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Linxin Yang

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6 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

QuadEnhancer: Leveraging Quadratic Transformations to Enhance Deep Neural Networks

Qian Chen
Linxin Yang
Akang Wang
Xiaodong Luo
Yin Zhang

The combination of linear transformations and nonlinear activation functions forms the foundation of most modern deep neural networks, enabling them to approximate highly complex functions. This paper explores the introduction of quadratic transformations to further increase the nonlinearity of the model, with the aim of enhancing the performance of existing architectures. To minimize the additional parameters and computational burden, we propose a lightweight quadratic enhancer that leverages matrix decomposition, weight sharing, and sparsification techniques. This approach introduces only a minimal and negligible increase in parameters and forward computation, while still yielding substantial improvements in model performance. We evaluate the effectiveness of the proposed method across three tasks: text classification, image classification, and fine-tuning large language models (LLMs). In all tasks, our approach demonstrates significant performance gains.

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TMLR Journal 2025 Journal Article

Solving Quadratic Programs via Deep Unrolled Douglas-Rachford Splitting

Jinxin Xiong
Xi Gao
Linxin Yang
Jiang Xue
Xiaodong Luo
Akang Wang

Convex quadratic programs (QPs) are fundamental to numerous applications, including finance, engineering, and energy systems. Among the various methods for solving them, the Douglas-Rachford (DR) splitting algorithm is notable for its robust convergence properties. Concurrently, the emerging field of Learning-to-Optimize offers promising avenues for enhancing algorithmic performance, with algorithm unrolling receiving considerable attention due to its computational efficiency and interpretability. In this work, we propose an approach that unrolls a modified DR splitting algorithm to efficiently learn solutions for convex QPs. Specifically, we introduce a tailored DR splitting algorithm that replaces the computationally expensive linear system-solving step with a simplified gradient-based update, while retaining convergence guarantees. Consequently, we unroll the resulting DR splitting method and present a well-crafted neural network architecture to predict QP solutions. Our method achieves up to 50% reductions in iteration counts and 40% in solve time across benchmarks on both synthetic and real-world QP datasets, demonstrating its scalability and superior performance in enhancing computational efficiency across varying sizes.

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NeurIPS Conference 2024 Conference Paper

On the Power of Small-size Graph Neural Networks for Linear Programming

Qian Li
Tian Ding
Linxin Yang
Minghui Ouyang
Qingjiang Shi
Ruoyu Sun

Graph neural networks (GNNs) have recently emerged as powerful tools for addressing complex optimization problems. It has been theoretically demonstrated that GNNs can universally approximate the solution mapping functions of linear programming (LP) problems. However, these theoretical results typically require GNNs to have large parameter sizes. Conversely, empirical experiments have shown that relatively small GNNs can solve LPs effectively, revealing a significant discrepancy between theoretical predictions and practical observations. In this work, we aim to bridge this gap by providing a theoretical foundation for the effectiveness of small-size GNNs. We prove that polylogarithmic-depth, constant-width GNNs are sufficient to solve packing and covering LPs, two widely used classes of LPs. Our proof leverages the capability of GNNs to simulate a variant of the gradient descent algorithm on a carefully selected potential function. Additionally, we introduce a new GNN architecture, termed GD-Net. Experimental results demonstrate that GD-Net significantly outperforms conventional GNN structures while using fewer parameters.

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ICML Conference 2024 Conference Paper

PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming

Bingheng Li
Linxin Yang
Yupeng Chen
Senmiao Wang
Haitao Mao
Qian Chen
Yao Ma 0001
Akang Wang

Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i) First-order methods (FOMs); (ii) Learning to optimize (L2O). In this work, we propose an FOM-unrolled neural network (NN) called PDHG-Net, and propose a two-stage L2O method to solve large-scale LP problems. The new architecture PDHG-Net is designed by unrolling the recently emerged PDHG method into a neural network, combined with channel-expansion techniques borrowed from graph neural networks. We prove that the proposed PDHG-Net can recover PDHG algorithm, thus can approximate optimal solutions of LP instances with a polynomial number of neurons. We propose a two-stage inference approach: first use PDHG-Net to generate an approximate solution, and then apply PDHG algorithm to further improve the solution. Experiments show that our approach can significantly accelerate LP solving, achieving up to a 3$\times$ speedup compared to FOMs for large-scale LP problems.

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NeurIPS Conference 2024 Conference Paper

SymILO: A Symmetry-Aware Learning Framework for Integer Linear Optimization

Qian Chen
Tianjian Zhang
Linxin Yang
Qingyu Han
Akang Wang
Ruoyu Sun
Xiaodong Luo
Tsung-Hui Chang

Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via supervised learning, with an ILP as the input and an optimal solution as the label. An ILP is symmetric if its variables can be permuted without changing the problem structure, resulting in numerous equivalent and optimal solutions. Randomly selecting an optimal solution as the label can introduce variability in the training data, which may hinder the model from learning stable patterns. In this work, we incorporate the intrinsic symmetry of ILPs and propose a novel training framework called SymILO. Specifically, we modify the learning task by introducing solution permutation along with neural network weights as learnable parameters and then design an alternating algorithm to jointly optimize the loss function. We conduct extensive experiments on ILPs involving different symmetries and the computational results demonstrate that our symmetry-aware approach significantly outperforms three existing methods----achieving $50. 3\\%$, $66. 5\\%$, and $45. 4\\%$ average improvements, respectively.

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ICLR Conference 2023 Conference Paper

A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming

Qingyu Han
Linxin Yang
Qian Chen
Xiang Zhou
Dong Zhang
Akang Wang
Ruoyu Sun 0001
Xiaodong Luo

Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are capable of capturing common patterns across these MILP instances. In this work, we combine ML with optimization and propose a novel predict-and-search framework for efficiently identifying high-quality feasible solutions. Specifically, we first utilize graph neural networks to predict the marginal probability of each variable, and then search for the best feasible solution within a properly defined ball around the predicted solution. We conduct extensive experiments on public datasets, and computational results demonstrate that our proposed framework achieves 51.1% and 9.9% performance improvements to MILP solvers SCIP and Gurobi on primal gaps, respectively.

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