with seven different answer types and four distinct physics reasoning skills, all rigorously screened for data leakage. Additionally, we develop a Model-Assistant Rule-based Judgment ( MARJ ) pipeline specifically tailored for assessing physics problems, ensuring accurate evaluation. Our evaluation of 31 leading LLMs shows that the highest overall accuracy, 49. 8% (achieved by OpenAI-o1-mini), emphasizes the need for models with stronger physics reasoning skills, beyond math abilities. We hope UGPhysics, along with MARJ, will drive future advancements in AI for physics reasoning. Codes and data are available at https: //github. com/YangLabHKUST/UGPhysics.

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ICML Conference 2024 Conference Paper

On the Convergence of Projected Bures-Wasserstein Gradient Descent under Euclidean Strong Convexity

Junyi Fan
Yuxuan Han
Zijian Liu 0003
Jian-Feng Cai 0001
Yang Wang 0020
Zhengyuan Zhou

The Bures-Wasserstein (BW) gradient descent method has gained considerable attention in various domains, including Gaussian barycenter, matrix recovery and variational inference problems, due to its alignment with the Wasserstein geometry of normal distributions. Despite its popularity, existing convergence analysis are often contingent upon specific loss functions, and the exploration of constrained settings within this framework remains limited. In this work, we make an attempt to bridge this gap by providing a general convergence rate guarantee for BW gradient descent when the Euclidean strong convexity of the loss and the constraints is assumed. In an effort to advance practical implementations, we also derive a closed-form solution for the projection onto BW distance-constrained sets, which enables the fast implementation of projected BW gradient descent for problems that arise in the constrained barycenter and distributionally robust optimization literature. Experimental results demonstrate significant improvements in computational efficiency and convergence speed, underscoring the efficacy of our method in practical scenarios.

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ICML Conference 2022 Conference Paper

Private Streaming SCO in ℓ p geometry with Applications in High Dimensional Online Decision Making

Yuxuan Han
Zhicong Liang
Zhipeng Liang
Yang Wang 0020
Yuan Yao 0011
Jiheng Zhang

Differentially private (DP) stochastic convex optimization (SCO) is ubiquitous in trustworthy machine learning algorithm design. This paper studies the DP-SCO problem with streaming data sampled from a distribution and arrives sequentially. We also consider the continual release model where parameters related to private information are updated and released upon each new data. Numerous algorithms have been developed to achieve optimal excess risks in different $\ell_p$ norm geometries, but none of the existing ones can be adapted to the streaming and continual release setting. We propose a private variant of the Frank-Wolfe algorithm with recursive gradients for variance reduction to update and reveal the parameters upon each data. Combined with the adaptive DP analysis, our algorithm achieves the first optimal excess risk in linear time in the case $1<p\leq 2$ and the state-of-the-art excess risk meeting the non-private lower ones when $2<p\leq \infty$. Our algorithm can also be extended to the case $p=1$ to achieve nearly dimension-independent excess risk. While previous variance reduction results on recursive gradient have theoretical guarantee only in the i. i. d. setting, we establish such a guarantee in a non-stationary setting. To demonstrate the virtues of our method, we design the first DP algorithm for high-dimensional generalized linear bandits with logarithmic regret.

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ICML Conference 2021 Conference Paper

Deep Generative Learning via Schrödinger Bridge

Gefei Wang
Yuling Jiao
Qian Xu
Yang Wang 0020
Can Yang 0002

We propose to learn a generative model via entropy interpolation with a Schr{ö}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the Kullback-Leibler divergence. At the population level, this entropy interpolation is characterized via an SDE on [0, 1] with a time-varying drift term. At the sample level, we derive our Schr{ö}dinger Bridge algorithm by plugging the drift term estimated by a deep score estimator and a deep density ratio estimator into the Euler-Maruyama method. Under some mild smoothness assumptions of the target distribution, we prove the consistency of both the score estimator and the density ratio estimator, and then establish the consistency of the proposed Schr{ö}dinger Bridge approach. Our theoretical results guarantee that the distribution learned by our approach converges to the target distribution. Experimental results on multimodal synthetic data and benchmark data support our theoretical findings and indicate that the generative model via Schr{ö}dinger Bridge is comparable with state-of-the-art GANs, suggesting a new formulation of generative learning. We demonstrate its usefulness in image interpolation and image inpainting.

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ICML Conference 2019 Conference Paper

Deep Generative Learning via Variational Gradient Flow

Yuan Gao 0044
Yuling Jiao
Yang Wang 0020
Yao Wang 0003
Can Yang 0002
Shunkang Zhang

We propose a framework to learn deep generative models via \textbf{V}ariational \textbf{Gr}adient Fl\textbf{ow} (VGrow) on probability spaces. The evolving distribution that asymptotically converges to the target distribution is governed by a vector field, which is the negative gradient of the first variation of the $f$-divergence between them. We prove that the evolving distribution coincides with the pushforward distribution through the infinitesimal time composition of residual maps that are perturbations of the identity map along the vector field. The vector field depends on the density ratio of the pushforward distribution and the target distribution, which can be consistently learned from a binary classification problem. Connections of our proposed VGrow method with other popular methods, such as VAE, GAN and flow-based methods, have been established in this framework, gaining new insights of deep generative learning. We also evaluated several commonly used divergences, including Kullback-Leibler, Jensen-Shannon, Jeffreys divergences as well as our newly discovered “logD” divergence which serves as the objective function of the logD-trick GAN. Experimental results on benchmark datasets demonstrate that VGrow can generate high-fidelity images in a stable and efficient manner, achieving competitive performance with state-of-the-art GANs.

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