Haoyang Liu

Haoyang Liu, Jie Wang, Boxuan Niu et al.

Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However, existing works often struggle to verify the correctness of the generated optimization models, without checking the rationality of the constraints and variables or the validity of solutions to the generated models. This hampers the subsequent verification and correction steps, and thus it severely hurts the modeling accuracy. To address this challenge, we propose a novel LLM-based framework with Dual-side Verification (Opt-Verifier) from both structure and solution perspectives, thereby improving the modeling accuracy. The structure-side verification ensures that the modeling structure of the generated optimization models aligns with the original problem description, accurately capturing the problem's constraints and requirements. Meanwhile, the solution-side verification interprets and evaluates the solutions' validity, confirming that the optimization models are logically and mathematically sound. Experiments on popular benchmarks demonstrate that our approach achieves over 20\% improvement in accuracy.

Wenyu Mao, Jiancan Wu, Haoyang Liu et al.

Graph out-of-distribution (OOD) generalization remains a major challenge in graph learning since graph neural networks (GNNs) often suffer from severe performance degradation under distribution shifts. Invariant learning, aiming to extract invariant features across varied distributions, has recently emerged as a promising approach for OOD generation. Despite the great success of invariant learning in OOD problems for Euclidean data (i.e., images), the exploration within graph data remains constrained by the complex nature of graphs. Existing studies, such as data augmentation or causal intervention, either suffer from disruptions to invariance during the graph manipulation process or face reliability issues due to a lack of supervised signals for causal parts. In this work, we propose a novel framework, called Invariant Graph Learning based on Information bottleneck theory (InfoIGL), to extract the invariant features of graphs and enhance models' generalization ability to unseen distributions. Specifically, InfoIGL introduces a redundancy filter to compress task-irrelevant information related to environmental factors. Cooperating with our designed multi-level contrastive learning, we maximize the mutual information among graphs of the same class in the downstream classification tasks, preserving invariant features for prediction to a great extent. An appealing feature of InfoIGL is its strong generalization ability without depending on supervised signal of invariance. Experiments on both synthetic and real-world datasets demonstrate that our method achieves state-of-the-art performance under OOD generalization for graph classification tasks. The source code is available at https://github.com/maowenyu-11/InfoIGL.

Haoyang Liu, Keqin Liu, Qing Zhao

We consider decentralized restless multi-armed bandit problems with unknown dynamics and multiple players. The reward state of each arm transits according to an unknown Markovian rule when it is played and evolves according to an arbitrary unknown random process when it is passive. Players activating the same arm at the same time collide and suffer from reward loss. The objective is to maximize the long-term reward by designing a decentralized arm selection policy to address unknown reward models and collisions among players. A decentralized policy is constructed that achieves a regret with logarithmic order when an arbitrary nontrivial bound on certain system parameters is known. When no knowledge about the system is available, we extend the policy to achieve a regret arbitrarily close to the logarithmic order. The result finds applications in communication networks, financial investment, and industrial engineering.

Peiyan Zhang, Haoyang Liu, Chaozhuo Li et al.

Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal robust model will probably behave similarly to the oracle (e.g., the human users), thus a good evaluation protocol is probably to evaluate the models' behaviors in comparison to the oracle. In this paper, we introduce a new robustness measurement that directly measures the image classification model's performance compared with a surrogate oracle (i.e., a foundation model). Besides, we design a simple method that can accomplish the evaluation beyond the scope of the benchmarks. Our method extends the image datasets with new samples that are sufficiently perturbed to be distinct from the ones in the original sets, but are still bounded within the same image-label structure the original test image represents, constrained by a foundation model pretrained with a large amount of samples. As a result, our new method will offer us a new way to evaluate the models' robustness performance, free of limitations of fixed benchmarks or constrained perturbations, although scoped by the power of the oracle. In addition to the evaluation results, we also leverage our generated data to understand the behaviors of the model and our new evaluation strategies.

Tianle Pu, Jianing Li, Yingying Gao et al.

Mixed-Integer Linear Programming (MILP) is a cornerstone of combinatorial optimization, yet solving large-scale instances remains a significant computational challenge. Recently, Graph Neural Networks (GNNs) have shown promise in accelerating MILP solvers by predicting high-quality solutions. However, we identify that existing methods misalign with the intrinsic structure of MILP problems at two levels. At the leaning objective level, the Binary Cross-Entropy (BCE) loss treats variables independently, neglecting their relative priority and yielding plausible logits. At the model architecture level, standard GNN message passing inherently smooths the representations across variables, missing the natural competitive relationships within constraints. To address these challenges, we propose CoCo-MILP, which explicitly models inter-variable Contrast and intra-constraint Competition for advanced MILP solution prediction. At the objective level, CoCo-MILP introduces the Inter-Variable Contrastive Loss (VCL), which explicitly maximizes the embedding margin between variables assigned one versus zero. At the architectural level, we design an Intra-Constraint Competitive GNN layer that, instead of homogenizing features, learns to differentiate representations of competing variables within a constraint, capturing their exclusionary nature. Experimental results on standard benchmarks demonstrate that CoCo-MILP significantly outperforms existing learning-based approaches, reducing the solution gap by up to 68.12% compared to traditional solvers. Our code is available at https://github.com/happypu326/CoCo-MILP.

Haoyang Liu, Maheep Chaudhary, Haohan Wang

The trustworthiness of machine learning has emerged as a critical topic in the field, encompassing various applications and research areas such as robustness, security, interpretability, and fairness. The last decade saw the development of numerous methods addressing these challenges. In this survey, we systematically review these advancements from a data-centric perspective, highlighting the shortcomings of traditional empirical risk minimization (ERM) training in handling challenges posed by the data. Interestingly, we observe a convergence of these methods, despite being developed independently across trustworthy machine learning subfields. Pearl's hierarchy of causality offers a unifying framework for these techniques. Accordingly, this survey presents the background of trustworthy machine learning development using a unified set of concepts, connects this language to Pearl's causal hierarchy, and finally discusses methods explicitly inspired by causality literature. We provide a unified language with mathematical vocabulary to link these methods across robustness, adversarial robustness, interpretability, and fairness, fostering a more cohesive understanding of the field. Further, we explore the trustworthiness of large pretrained models. After summarizing dominant techniques like fine-tuning, parameter-efficient fine-tuning, prompting, and reinforcement learning with human feedback, we draw connections between them and the standard ERM. This connection allows us to build upon the principled understanding of trustworthy methods, extending it to these new techniques in large pretrained models, paving the way for future methods. Existing methods under this perspective are also reviewed. Lastly, we offer a brief summary of the applications of these methods and discuss potential future aspects related to our survey. For more information, please visit http://trustai.one.

Haoyang Liu, Yufei Kuang, Jie Wang et al.

Machine learning has been successfully applied to improve the efficiency of Mixed-Integer Linear Programming (MILP) solvers. However, the learning-based solvers often suffer from severe performance degradation on unseen MILP instances -- especially on large-scale instances from a perturbed environment -- due to the limited diversity of training distributions. To tackle this problem, we propose a novel approach, which is called Adversarial Instance Augmentation and does not require to know the problem type for new instance generation, to promote data diversity for learning-based branching modules in the branch-and-bound (B&B) Solvers (AdaSolver). We use the bipartite graph representations for MILP instances and obtain various perturbed instances to regularize the solver by augmenting the graph structures with a learned augmentation policy. The major technical contribution of AdaSolver is that we formulate the non-differentiable instance augmentation as a contextual bandit problem and adversarially train the learning-based solver and augmentation policy, enabling efficient gradient-based training of the augmentation policy. To the best of our knowledge, AdaSolver is the first general and effective framework for understanding and improving the generalization of both imitation-learning-based (IL-based) and reinforcement-learning-based (RL-based) B&B solvers. Extensive experiments demonstrate that by producing various augmented instances, AdaSolver leads to a remarkable efficiency improvement across various distributions.

Lin Liu, Xinxin Fan, Haoyang Liu et al.

Rigid pre-registration involving local-global matching or other large deformation scenarios is crucial. Current popular methods rely on unsupervised learning based on grayscale similarity, but under circumstances where different poses lead to varying tissue structures, or where image quality is poor, these methods tend to exhibit instability and inaccuracies. In this study, we propose a novel method for medical image registration based on arbitrary voxel point of interest matching, called query point quizzer (QUIZ). QUIZ focuses on the correspondence between local-global matching points, specifically employing CNN for feature extraction and utilizing the Transformer architecture for global point matching queries, followed by applying average displacement for local image rigid transformation. We have validated this approach on a large deformation dataset of cervical cancer patients, with results indicating substantially smaller deviations compared to state-of-the-art methods. Remarkably, even for cross-modality subjects, it achieves results surpassing the current state-of-the-art.

Haoyang Liu, Yijiang Li, Tiancheng Xing et al.

Dataset Distillation (DD) aims to generate a compact synthetic dataset that enables models to achieve performance comparable to training on the full large dataset, significantly reducing computational costs. Drawing from optimal transport theory, we introduce WMDD (Wasserstein Metric-based Dataset Distillation), a straightforward yet powerful method that employs the Wasserstein metric to enhance distribution matching. We compute the Wasserstein barycenter of features from a pretrained classifier to capture essential characteristics of the original data distribution. By optimizing synthetic data to align with this barycenter in feature space and leveraging per-class BatchNorm statistics to preserve intra-class variations, WMDD maintains the efficiency of distribution matching approaches while achieving state-of-the-art results across various high-resolution datasets. Our extensive experiments demonstrate WMDD's effectiveness and adaptability, highlighting its potential for advancing machine learning applications at scale.

Thomson Yen, Julian Poeltl, Harshith Srinivas Gear et al.

LLM agents are increasingly expected to carry out end-to-end workflows, producing complete artifacts from high-level user instructions. To meet enterprise needs, frontier AI labs have developed agents that can construct entire spreadsheets from scratch. This is especially relevant in finance, where core workflows such as financial modeling, forecasting, and scenario analysis are commonly conducted through spreadsheets. Yet, existing spreadsheet benchmarks do not measure this advanced capability, focusing instead on question-answering or single-formula edits. To address this gap, we provide one of the first evaluations of agents on end-to-end spreadsheet tasks, focusing on economically critical financial workflows such as modeling and scenario analysis. Since deliverables therein are routinely reviewed and revised by multiple stakeholders, judging their quality necessarily involves high-level criteria such as readability or ease of modification. To reflect the multidimensional nature of solution quality, we develop an evaluation taxonomy comprising three dimensions: Accuracy, Formula, and Format, each comprising fine-grained criteria that reflect professional standards. The Claude family leads the benchmark and produces the most professional-looking outputs in our qualitative review, but even the strongest agents frequently fall short of professional finance standards and degrade sharply as the difficulty increases beyond a few chained calculations. This suggests that current agents are not yet able to reliably produce professional-quality spreadsheets at the level of complexity real-world workflows demand.

Tianle Pu, Zijie Geng, Haoyang Liu et al.

Mixed-Integer Linear Programming (MILP) is a fundamental and powerful framework for modeling complex optimization problems across diverse domains. Recently, learning-based methods have shown great promise in accelerating MILP solvers by predicting high-quality solutions. However, most existing approaches are developed and evaluated in single-domain settings, limiting their ability to generalize to unseen problem distributions. This limitation poses a major obstacle to building scalable and general-purpose learning-based solvers. To address this challenge, we introduce RoME, a domain-Robust Mixture-of-Experts framework for predicting MILP solutions across domains. RoME dynamically routes problem instances to specialized experts based on learned task embeddings. The model is trained using a two-level distributionally robust optimization strategy: inter-domain to mitigate global shifts across domains, and intra-domain to enhance local robustness by introducing perturbations on task embeddings. We reveal that cross-domain training not only enhances the model's generalization capability to unseen domains but also improves performance within each individual domain by encouraging the model to capture more general intrinsic combinatorial patterns. Specifically, a single RoME model trained on three domains achieves an average improvement of 67.7% then evaluated on five diverse domains. We further test the pretrained model on MIPLIB in a zero-shot setting, demonstrating its ability to deliver measurable performance gains on challenging real-world instances where existing learning-based approaches often struggle to generalize.

Eric Xue, Yijiang Li, Haoyang Liu et al.

Dataset distillation (DD) allows datasets to be distilled to fractions of their original size while preserving the rich distributional information, so that models trained on the distilled datasets can achieve a comparable accuracy while saving significant computational loads. Recent research in this area has been focusing on improving the accuracy of models trained on distilled datasets. In this paper, we aim to explore a new perspective of DD. We study how to embed adversarial robustness in distilled datasets, so that models trained on these datasets maintain the high accuracy and meanwhile acquire better adversarial robustness. We propose a new method that achieves this goal by incorporating curvature regularization into the distillation process with much less computational overhead than standard adversarial training. Extensive empirical experiments suggest that our method not only outperforms standard adversarial training on both accuracy and robustness with less computation overhead but is also capable of generating robust distilled datasets that can withstand various adversarial attacks. Our implementation is available at: https://github.com/yumozi/GUARD.

Tong Zhang, Haoyang Liu, Peiyan Zhang et al.

In the field of computer graphics, the use of vector graphics, particularly Scalable Vector Graphics (SVG), represents a notable development from traditional pixel-based imagery. SVGs, with their XML-based format, are distinct in their ability to directly and explicitly represent visual elements such as shape, color, and path. This direct representation facilitates a more accurate and logical depiction of graphical elements, enhancing reasoning and interpretability. Recognizing the potential of SVGs, the machine learning community has introduced multiple methods for image vectorization. However, transforming images into SVG format while retaining the relational properties and context of the original scene remains a key challenge. Most vectorization methods often yield SVGs that are overly complex and not easily interpretable. In response to this challenge, we introduce our method, Simple-SVG-Generation (S\textsuperscript{2}VG\textsuperscript{2}). Our method focuses on producing SVGs that are both accurate and simple, aligning with human readability and understanding. With simple images, we evaluate our method with reasoning tasks together with advanced language models, the results show a clear improvement over previous SVG generation methods. We also conducted surveys for human evaluation on the readability of our generated SVGs, the results also favor our methods.

Haoyang Liu, Jie Wang, Yuyang Cai et al.

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-the-art, achieving over 10\% improvements on the challenging benchmarks. The code is released at https://github.com/MIRALab-USTC/OptiTree/tree/main.

Haoyang Liu

The project leverages advanced machine and deep learning techniques to address the challenge of emotion recognition by focusing on non-facial cues, specifically hands, body gestures, and gestures. Traditional emotion recognition systems mainly rely on facial expression analysis and often ignore the rich emotional information conveyed through body language. To bridge this gap, this method leverages the Aff-Wild2 and DFEW databases to train and evaluate a model capable of recognizing seven basic emotions (angry, disgust, fear, happiness, sadness, surprise, and neutral) and estimating valence and continuous scales wakeup descriptor. Leverage OpenPose for pose estimation to extract detailed body posture and posture features from images and videos. These features serve as input to state-of-the-art neural network architectures, including ResNet, and ANN for emotion classification, and fully connected layers for valence arousal regression analysis. This bifurcation strategy can solve classification and regression problems in the field of emotion recognition. The project aims to contribute to the field of affective computing by enhancing the ability of machines to interpret and respond to human emotions in a more comprehensive and nuanced way. By integrating multimodal data and cutting-edge computational models, I aspire to develop a system that not only enriches human-computer interaction but also has potential applications in areas as diverse as mental health support, educational technology, and autonomous vehicle systems.

Zhezheng Hao, Hong Wang, Haoyang Liu et al.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent \coloredtext{entropy collapse}, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

Haoyang Liu, Yijiang Li, Haohan Wang

Gene expression analysis holds the key to many biomedical discoveries, yet extracting insights from raw transcriptomic data remains formidable due to the complexity of multiple large, semi-structured files and the need for extensive domain expertise. Current automation approaches are often limited by either inflexible workflows that break down in edge cases or by fully autonomous agents that lack the necessary precision for rigorous scientific inquiry. GenoMAS charts a different course by presenting a team of LLM-based scientists that integrates the reliability of structured workflows with the adaptability of autonomous agents. GenoMAS orchestrates six specialized LLM agents through typed message-passing protocols, each contributing complementary strengths to a shared analytic canvas. At the heart of GenoMAS lies a guided-planning framework: programming agents unfold high-level task guidelines into Action Units and, at each juncture, elect to advance, revise, bypass, or backtrack, thereby maintaining logical coherence while bending gracefully to the idiosyncrasies of genomic data. On the GenoTEX benchmark, GenoMAS reaches a Composite Similarity Correlation of 89.13% for data preprocessing and an F$_1$ of 60.48% for gene identification, surpassing the best prior art by 10.61% and 16.85% respectively. Beyond metrics, GenoMAS surfaces biologically plausible gene-phenotype associations corroborated by the literature, all while adjusting for latent confounders. Code is available at https://github.com/Liu-Hy/GenoMAS.

Haoyang Liu, Aditya Singh, Yijiang Li et al.

Enhancing the robustness of deep learning models, particularly in the realm of vision transformers (ViTs), is crucial for their real-world deployment. In this work, we provide a finetuning approach to enhance the robustness of vision transformers inspired by the concept of nullspace from linear algebra. Our investigation centers on whether a vision transformer can exhibit resilience to input variations akin to the nullspace property in linear mappings, which would imply that perturbations sampled from this nullspace do not influence the model's output when added to the input. We start from the observation that many existing ViTs satisfy this property because their patch embedding layer has a non-trivial nullspace. Then, we extend the notion of nullspace to nonlinear settings and demonstrate that it is possible to synthesize approximate nullspace elements for ViT's encoder blocks through optimization. Finally, we propose a finetuning strategy for ViTs wherein we augment the training data with synthesized approximate nullspace noise. We find that our finetuning approach significantly improves the models' robustness to both adversarial and natural image perturbations.\footnote{Code is available at: https://github.com/Liu-Hy/ns-vit.

Ruicheng Ao, Hongyu Chen, Haoyang Liu et al.

We study semi-supervised stochastic optimization when labeled data is scarce but predictions from pre-trained models are available. PPI and SVRG both reduce variance through control variates -- PPI uses predictions, SVRG uses reference gradients. We show they are mathematically equivalent and develop PPI-SVRG, which combines both. Our convergence bound decomposes into the standard SVRG rate plus an error floor from prediction uncertainty. The rate depends only on loss geometry; predictions affect only the neighborhood size. When predictions are perfect, we recover SVRG exactly. When predictions degrade, convergence remains stable but reaches a larger neighborhood. Experiments confirm the theory: PPI-SVRG reduces MSE by 43--52\% under label scarcity on mean estimation benchmarks and improves test accuracy by 2.7--2.9 percentage points on MNIST with only 10\% labeled data.

Haoyang Liu, Shuyu Chen, Ye Zhang et al.

Recent advancements in machine learning have significantly improved the identification of disease-associated genes from gene expression datasets. However, these processes often require extensive expertise and manual effort, limiting their scalability. Large Language Model (LLM)-based agents have shown promise in automating these tasks due to their increasing problem-solving abilities. To support the evaluation and development of such methods, we introduce GenoTEX, a benchmark dataset for the automated analysis of gene expression data. GenoTEX provides analysis code and results for solving a wide range of gene-trait association problems, encompassing dataset selection, preprocessing, and statistical analysis, in a pipeline that follows computational genomics standards. The benchmark includes expert-curated annotations from bioinformaticians to ensure accuracy and reliability. To provide baselines for these tasks, we present GenoAgent, a team of LLM-based agents that adopt a multi-step programming workflow with flexible self-correction, to collaboratively analyze gene expression datasets. Our experiments demonstrate the potential of LLM-based methods in analyzing genomic data, while error analysis highlights the challenges and areas for future improvement. We propose GenoTEX as a promising resource for benchmarking and enhancing automated methods for gene expression data analysis. The benchmark is available at https://github.com/Liu-Hy/GenoTEX.

Haoyang Liu, M. Janina Sarol, Halil Kilicoglu

We propose a cascade of neural models that performs sentence classification, phrase recognition, and triple extraction to automatically structure the scholarly contributions of NLP publications. To identify the most important contribution sentences in a paper, we used a BERT-based classifier with positional features (Subtask 1). A BERT-CRF model was used to recognize and characterize relevant phrases in contribution sentences (Subtask 2). We categorized the triples into several types based on whether and how their elements were expressed in text, and addressed each type using separate BERT-based classifiers as well as rules (Subtask 3). Our system was officially ranked second in Phase 1 evaluation and first in both parts of Phase 2 evaluation. After fixing a submission error in Pharse 1, our approach yields the best results overall. In this paper, in addition to a system description, we also provide further analysis of our results, highlighting its strengths and limitations. We make our code publicly available at https://github.com/Liu-Hy/nlp-contrib-graph.

Haoyang Liu, Jie Wang, Wanbo Zhang et al.

Mixed-integer linear programming (MILP) is one of the most popular mathematical formulations with numerous applications. In practice, improving the performance of MILP solvers often requires a large amount of high-quality data, which can be challenging to collect. Researchers thus turn to generation techniques to generate additional MILP instances. However, existing approaches do not take into account specific block structures -- which are closely related to the problem formulations -- in the constraint coefficient matrices (CCMs) of MILPs. Consequently, they are prone to generate computationally trivial or infeasible instances due to the disruptions of block structures and thus problem formulations. To address this challenge, we propose a novel MILP generation framework, called Block Structure Decomposition (MILP-StuDio), to generate high-quality instances by preserving the block structures. Specifically, MILP-StuDio begins by identifying the blocks in CCMs and decomposing the instances into block units, which serve as the building blocks of MILP instances. We then design three operators to construct new instances by removing, substituting, and appending block units in the original instances, enabling us to generate instances with flexible sizes. An appealing feature of MILP-StuDio is its strong ability to preserve the feasibility and computational hardness of the generated instances. Experiments on the commonly-used benchmarks demonstrate that using instances generated by MILP-StuDio is able to significantly reduce over 10% of the solving time for learning-based solvers.

Haoyang Liu, Jie Wang, Zijie Geng et al.

Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the problem dimension. Then, they solve the reduced problem to obtain the final solutions. However, directly fixing variable values can lead to low-quality solutions or even infeasible reduced problems if the predicted solution is not accurate enough. To address this challenge, we propose an Alternating prediction-correction neural solving framework (Apollo-MILP) that can identify and select accurate and reliable predicted values to fix. In each iteration, Apollo-MILP conducts a prediction step for the unfixed variables, followed by a correction step to obtain an improved solution (called reference solution) through a trust-region search. By incorporating the predicted and reference solutions, we introduce a novel Uncertainty-based Error upper BOund (UEBO) to evaluate the uncertainty of the predicted values and fix those with high confidence. A notable feature of Apollo-MILP is the superior ability for problem reduction while preserving optimality, leading to high-quality final solutions. Experiments on commonly used benchmarks demonstrate that our proposed Apollo-MILP significantly outperforms other ML-based approaches in terms of solution quality, achieving over a 50% reduction in the solution gap.

Huanshuo Dong, Hong Wang, Haoyang Liu et al.

Recent advancements in data-driven approaches, such as Neural Operator (NO), have demonstrated their effectiveness in reducing the solving time of Partial Differential Equations (PDEs). However, one major challenge faced by these approaches is the requirement for a large amount of high-precision training data, which needs significant computational costs during the generation process. To address this challenge, we propose a novel PDE dataset generation algorithm, namely Differential Operator Action in Solution space (DiffOAS), which speeds up the data generation process and enhances the precision of the generated data simultaneously. Specifically, DiffOAS obtains a few basic PDE solutions and then combines them to get solutions. It applies differential operators on these solutions, a process we call 'operator action', to efficiently generate precise PDE data points. Theoretical analysis shows that the time complexity of DiffOAS method is one order lower than the existing generation method. Experimental results show that DiffOAS accelerates the generation of large-scale datasets with 10,000 instances by 300 times. Even with just 5% of the generation time, NO trained on the data generated by DiffOAS exhibits comparable performance to that using the existing generation method, which highlights the efficiency of DiffOAS.

Haoyang Liu, Yijiang Li, Jinglin Jian et al.

Machine learning has emerged as a powerful tool for scientific discovery, enabling researchers to extract meaningful insights from complex datasets. For instance, it has facilitated the identification of disease-predictive genes from gene expression data, significantly advancing healthcare. However, the traditional process for analyzing such datasets demands substantial human effort and expertise for the data selection, processing, and analysis. To address this challenge, we introduce a novel framework, a Team of AI-made Scientists (TAIS), designed to streamline the scientific discovery pipeline. TAIS comprises simulated roles, including a project manager, data engineer, and domain expert, each represented by a Large Language Model (LLM). These roles collaborate to replicate the tasks typically performed by data scientists, with a specific focus on identifying disease-predictive genes. Furthermore, we have curated a benchmark dataset to assess TAIS's effectiveness in gene identification, demonstrating our system's potential to significantly enhance the efficiency and scope of scientific exploration. Our findings represent a solid step towards automating scientific discovery through large language models.

Xijun Li, Fangzhou Zhu, Hui-Ling Zhen et al.

In an era of digital ubiquity, efficient resource management and decision-making are paramount across numerous industries. To this end, we present a comprehensive study on the integration of machine learning (ML) techniques into Huawei Cloud's OptVerse AI Solver, which aims to mitigate the scarcity of real-world mathematical programming instances, and to surpass the capabilities of traditional optimization techniques. We showcase our methods for generating complex SAT and MILP instances utilizing generative models that mirror multifaceted structures of real-world problem. Furthermore, we introduce a training framework leveraging augmentation policies to maintain solvers' utility in dynamic environments. Besides the data generation and augmentation, our proposed approaches also include novel ML-driven policies for personalized solver strategies, with an emphasis on applications like graph convolutional networks for initial basis selection and reinforcement learning for advanced presolving and cut selection. Additionally, we detail the incorporation of state-of-the-art parameter tuning algorithms which markedly elevate solver performance. Compared with traditional solvers such as Cplex and SCIP, our ML-augmented OptVerse AI Solver demonstrates superior speed and precision across both established benchmarks and real-world scenarios, reinforcing the practical imperative and effectiveness of machine learning techniques in mathematical programming solvers.

Hong Wang, Jie Wang, Minghao Ma et al.

Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Traditional parameter selection approaches often define fixed constants for specific scenarios. However, they rely on domain expertise and fail to consider the instance-wise features for individual problems, limiting their performance. In contrast, machine learning (ML) approaches, though promising, are hindered by high inference costs and limited interpretability. To combine the strengths of both approaches, we propose a symbolic discovery framework-namely, Symbolic Matrix Preconditioning (SymMaP)-to learn efficient symbolic expressions for preconditioning parameters. Specifically, we employ a neural network to search the high-dimensional discrete space for expressions that can accurately predict the optimal parameters. The learned expression allows for high inference efficiency and excellent interpretability (expressed in concise symbolic formulas), making it simple and reliable for deployment. Experimental results show that SymMaP consistently outperforms traditional strategies across various benchmarks.

Wenyu Mao, Haoyang Liu, Zhao Liu et al.

Memory systems are crucial to personalized LLMs by mitigating the context window limitation in capturing long-term user-LLM conversations. Typically, such systems leverage multiple agents to handle multi-granular memory construction and personalized memory retrieval tasks. To optimize the system, existing methods focus on specializing agents on their local tasks independently via prompt engineering or fine-tuning. However, they overlook cross-agent collaboration, where independent optimization on local agents hardly guarantees the global system performance. To address this issue, we propose a Collaborative Reinforcement Learning Framework for Multi-Agent Memory Systems (CoMAM), jointly optimizing local agents to facilitate collaboration. Specifically, we regularize agents' execution as a sequential Markov decision process (MDP) to embed inter-agent dependencies into the state transition, yielding both local task rewards (e.g., information coverage for memory construction) and global rewards (i.e., query-answer accuracy). Then, we quantify each agent's contribution via group-level ranking consistency between local and global rewards, treating them as adaptive weights to assign global credit and integrate local-global rewards. Each agent is optimized by these integrated rewards, aligning local improvements with the global performance. Experiments show CoMAM outperforms leading memory systems, validating the efficacy of our proposed collaborative reinforcement learning for joint optimization.

Zhijing Hu, Yufan Deng, Haoyang Liu et al.

Automating the translation of Operations Research (OR) problems from natural language to executable models is a critical challenge. While Large Language Models (LLMs) have shown promise in linear tasks, they suffer from severe performance degradation in real-world nonlinear scenarios due to semantic misalignment between mathematical formulations and solver codes, as well as unstable information extraction. In this study, we introduce NED-Tree, a systematic framework designed to bridge the semantic gap. NED-Tree employs (a) a sentence-by-sentence extraction strategy to ensure robust parameter mapping and traceability; and (b) a recursive tree-based structure that adaptively decomposes complex nonlinear terms into solver-compatible sub-elements. Additionally, we present NEXTOR, a novel benchmark specifically designed for complex nonlinear, extensive-constraint OR problems. Experiments across 10 benchmarks demonstrate that NED-Tree establishes a new state-of-the-art with 72.51% average accuracy, NED-Tree is the first framework that drives LLMs to resolve nonlinear modeling difficulties through element decomposition, achieving alignment between modeling semantics and code semantics. The NED-Tree framework and benchmark are accessible in the anonymous repository https://anonymous.4open.science/r/NORA-NEXTOR.

Yiyi Wang, Jian'an Zhang, Hongyi Duan et al.

State Space Models (SSMs), particularly recent selective variants like Mamba, have emerged as a leading architecture for sequence modeling, challenging the dominance of Transformers. However, the success of these state-of-the-art models largely relies on heuristically designed selective mechanisms, which lack a rigorous first-principle derivation. This theoretical gap raises questions about their optimality and robustness against spurious correlations. To address this, we introduce the Principle of Predictive Sufficiency, a novel information-theoretic criterion stipulating that an ideal hidden state should be a minimal sufficient statistic of the past for predicting the future. Based on this principle, we propose the Minimal Predictive Sufficiency State Space Model (MPS-SSM), a new framework where the selective mechanism is guided by optimizing an objective function derived from our principle. This approach encourages the model to maximally compress historical information without losing predictive power, thereby learning to ignore non-causal noise and spurious patterns. Extensive experiments on a wide range of benchmark datasets demonstrate that MPS-SSM not only achieves state-of-the-art performance, significantly outperforming existing models in long-term forecasting and noisy scenarios, but also exhibits superior robustness. Furthermore, we show that the MPS principle can be extended as a general regularization framework to enhance other popular architectures, highlighting its broad potential.

Hongyi Duan, Haoyang Liu, Jian'an Zhang et al.

We present a JIT PL semantics for ReLU-type networks that compiles models into a guarded CPWL transducer with shared guards. The system adds hyperplanes only when operands are affine on the current cell, maintains global lower/upper envelopes, and uses a budgeted branch-and-bound. We obtain anytime soundness, exactness on fully refined cells, monotone progress, guard-linear complexity (avoiding global $\binom{k}{2}$), dominance pruning, and decidability under finite refinement. The shared carrier supports region extraction, decision complexes, Jacobians, exact/certified Lipschitz, LP/SOCP robustness, and maximal causal influence. A minimal prototype returns certificates or counterexamples with cost proportional to visited subdomains.

Xiaolin Yan, Yangxing Liu, Jiazhang Zheng et al.

Large language models (LLMs) have recently achieved significant advances in reasoning and demonstrated their advantages in solving challenging problems. Yet, their effectiveness in the semiconductor display industry remains limited due to a lack of domain-specific training and expertise. To bridge this gap, we present X-Intelligence 3.0, the first high-performance reasoning model specifically developed for the semiconductor display industry. This model is designed to deliver expert-level understanding and reasoning for the industry's complex challenges. Leveraging a carefully curated industry knowledge base, the model undergoes supervised fine-tuning and reinforcement learning to enhance its reasoning and comprehension capabilities. To further accelerate development, we implemented an automated evaluation framework that simulates expert-level assessments. We also integrated a domain-specific retrieval-augmented generation (RAG) mechanism, resulting in notable performance gains on benchmark datasets. Despite its relatively compact size of 32 billion parameters, X-Intelligence 3.0 outperforms SOTA DeepSeek-R1-671B across multiple evaluations. This demonstrates its exceptional efficiency and establishes it as a powerful solution to the longstanding reasoning challenges faced by the semiconductor display industry.

Hongyu Liu, Haoyang Liu, Yufei Kuang et al.

Combinatorial optimization (CO) is one of the most fundamental mathematical models in real-world applications. Traditional CO solvers, such as Branch-and-Bound (B&B) solvers, heavily rely on expert-designed heuristics, which are reliable but require substantial manual tuning. Recent studies have leveraged deep learning (DL) models as an alternative to capture rich feature patterns for improved performance on GPU machines. Nonetheless, the drawbacks of high training and inference costs, as well as limited interpretability, severely hinder the adoption of DL methods in real-world applications. To address these challenges, we propose a novel deep symbolic optimization learning framework that combines their advantages. Specifically, we focus on the node selection module within B&B solvers -- namely, deep symbolic optimization for node selection (Dso4NS). With data-driven approaches, Dso4NS guides the search for mathematical expressions within the high-dimensional discrete symbolic space and then incorporates the highest-performing mathematical expressions into a solver. The data-driven model captures the rich feature information in the input data and generates symbolic expressions, while the expressions deployed in solvers enable fast inference with high interpretability. Experiments demonstrate the effectiveness of Dso4NS in learning high-quality expressions, outperforming existing approaches on a CPU machine. Encouragingly, the learned CPU-based policies consistently achieve performance comparable to state-of-the-art GPU-based approaches.

Haoyang Liu

The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$ grows to $\infty$ in a fixed ratio $p/n\rightarrow δ$. We propose a set of equations that exactly characterizes the asymptotic behavior of support vector machine. In particular, we give exact formulas for (1) the variability of the optimal coefficients, (2) the proportion of data points lying on the margin boundary (i.e. number of support vectors), (3) the final objective function value, and (4) the expected misclassification error on new data points, which in particular implies the exact formula for the optimal tuning parameter given a data generating mechanism. We first establish these formulas in the case where the label $y\in\{+1,-1\}$ is independent of the feature $x$. Then the results are generalized to the case where the label $y\in\{+1,-1\}$ is allowed to have a general dependence on the feature $x$ through a linear combination $a_0^Tx$. These formulas for the non-smooth hinge loss are analogous to the recent results in \citep{sur2018modern} for smooth logistic loss. Our approach is based on heuristic leave-one-out calculations.

Haoyang Liu, Rina Foygel Barber

Iterative thresholding algorithms seek to optimize a differentiable objective function over a sparsity or rank constraint by alternating between gradient steps that reduce the objective, and thresholding steps that enforce the constraint. This work examines the choice of the thresholding operator, and asks whether it is possible to achieve stronger guarantees than what is possible with hard thresholding. We develop the notion of relative concavity of a thresholding operator, a quantity that characterizes the worst-case convergence performance of any thresholding operator on the target optimization problem. Surprisingly, we find that commonly used thresholding operators, such as hard thresholding and soft thresholding, are suboptimal in terms of worst-case convergence guarantees. Instead, a general class of thresholding operators, lying between hard thresholding and soft thresholding, is shown to be optimal with the strongest possible convergence guarantee among all thresholding operators. Examples of this general class includes $\ell_q$ thresholding with appropriate choices of $q$, and a newly defined {\em reciprocal thresholding} operator. We also investigate the implications of the improved optimization guarantee in the statistical setting of sparse linear regression, and show that this new class of thresholding operators attain the optimal rate for computationally efficient estimators, matching the Lasso.