Qingfu Zhang

Fu Luo, Xi Lin, Fei Liu et al.

Neural combinatorial optimization (NCO) is a promising learning-based approach for solving challenging combinatorial optimization problems without specialized algorithm design by experts. However, most constructive NCO methods cannot solve problems with large-scale instance sizes, which significantly diminishes their usefulness for real-world applications. In this work, we propose a novel Light Encoder and Heavy Decoder (LEHD) model with a strong generalization ability to address this critical issue. The LEHD model can learn to dynamically capture the relationships between all available nodes of varying sizes, which is beneficial for model generalization to problems of various scales. Moreover, we develop a data-efficient training scheme and a flexible solution construction mechanism for the proposed LEHD model. By training on small-scale problem instances, the LEHD model can generate nearly optimal solutions for the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 1000 nodes, and also generalizes well to solve real-world TSPLib and CVRPLib problems. These results confirm our proposed LEHD model can significantly improve the state-of-the-art performance for constructive NCO. The code is available at https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/LEHD.

Fei Liu, Xi Lin, Zhenkun Wang et al.

Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the search operators need a carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and the learned operators might not generalize well on new problems. To tackle the above challenges, this work investigates a novel approach that leverages the powerful large language model (LLM) to design MOEA operators. With proper prompt engineering, we successfully let a general LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D) in a zero-shot manner. In addition, by learning from the LLM behavior, we further design an explicit white-box operator with randomness and propose a new version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on different test benchmarks show that our proposed method can achieve competitive performance with widely used MOEAs. It is also promising to see the operator only learned from a few instances can have robust generalization performance on unseen problems with quite different patterns and settings. The results reveal the potential benefits of using pre-trained LLMs in the design of MOEAs.To foster reproducibility and accessibility, the source code is https://github.com/FeiLiu36/LLM4MOEA.

Xi Lin, Zhiyuan Yang, Qingfu Zhang

Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic methods have been proposed to tackle different MOCO problems over the past decades. In this work, we generalize the idea of neural combinatorial optimization, and develop a learning-based approach to approximate the whole Pareto set for a given MOCO problem without further search procedure. We propose a single preference-conditioned model to directly generate approximate Pareto solutions for any trade-off preference, and design an efficient multiobjective reinforcement learning algorithm to train this model. Our proposed method can be treated as a learning-based extension for the widely-used decomposition-based multiobjective evolutionary algorithm (MOEA/D). It uses a single model to accommodate all the possible preferences, whereas other methods use a finite number of solutions to approximate the Pareto set. Experimental results show that our proposed method significantly outperforms some other methods on the multiobjective traveling salesman problem, multiobjective vehicle routing problem, and multiobjective knapsack problem in terms of solution quality, speed, and model efficiency.

Xi Lin, Zhiyuan Yang, Xiaoyuan Zhang et al.

Expensive multi-objective optimization problems can be found in many real-world applications, where their objective function evaluations involve expensive computations or physical experiments. It is desirable to obtain an approximate Pareto front with a limited evaluation budget. Multi-objective Bayesian optimization (MOBO) has been widely used for finding a finite set of Pareto optimal solutions. However, it is well-known that the whole Pareto set is on a continuous manifold and can contain infinite solutions. The structural properties of the Pareto set are not well exploited in existing MOBO methods, and the finite-set approximation may not contain the most preferred solution(s) for decision-makers. This paper develops a novel learning-based method to approximate the whole Pareto set for MOBO, which generalizes the decomposition-based multi-objective optimization algorithm (MOEA/D) from finite populations to models. We design a simple and powerful acquisition search method based on the learned Pareto set, which naturally supports batch evaluation. In addition, with our proposed model, decision-makers can readily explore any trade-off area in the approximate Pareto set for flexible decision-making. This work represents the first attempt to model the Pareto set for expensive multi-objective optimization. Experimental results on different synthetic and real-world problems demonstrate the effectiveness of our proposed method.

Rui Zhang, Fei Liu, Xi Lin et al.

Automated heuristic design (AHD) has gained considerable attention for its potential to automate the development of effective heuristics. The recent advent of large language models (LLMs) has paved a new avenue for AHD, with initial efforts focusing on framing AHD as an evolutionary program search (EPS) problem. However, inconsistent benchmark settings, inadequate baselines, and a lack of detailed component analysis have left the necessity of integrating LLMs with search strategies and the true progress achieved by existing LLM-based EPS methods to be inadequately justified. This work seeks to fulfill these research queries by conducting a large-scale benchmark comprising four LLM-based EPS methods and four AHD problems across nine LLMs and five independent runs. Our extensive experiments yield meaningful insights, providing empirical grounding for the importance of evolutionary search in LLM-based AHD approaches, while also contributing to the advancement of future EPS algorithmic development. To foster accessibility and reproducibility, we have fully open-sourced our benchmark and corresponding results.

Xiaoyuan Zhang, Liang Zhao, Yingying Yu et al.

Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, learning under fairness or robustness constraints, etc. Instead of reducing multiple objective functions into a scalar objective, MOPs aim to optimize for the so-called Pareto optimality or Pareto set learning, which involves optimizing more than one objective function simultaneously, over models with thousands / millions of parameters. Existing benchmark libraries for MOPs mainly focus on evolutionary algorithms, most of which are zeroth-order / meta-heuristic methods that do not effectively utilize higher-order information from objectives and cannot scale to large-scale models with thousands / millions of parameters. In light of the above gap, this paper introduces LibMOON, the first multiobjective optimization library that supports state-of-the-art gradient-based methods, provides a fair benchmark, and is open-sourced for the community.

Fei Liu, Chengyu Lu, Lin Gui et al.

Vehicle routing is a well-known optimization research topic with significant practical importance. Among different approaches to solving vehicle routing, heuristics can produce a satisfactory solution at a reasonable computational cost. Consequently, much effort has been made in the past decades to develop vehicle routing heuristics. In this article, we systematically survey the existing vehicle routing heuristics, particularly on works carried out in recent years. A classification of vehicle routing heuristics is presented, followed by a review of their methodologies, recent developments, and applications. Moreover, we present a general framework of state-of-the-art methods and provide insights into their success. Finally, three emerging research topics with notable works and future directions are discussed.

Xi Lin, Zhiyuan Yang, Xiaoyuan Zhang et al.

Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and might lead to a suboptimal solution to the original problem. In addition, the intermediate solutions, often ignored by classic homotopy optimization, could be useful for many real-world applications. In this work, we propose a novel model-based approach to learn the whole continuation path for homotopy optimization, which contains infinite intermediate solutions for any surrogate subproblems. Rather than the classic unidirectional easy-to-hard optimization, our method can simultaneously optimize the original problem and all surrogate subproblems in a collaborative manner. The proposed model also supports real-time generation of any intermediate solution, which could be desirable for many applications. Experimental studies on different problems show that our proposed method can significantly improve the performance of homotopy optimization and provide extra helpful information to support better decision-making.

Fei Liu, Xialiang Tong, Mingxuan Yuan et al.

Optimization can be found in many real-life applications. Designing an effective algorithm for a specific optimization problem typically requires a tedious amount of effort from human experts with domain knowledge and algorithm design skills. In this paper, we propose a novel approach called Algorithm Evolution using Large Language Model (AEL). It utilizes a large language model (LLM) to automatically generate optimization algorithms via an evolutionary framework. AEL does algorithm-level evolution without model training. Human effort and requirements for domain knowledge can be significantly reduced. We take constructive methods for the salesman traveling problem as a test example, we show that the constructive algorithm obtained by AEL outperforms simple hand-crafted and LLM-generated heuristics. Compared with other domain deep learning model-based algorithms, these methods exhibit excellent scalability across different problem sizes. AEL is also very different from previous attempts that utilize LLMs as search operators in algorithms.

Shunyu Yao, Fei Liu, Xi Lin et al.

Heuristics are commonly used to tackle various search and optimization problems. Design heuristics usually require tedious manual crafting with domain knowledge. Recent works have incorporated Large Language Models (LLMs) into automatic heuristic search, leveraging their powerful language and coding capacity. However, existing research focuses on the optimal performance on the target problem as the sole objective, neglecting other criteria such as efficiency and scalability, which are vital in practice. To tackle this challenge, we propose to model the heuristic search as a multi-objective optimization problem and consider introducing additional practical criteria beyond optimal performance. Due to the complexity of the search space, conventional multi-objective optimization methods struggle to effectively handle LLM-based multi-objective heuristic search. We propose the first LLM-based multi-objective heuristic search framework, Multi-objective Evolution of Heuristic (MEoH), which integrates LLMs in a zero-shot manner to generate a non-dominated set of heuristics to meet multiple design criteria. We design a new dominance-dissimilarity mechanism for effective population management and selection, which incorporates both code dissimilarity in the search space and dominance in the objective space. MEoH is demonstrated in two well-known combinatorial optimization problems: the online Bin Packing Problem (BPP) and the Traveling Salesman Problem (TSP). The results indicate that a variety of elite heuristics are automatically generated in a single run, offering more trade-off options than the existing methods. It successfully achieves competitive or superior performance while improving efficiency up to 10 times. Moreover, we also observe that the multi-objective search introduces novel insights into heuristic design and leads to the discovery of diverse heuristics.

Fei Liu, Xi Lin, Zhenkun Wang et al.

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a learning-based model to solve VRPs without manual algorithm design has gained substantial attention. However, current NCO methods typically require building one model for each routing problem, which significantly hinders their practical application for real-world industry problems with diverse attributes. In this work, we make the first attempt to tackle the crucial challenge of cross-problem generalization. In particular, we formulate VRPs as different combinations of a set of shared underlying attributes and solve them simultaneously via a single model through attribute composition. In this way, our proposed model can successfully solve VRPs with unseen attribute combinations in a zero-shot generalization manner. Extensive experiments are conducted on eleven VRP variants, benchmark datasets, and industry logistic scenarios. The results show that the unified model demonstrates superior performance in the eleven VRPs, reducing the average gap to around 5% from over 20% in the existing approach and achieving a significant performance boost on benchmark datasets as well as a real-world logistics application. The source code is included in https://github.com/FeiLiu36/MTNCO.

Haokun Lin, Teng Wang, Yixiao Ge et al.

Pioneering token-based works such as Chameleon and Emu3 have established a foundation for multimodal unification but face challenges of high training computational overhead and limited comprehension performance due to a lack of high-level semantics. In this paper, we introduce TokLIP, a visual tokenizer that enhances comprehension by semanticizing vector-quantized (VQ) tokens and incorporating CLIP-level semantics while enabling end-to-end multimodal autoregressive training with standard VQ tokens. TokLIP integrates a low-level discrete VQ tokenizer with a ViT-based token encoder to capture high-level continuous semantics. Unlike previous approaches (e.g., VILA-U) that discretize high-level features, TokLIP disentangles training objectives for comprehension and generation, allowing the direct application of advanced VQ tokenizers without the need for tailored quantization operations. Our empirical results demonstrate that TokLIP achieves exceptional data efficiency, empowering visual tokens with high-level semantic understanding while enhancing low-level generative capacity, making it well-suited for autoregressive Transformers in both comprehension and generation tasks. The code and models are available at https://github.com/TencentARC/TokLIP.

Weiyu Chen, Baijiong Lin, Xiaoyuan Zhang et al.

Many modern deep learning applications require balancing multiple objectives that are often conflicting. Examples include multi-task learning, fairness-aware learning, and the alignment of Large Language Models (LLMs). This leads to multi-objective deep learning, which tries to find optimal trade-offs or Pareto-optimal solutions by adapting mathematical principles from the field of Multi-Objective Optimization (MOO). However, directly applying gradient-based MOO techniques to deep neural networks presents unique challenges, including high computational costs, optimization instability, and the difficulty of effectively incorporating user preferences. This paper provides a comprehensive survey of gradient-based techniques for multi-objective deep learning. We systematically categorize existing algorithms based on their outputs: (i) methods that find a single, well-balanced solution, (ii) methods that generate a finite set of diverse Pareto-optimal solutions, and (iii) methods that learn a continuous Pareto set of solutions. In addition to this taxonomy, the survey covers theoretical analyses, key applications, practical resources, and highlights open challenges and promising directions for future research. A comprehensive list of multi-objective deep learning algorithms is available at https://github.com/Baijiong-Lin/Awesome-Multi-Objective-Deep-Learning.

Xiaoyuan Zhang, Xi Lin, Qingfu Zhang

It is desirable in many multi-objective machine learning applications, such as multi-task learning with conflicting objectives and multi-objective reinforcement learning, to find a Pareto solution that can match a given preference of a decision maker. These problems are often large-scale with available gradient information but cannot be handled very well by the existing algorithms. To tackle this critical issue, this paper proposes a novel predict-and-correct framework for locating a Pareto solution that fits the preference of a decision maker. In the proposed framework, a constraint function is introduced in the search progress to align the solution with a user-specific preference, which can be optimized simultaneously with multiple objective functions. Experimental results show that our proposed method can efficiently find a particular Pareto solution under the demand of a decision maker for standard multiobjective benchmark, multi-task learning, and multi-objective reinforcement learning problems with more than thousands of decision variables. Code is available at: https://github.com/xzhang2523/pmgda. Our code is current provided in the pgmda.rar attached file and will be open-sourced after publication.}

Dake Bu, Wei Huang, Andi Han et al.

Recent curriculum techniques in the post-training stage of LLMs have been widely observed to outperform non-curriculum approaches in enhancing reasoning performance, yet a principled understanding of why and to what extent they work remains elusive. To address this gap, we develop a theoretical framework grounded in the intuition that progressively learning through manageable steps is more efficient than directly tackling a hard reasoning task, provided each stage stays within the model's effective competence. Under mild complexity conditions linking consecutive curriculum stages, we show that curriculum post-training avoids the exponential complexity bottleneck. To substantiate this result, drawing insights from the Chain-of-Thoughts (CoTs) solving mathematical problems such as Countdown and parity, we model CoT generation as a states-conditioned autoregressive reasoning tree, define a uniform-branching base model to capture pretrained behavior, and formalize curriculum stages as either depth-increasing (longer reasoning chains) or hint-decreasing (shorter prefixes) subtasks. Our analysis shows that, under outcome-only reward signals, reinforcement learning finetuning achieves high accuracy with polynomial sample complexity, whereas direct learning suffers from an exponential bottleneck. We further establish analogous guarantees for test-time scaling, where curriculum-aware querying reduces both reward oracle calls and sampling cost from exponential to polynomial order.

Haokun Lin, Haobo Xu, Yichen Wu et al.

Recent advances in diffusion large language models (dLLMs) have introduced a promising alternative to autoregressive (AR) LLMs for natural language generation tasks, leveraging full attention and denoising-based decoding strategies. However, the deployment of these models on edge devices remains challenging due to their massive parameter scale and high resource demands. While post-training quantization (PTQ) has emerged as a widely adopted technique for compressing AR LLMs, its applicability to dLLMs remains largely unexplored. In this work, we present the first systematic study on quantizing diffusion-based language models. We begin by identifying the presence of activation outliers, characterized by abnormally large activation values that dominate the dynamic range. These outliers pose a key challenge to low-bit quantization, as they make it difficult to preserve precision for the majority of values. More importantly, we implement state-of-the-art PTQ methods and conduct a comprehensive evaluation across multiple task types and model variants. Our analysis is structured along four key dimensions: bit-width, quantization method, task category, and model type. Through this multi-perspective evaluation, we offer practical insights into the quantization behavior of dLLMs under different configurations. We hope our findings provide a foundation for future research in efficient dLLM deployment. Our code is publicly available at https://github.com/FelixMessi/QDLM.

Fei Liu, Xi Lin, Weiduo Liao et al.

Neural combinatorial optimization (NCO) is a promising learning-based approach to solving various vehicle routing problems without much manual algorithm design. However, the current NCO methods mainly focus on the in-distribution performance, while the real-world problem instances usually come from different distributions. A costly fine-tuning approach or generalized model retraining from scratch could be needed to tackle the out-of-distribution instances. Unlike the existing methods, this work investigates an efficient prompt learning approach in NCO for cross-distribution adaptation. To be concrete, we propose a novel prompt learning method to facilitate fast zero-shot adaptation of a pre-trained model to solve routing problem instances from different distributions. The proposed model learns a set of prompts among various distributions and then selects the best-matched one to prompt a pre-trained attention model for each problem instance. Extensive experiments show that the proposed prompt learning approach facilitates the fast adaptation of pre-trained routing models. It also outperforms existing generalized models on both in-distribution prediction and zero-shot generalization to a diverse set of new tasks. Our code implementation is available online https://github.com/FeiLiu36/PromptVRP.

Ping Guo, Qingfu Zhang, Xi Lin

The discovery of symbolic solutions -- mathematical expressions, logical rules, and algorithmic structures -- is fundamental to advancing scientific and engineering progress. However, traditional methods often struggle with search efficiency and fail to integrate knowledge effectively. While recent large language model-based (LLM-based) approaches have demonstrated improvements in search efficiency, they lack the ability to continually refine and expand upon discovered solutions and their underlying knowledge, limiting their potential for open-ended innovation. To address these limitations, we introduce CoEvo, a novel framework that leverages large language models within an evolutionary search methodology to continually generate and refine symbolic solutions. CoEvo integrates a dynamic knowledge library, enabling open-ended innovation of solutions through effective knowledge management. Additionally, CoEvo leverages multiple representations of solutions -- including natural language, mathematical expressions, and code -- to further enhance search efficiency. By combining the reasoning capabilities of LLMs with the exploratory power of evolutionary algorithms, CoEvo significantly improves the efficiency and scope of symbolic discovery. Our experimental results demonstrate that this method not only enhances the efficiency of searching for symbolic solutions but also supports the ongoing discovery process, akin to human scientific endeavors. This study represents a first effort in conceptualizing the search for symbolic solutions as a lifelong, iterative process, marking a significant step towards harnessing LLMs in the perpetual pursuit of scientific and engineering breakthroughs. Our code is available at https://github.com/pgg3/CoEvo.

Changliang Zhou, Xi Lin, Zhenkun Wang et al.

The neural combinatorial optimization (NCO) method has shown great potential for solving routing problems of intelligent transportation systems without requiring expert knowledge. However, existing constructive NCO methods still struggle to solve large-scale instances, which significantly limits their application prospects. To address these crucial shortcomings, this work proposes a novel Instance-Conditioned Adaptation Model (ICAM) for better large-scale generalization of neural routing solvers. In particular, we design a simple yet efficient instance-conditioned adaptation function to significantly improve the generalization performance of existing NCO models with a small time and memory overhead. In addition, with a systematic investigation on the performance of information incorporation between different attention mechanisms, we further propose a powerful yet low-complexity instance-conditioned adaptation module to generate better solutions for instances across different scales. Extensive experimental results on both synthetic and benchmark instances show that our proposed method is capable of obtaining promising results with a very fast inference time in solving large-scale Traveling Salesman Problems (TSPs), Capacitated Vehicle Routing Problems (CVRPs), and Asymmetric Traveling Salesman Problems (ATSPs). Our code is available at https://github.com/CIAM-Group/ICAM.

Xiaoyuan Zhang, Xi Lin, Yichi Zhang et al.

Multiobjective optimization (MOO) is prevalent in numerous applications, in which a Pareto front (PF) is constructed to display optima under various preferences. Previous methods commonly utilize the set of Pareto objectives (particles on the PF) to represent the entire PF. However, the empirical distribution of the Pareto objectives on the PF is rarely studied, which implicitly impedes the generation of diverse and representative Pareto objectives in previous methods. To bridge the gap, we suggest in this paper constructing \emph{uniformly distributed} Pareto objectives on the PF, so as to alleviate the limited diversity found in previous MOO approaches. We are the first to formally define the concept of ``uniformity" for an MOO problem. We optimize the maximal minimal distances on the Pareto front using a neural network, resulting in both asymptotically and non-asymptotically uniform Pareto objectives. Our proposed method is validated through experiments on real-world and synthetic problems, which demonstrates the efficacy in generating high-quality uniform Pareto objectives and the encouraging performance exceeding existing state-of-the-art methods. The detailed model implementation and the code are scheduled to be open-sourced upon publication.

Fei Liu, Xialiang Tong, Mingxuan Yuan et al.

Heuristics are widely used for dealing with complex search and optimization problems. However, manual design of heuristics can be often very labour extensive and requires rich working experience and knowledge. This paper proposes Evolution of Heuristic (EoH), a novel evolutionary paradigm that leverages both Large Language Models (LLMs) and Evolutionary Computation (EC) methods for Automatic Heuristic Design (AHD). EoH represents the ideas of heuristics in natural language, termed thoughts. They are then translated into executable codes by LLMs. The evolution of both thoughts and codes in an evolutionary search framework makes it very effective and efficient for generating high-performance heuristics. Experiments on three widely studied combinatorial optimization benchmark problems demonstrate that EoH outperforms commonly used handcrafted heuristics and other recent AHD methods including FunSearch. Particularly, the heuristic produced by EoH with a low computational budget (in terms of the number of queries to LLMs) significantly outperforms widely-used human hand-crafted baseline algorithms for the online bin packing problem.

Ping Guo, Cheng Gong, Xi Lin et al.

Crafting adversarial examples is crucial for evaluating and enhancing the robustness of Deep Neural Networks (DNNs), presenting a challenge equivalent to maximizing a non-differentiable 0-1 loss function. However, existing single objective methods, namely adversarial attacks focus on a surrogate loss function, do not fully harness the benefits of engaging multiple loss functions, as a result of insufficient understanding of their synergistic and conflicting nature. To overcome these limitations, we propose the Multi-Objective Set-based Attack (MOS Attack), a novel adversarial attack framework leveraging multiple loss functions and automatically uncovering their interrelations. The MOS Attack adopts a set-based multi-objective optimization strategy, enabling the incorporation of numerous loss functions without additional parameters. It also automatically mines synergistic patterns among various losses, facilitating the generation of potent adversarial attacks with fewer objectives. Extensive experiments have shown that our MOS Attack outperforms single-objective attacks. Furthermore, by harnessing the identified synergistic patterns, MOS Attack continues to show superior results with a reduced number of loss functions. Our code is available at https://github.com/pgg3/MOS-Attack.

Zhiyu Zhu, Hui Liu, Junhui Hou et al.

This paper investigates the problem of reconstructing hyperspectral (HS) images from single RGB images captured by commercial cameras, \textbf{without} using paired HS and RGB images during training. To tackle this challenge, we propose a new lightweight and end-to-end learning-based framework. Specifically, on the basis of the intrinsic imaging degradation model of RGB images from HS images, we progressively spread the differences between input RGB images and re-projected RGB images from recovered HS images via effective unsupervised camera spectral response function estimation. To enable the learning without paired ground-truth HS images as supervision, we adopt the adversarial learning manner and boost it with a simple yet effective $\mathcal{L}_1$ gradient clipping scheme. Besides, we embed the semantic information of input RGB images to locally regularize the unsupervised learning, which is expected to promote pixels with identical semantics to have consistent spectral signatures. In addition to conducting quantitative experiments over two widely-used datasets for HS image reconstruction from synthetic RGB images, we also evaluate our method by applying recovered HS images from real RGB images to HS-based visual tracking. Extensive results show that our method significantly outperforms state-of-the-art unsupervised methods and even exceeds the latest supervised method under some settings. The source code is public available at https://github.com/zbzhzhy/Unsupervised-Spectral-Reconstruction.

Zhiyu Zhu, Hui Liu, Junhui Hou et al.

This paper investigates the problem of recovering hyperspectral (HS) images from single RGB images. To tackle such a severely ill-posed problem, we propose a physically-interpretable, compact, efficient, and end-to-end learning-based framework, namely AGD-Net. Precisely, by taking advantage of the imaging process, we first formulate the problem explicitly based on the classic gradient descent algorithm. Then, we design a lightweight neural network with a multi-stage architecture to mimic the formed amended gradient descent process, in which efficient convolution and novel spectral zero-mean normalization are proposed to effectively extract spatial-spectral features for regressing an initialization, a basic gradient, and an incremental gradient. Besides, based on the approximate low-rank property of HS images, we propose a novel rank loss to promote the similarity between the global structures of reconstructed and ground-truth HS images, which is optimized with our singular value weighting strategy during training. Moreover, AGD-Net, a single network after one-time training, is flexible to handle the reconstruction with various spectral response functions. Extensive experiments over three commonly-used benchmark datasets demonstrate that AGD-Net can improve the reconstruction quality by more than 1.0 dB on average while saving 67$\times$ parameters and 32$\times$ FLOPs, compared with state-of-the-art methods. The code will be publicly available at https://github.com/zbzhzhy/GD-Net.

Yuheng Jia, Hui Liu, Junhui Hou et al.

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of variables. Inspired by ensemble clustering that aims to seek a better clustering result from a set of clustering results, we propose self-supervised SNMF (S$^3$NMF), which is capable of boosting clustering performance progressively by taking advantage of the sensitivity to initialization characteristic of SNMF, without relying on any additional information. Specifically, we first perform SNMF repeatedly with a random nonnegative matrix for initialization each time, leading to multiple decomposed matrices. Then, we rank the quality of the resulting matrices with adaptively learned weights, from which a new similarity matrix that is expected to be more discriminative is reconstructed for SNMF again. These two steps are iterated until the stopping criterion/maximum number of iterations is achieved. We mathematically formulate S$^3$NMF as a constraint optimization problem, and provide an alternative optimization algorithm to solve it with the theoretical convergence guaranteed. Extensive experimental results on $10$ commonly used benchmark datasets demonstrate the significant advantage of our S$^3$NMF over $12$ state-of-the-art methods in terms of $5$ quantitative metrics. The source code is publicly available at https://github.com/jyh-learning/SSSNMF.

Yifan Zhong, Chengdong Ma, Xiaoyuan Zhang et al.

Current methods for large language model alignment typically use scalar human preference labels. However, this convention tends to oversimplify the multi-dimensional and heterogeneous nature of human preferences, leading to reduced expressivity and even misalignment. This paper presents Panacea, an innovative approach that reframes alignment as a multi-dimensional preference optimization problem. Panacea trains a single model capable of adapting online and Pareto-optimally to diverse sets of preferences without the need for further tuning. A major challenge here is using a low-dimensional preference vector to guide the model's behavior, despite it being governed by an overwhelmingly large number of parameters. To address this, Panacea is designed to use singular value decomposition (SVD)-based low-rank adaptation, which allows the preference vector to be simply injected online as singular values. Theoretically, we prove that Panacea recovers the entire Pareto front with common loss aggregation methods under mild conditions. Moreover, our experiments demonstrate, for the first time, the feasibility of aligning a single LLM to represent an exponentially vast spectrum of human preferences through various optimization methods. Our work marks a step forward in effectively and efficiently aligning models to diverse and intricate human preferences in a controllable and Pareto-optimal manner.

Fei Liu, Yiming Yao, Ping Guo et al.

Algorithm Design (AD) is crucial for effective problem-solving across various domains. The advent of Large Language Models (LLMs) has notably enhanced the automation and innovation within this field, offering new perspectives and promising solutions. Over the past three years, the integration of LLMs into AD (LLM4AD) has seen substantial progress, with applications spanning optimization, machine learning, mathematical reasoning, and scientific discovery. Given the rapid advancements and expanding scope of this field, a systematic review is both timely and necessary. This paper provides a systematic review of LLM4AD. First, we offer an overview and summary of existing studies. Then, we introduce a taxonomy and review the literature across four dimensions: the roles of LLMs, search methods, prompt methods, and application domains with a discussion of potential and achievements of LLMs in AD. Finally, we identify current challenges and highlight several promising directions for future research.

Xi Lin, Xiaoyuan Zhang, Zhiyuan Yang et al.

Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. In the past few decades, numerous methods have been proposed to find Pareto solutions that represent optimal trade-offs among the objectives for a given problem. However, these existing methods could have high computational complexity or may not have good theoretical properties for solving a general differentiable multi-objective optimization problem. In this work, by leveraging the smooth optimization technique, we propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization. It has good theoretical properties for finding all Pareto solutions with valid trade-off preferences, while enjoying significantly lower computational complexity compared to other methods. Experimental results on various real-world application problems fully demonstrate the effectiveness of our proposed method.

Fu Luo, Xi Lin, Zhenkun Wang et al.

The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better scalability of neural combinatorial optimization. Specifically, we develop an efficient self-improved mechanism that enables direct model training on large-scale problem instances without any labeled data. Powered by an innovative local reconstruction approach, this method can iteratively generate better solutions by itself as pseudo-labels to guide efficient model training. In addition, we design a linear complexity attention mechanism for the model to efficiently handle large-scale combinatorial problem instances with low computation overhead. Comprehensive experiments on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes in both uniform and real-world distributions demonstrate the superior scalability of our method.

Yiming Yao, Fei Liu, Ji Cheng et al.

Many real-world optimization scenarios involve expensive evaluation with unknown and heterogeneous costs. Cost-aware Bayesian optimization stands out as a prominent solution in addressing these challenges. To approach the global optimum within a limited budget in a cost-efficient manner, the design of cost-aware acquisition functions (AFs) becomes a crucial step. However, traditional manual design paradigm typically requires extensive domain knowledge and involves a labor-intensive trial-and-error process. This paper introduces EvolCAF, a novel framework that integrates large language models (LLMs) with evolutionary computation (EC) to automatically design cost-aware AFs. Leveraging the crossover and mutation in the algorithmic space, EvolCAF offers a novel design paradigm, significantly reduces the reliance on domain expertise and model training. The designed cost-aware AF maximizes the utilization of available information from historical data, surrogate models and budget details. It introduces novel ideas not previously explored in the existing literature on acquisition function design, allowing for clear interpretations to provide insights into its behavior and decision-making process. In comparison to the well-known EIpu and EI-cool methods designed by human experts, our approach showcases remarkable efficiency and generalization across various tasks, including 12 synthetic problems and 3 real-world hyperparameter tuning test sets.

Fei Liu, Rui Zhang, Zhuoliang Xie et al.

We introduce LLM4AD, a unified Python platform for algorithm design (AD) with large language models (LLMs). LLM4AD is a generic framework with modularized blocks for search methods, algorithm design tasks, and LLM interface. The platform integrates numerous key methods and supports a wide range of algorithm design tasks across various domains including optimization, machine learning, and scientific discovery. We have also designed a unified evaluation sandbox to ensure a secure and robust assessment of algorithms. Additionally, we have compiled a comprehensive suite of support resources, including tutorials, examples, a user manual, online resources, and a dedicated graphical user interface (GUI) to enhance the usage of LLM4AD. We believe this platform will serve as a valuable tool for fostering future development in the merging research direction of LLM-assisted algorithm design.

Changliang Zhou, Xi Lin, Zhenkun Wang et al.

Constructive neural combinatorial optimization (NCO) has attracted growing research attention due to its ability to solve complex routing problems without relying on handcrafted rules. However, existing NCO methods face significant challenges in generalizing to large-scale problems due to high computational complexity and inefficient capture of structural patterns. To address this issue, we propose a novel learning-based search space reduction method that adaptively selects a small set of promising candidate nodes at each step of the constructive NCO process. Unlike traditional methods that rely on fixed heuristics, our selection model dynamically prioritizes nodes based on learned patterns, significantly reducing the search space while maintaining solution quality. Experimental results demonstrate that our method, trained solely on 100-node instances from uniform distribution, generalizes remarkably well to large-scale Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) instances with up to 1 million nodes from the uniform distribution and over 80K nodes from other distributions.

Ke Li, Fei Liu, Zhengkun Wang et al.

Recent advancements in Neural Combinatorial Optimization (NCO) have shown promise in solving routing problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) without handcrafted designs. Research in this domain has explored two primary categories of methods: iterative and non-iterative. While non-iterative methods struggle to generate near-optimal solutions directly, iterative methods simplify the task by learning local search steps. However, existing iterative methods are often limited by restricted neighborhood searches, leading to suboptimal results. To address this limitation, we propose a novel approach that extends the search to larger neighborhoods by learning a destroy-and-repair strategy. Specifically, we introduce a Destroy-and-Repair framework based on Hyper-Graphs (DRHG). This framework reduces consecutive intact edges to hyper-edges, allowing the model to pay more attention to the destroyed part and decrease the complexity of encoding all nodes. Experiments demonstrate that DRHG achieves stateof-the-art performance on TSP with up to 10,000 nodes and shows strong generalization to real-world TSPLib and CVRPLib problems.

Ping Guo, Fei Liu, Xi Lin et al.

In the rapidly evolving field of machine learning, adversarial attacks present a significant challenge to model robustness and security. Decision-based attacks, which only require feedback on the decision of a model rather than detailed probabilities or scores, are particularly insidious and difficult to defend against. This work introduces L-AutoDA (Large Language Model-based Automated Decision-based Adversarial Attacks), a novel approach leveraging the generative capabilities of Large Language Models (LLMs) to automate the design of these attacks. By iteratively interacting with LLMs in an evolutionary framework, L-AutoDA automatically designs competitive attack algorithms efficiently without much human effort. We demonstrate the efficacy of L-AutoDA on CIFAR-10 dataset, showing significant improvements over baseline methods in both success rate and computational efficiency. Our findings underscore the potential of language models as tools for adversarial attack generation and highlight new avenues for the development of robust AI systems.

Ziru Liu, Cheng Gong, Xinyu Fu et al.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for facilitating the self-improvement of large language models (LLMs), particularly in the domain of complex reasoning tasks. However, prevailing on-policy RL methods often contend with significant training instability and inefficiency. This is primarily due to a capacity-difficulty mismatch, where the complexity of training data frequently outpaces the model's current capabilities, leading to critically sparse reward signals and stalled learning progress. This challenge is particularly acute for smaller, more resource-efficient LLMs. To overcome this, we introduce the Guided Hybrid Policy Optimization (GHPO), a novel difficulty-aware reinforcement learning framework. GHPO dynamically calibrates task difficulty by employing adaptive prompt refinement to provide targeted guidance. This unique approach adaptively balances direct imitation learning for problems currently beyond the model's reach with exploration-based reinforcement learning for more manageable tasks, effectively creating a smooth and optimized learning curriculum. Extensive experiments demonstrate that GHPO achieves an average performance gain of approximately 5% across six challenging mathematics benchmarks, consistently outperforming strong on-policy reinforcement learning and curriculum learning baselines. Further analysis confirms that our framework significantly enhances both training stability and final reasoning performance, thus offering a scalable and efficient solution for developing powerful and robust reasoning models.

Changliang Zhou, Canhong Yu, Shunyu Yao et al.

Multi-task neural routing solvers have emerged as a promising paradigm for their ability to solve multiple vehicle routing problems (VRPs) using a single model. However, existing neural solvers typically rely on predefined problem constraints or require per-problem fine-tuning, which substantially limits their zero-shot generalization ability to unseen VRP variants. To address this critical bottleneck, we propose URS, a unified neural routing solver capable of zero-shot generalization across a wide range of unseen VRPs using a single model without any fine-tuning. The key component of URS is the unified data representation (UDR), which replaces problem enumeration with data unification, thereby broadening the problem coverage and reducing reliance on domain expertise. In addition, we propose a Mixed Bias Module (MBM) to efficiently learn the geometric and relational biases inherent in various problems. On top of the proposed UDR, we further develop a parameter generator that adaptively adjusts the decoder and bias weights of MBM to enhance zero-shot generalization. Moreover, we propose an LLM-driven constraint satisfaction mechanism, which translates raw problem descriptions into executable stepwise masking functions to ensure solution feasibility. Extensive experiments demonstrate that URS can consistently produce high-quality solutions for more than 100 distinct VRP variants without any fine-tuning, which includes more than 90 unseen variants. To the best of our knowledge, URS is the first neural solver capable of handling over 100 VRP variants with a single model.

Yiting Wang, Wanghao Ye, Ping Guo et al.

Optimizing Register Transfer Level (RTL) code is crucial for improving the power, performance, and area (PPA) of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts. This paper presents SymRTLO, a novel neuron-symbolic RTL optimization framework that seamlessly integrates LLM-based code rewriting with symbolic reasoning techniques. Our method incorporates a retrieval-augmented generation (RAG) system of optimization rules and Abstract Syntax Tree (AST)-based templates, enabling LLM-based rewriting that maintains syntactic correctness while minimizing undesired circuit behaviors. A symbolic module is proposed for analyzing and optimizing finite state machine (FSM) logic, allowing fine-grained state merging and partial specification handling beyond the scope of pattern-based compilers. Furthermore, a fast verification pipeline, combining formal equivalence checks with test-driven validation, further reduces the complexity of verification. Experiments on the RTL-Rewriter benchmark with Synopsys Design Compiler and Yosys show that SymRTLO improves power, performance, and area (PPA) by up to 43.9%, 62.5%, and 51.1%, respectively, compared to the state-of-the-art methods.

Dake Bu, Wei Huang, Andi Han et al.

Transformer-based large language models (LLMs) have displayed remarkable creative prowess and emergence capabilities. Existing empirical studies have revealed a strong connection between these LLMs' impressive emergence abilities and their in-context learning (ICL) capacity, allowing them to solve new tasks using only task-specific prompts without further fine-tuning. On the other hand, existing empirical and theoretical studies also show that there is a linear regularity of the multi-concept encoded semantic representation behind transformer-based LLMs. However, existing theoretical work fail to build up an understanding of the connection between this regularity and the innovative power of ICL. Additionally, prior work often focuses on simplified, unrealistic scenarios involving linear transformers or unrealistic loss functions, and they achieve only linear or sub-linear convergence rates. In contrast, this work provides a fine-grained mathematical analysis to show how transformers leverage the multi-concept semantics of words to enable powerful ICL and excellent out-of-distribution ICL abilities, offering insights into how transformers innovate solutions for certain unseen tasks encoded with multiple cross-concept semantics. Inspired by empirical studies on the linear latent geometry of LLMs, the analysis is based on a concept-based low-noise sparse coding prompt model. Leveraging advanced techniques, this work showcases the exponential 0-1 loss convergence over the highly non-convex training dynamics, which pioneeringly incorporates the challenges of softmax self-attention, ReLU-activated MLPs, and cross-entropy loss. Empirical simulations corroborate the theoretical findings.

Ping Guo, Cheng Gong, Xi Lin et al.

The escalating threat of adversarial attacks on deep learning models, particularly in security-critical fields, has underscored the need for robust deep learning systems. Conventional robustness evaluations have relied on adversarial accuracy, which measures a model's performance under a specific perturbation intensity. However, this singular metric does not fully encapsulate the overall resilience of a model against varying degrees of perturbation. To address this gap, we propose a new metric termed adversarial hypervolume, assessing the robustness of deep learning models comprehensively over a range of perturbation intensities from a multi-objective optimization standpoint. This metric allows for an in-depth comparison of defense mechanisms and recognizes the trivial improvements in robustness afforded by less potent defensive strategies. Additionally, we adopt a novel training algorithm that enhances adversarial robustness uniformly across various perturbation intensities, in contrast to methods narrowly focused on optimizing adversarial accuracy. Our extensive empirical studies validate the effectiveness of the adversarial hypervolume metric, demonstrating its ability to reveal subtle differences in robustness that adversarial accuracy overlooks. This research contributes a new measure of robustness and establishes a standard for assessing and benchmarking the resilience of current and future defensive models against adversarial threats.

Wenkang Wang, Ran Xu, Jingsen Feng et al.

We evaluated the performance of OpenFOAMGPT incorporating multiple large-language models. Some of the present models efficiently manage different CFD tasks such as adjusting boundary conditions, turbulence models, and solver configurations, although their token cost and stability vary. Locally deployed smaller models like QwQ-32B struggled with generating valid solver files for complex processes. Zero-shot prompting commonly failed in simulations with intricate settings, even for large models. Challenges with boundary conditions and solver keywords stress the requirement for expert supervision, indicating that further development is needed to fully automate specialized CFD simulations.

Fei Liu, Rui Zhang, Xi Lin et al.

The integration of large language models (LLMs) into automated algorithm design has shown promising potential. A prevalent approach embeds LLMs within search routines to iteratively generate and refine candidate algorithms. However, most existing methods rely on off-the-shelf LLMs trained for general coding tasks,leaving a key question open: Do we need LLMs specifically tailored for algorithm design? If so, how can such LLMs be effectively obtained and how well can they generalize across different algorithm design tasks? In this paper, we take a first step toward answering these questions by exploring fine-tuning of LLMs for algorithm design. We introduce a Diversity-Aware Rank based (DAR) sampling strategy to balance training data diversity and quality, then we leverage direct preference optimization to efficiently align LLM outputs with task objectives. Our experiments, conducted on Llama-3.2-1B-Instruct and Llama- 3.1-8B-Instruct, span three distinct algorithm design tasks. Results suggest that finetuned LLMs can significantly outperform their off-the-shelf counterparts with the smaller Llama-3.2-1B-Instruct and match the larger Llama-3.1-8B-Instruct on the admissible set problem. Moreover, we observe promising generalization: LLMs finetuned on specific algorithm design tasks also improve performance on related tasks with varying settings. These findings highlight the value of task-specific adaptation for LLMs in algorithm design and open new avenues for future research.

Wei Wang, Jialong Shi, Jianyong Sun et al.

Combinatorial optimization problem (COP) is difficult to solve because of the massive number of local optimal solutions in his solution space. Various methods have been put forward to smooth the solution space of COPs, including homotopic convex (HC) transformation for the traveling salesman problem (TSP). This paper extends the HC transformation approach to unconstrained binary quadratic programming (UBQP) by proposing a method to construct a unimodal toy UBQP of any size. We theoretically prove the unimodality of the constructed toy UBQP. After that, we apply this unimodal toy UBQP to smooth the original UBQP by using the HC transformation framework and empirically verify the smoothing effects. Subsequently, we introduce an iterative algorithmic framework incorporating HC transformation, referred as landscape smoothing iterated local search (LSILS). Our experimental analyses, conducted on various UBQP instances show the effectiveness of LSILS. Furthermore, this paper proposes a parallel cooperative variant of LSILS, denoted as PC-LSILS and apply it to both the UBQP and the TSP. Our experimental findings highlight that PC-LSILS improves the smoothing performance of the HC transformation, and further improves the overall performance of the algorithm.

Song Lai, Zhe Zhao, Fei Zhu et al.

Continual learning aims to learn multiple tasks sequentially. A key challenge in continual learning is balancing between two objectives: retaining knowledge from old tasks (stability) and adapting to new tasks (plasticity). Experience replay methods, which store and replay past data alongside new data, have become a widely adopted approach to mitigate catastrophic forgetting. However, these methods neglect the dynamic nature of the stability-plasticity trade-off and aim to find a fixed and unchanging balance, resulting in suboptimal adaptation during training and inference. In this paper, we propose Pareto Continual Learning (ParetoCL), a novel framework that reformulates the stability-plasticity trade-off in continual learning as a multi-objective optimization (MOO) problem. ParetoCL introduces a preference-conditioned model to efficiently learn a set of Pareto optimal solutions representing different trade-offs and enables dynamic adaptation during inference. From a generalization perspective, ParetoCL can be seen as an objective augmentation approach that learns from different objective combinations of stability and plasticity. Extensive experiments across multiple datasets and settings demonstrate that ParetoCL outperforms state-of-the-art methods and adapts to diverse continual learning scenarios.

Zhe Zhao, Haibin Wen, Pengkun Wang et al.

Large language models (LLMs) have greatly accelerated the automation of algorithm generation and optimization. However, current methods such as EoH and FunSearch mainly rely on predefined templates and expert-specified functions that focus solely on the local evolution of key functionalities. Consequently, they fail to fully leverage the synergistic benefits of the overall architecture and the potential of global optimization. In this paper, we introduce an end-to-end algorithm generation and optimization framework based on LLMs. Our approach utilizes the deep semantic understanding of LLMs to convert natural language requirements or human-authored papers into code solutions, and employs a two-dimensional co-evolution strategy to optimize both functional and structural aspects. This closed-loop process spans problem analysis, code generation, and global optimization, automatically identifying key algorithm modules for multi-level joint optimization and continually enhancing performance and design innovation. Extensive experiments demonstrate that our method outperforms traditional local optimization approaches in both performance and innovation, while also exhibiting strong adaptability to unknown environments and breakthrough potential in structural design. By building on human research, our framework generates and optimizes novel algorithms that surpass those designed by human experts, broadening the applicability of LLMs for algorithm design and providing a novel solution pathway for automated algorithm development.

Fu Luo, Xi Lin, Mengyuan Zhong et al.

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm that sequentially adds unvisited nodes to partial solutions, this rigid approach often leads to suboptimal results. To overcome this limitation, we explore the idea of insertion-based paradigm and propose Learning to Construct with Insertion-based Paradigm (L2C-Insert), a novel learning-based method for constructive NCO. Unlike traditional approaches, L2C-Insert builds solutions by strategically inserting unvisited nodes at any valid position in the current partial solution, which can significantly enhance the flexibility and solution quality. The proposed framework introduces three key components: a novel model architecture for precise insertion position prediction, an efficient training scheme for model optimization, and an advanced inference technique that fully exploits the insertion paradigm's flexibility. Extensive experiments on both synthetic and real-world instances of the Travelling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that L2C-Insert consistently achieves superior performance across various problem sizes.

Ping Guo, Chenyu Zhu, Siyuan Chen et al.

CUDA kernel optimization has become a critical bottleneck for AI performance, as deep learning training and inference efficiency directly depends on highly optimized GPU kernels. Despite the promise of Large Language Models (LLMs) for automating kernel optimization, this field suffers from a fragmented ecosystem of isolated and incomparable approaches with unclear problem formulations. Furthermore, general-purpose LLM code evolution methods cannot meet strict correctness requirements of CUDA kernel optimization. We address these fundamental challenges by first formalizing CUDA kernel optimization as a code optimization task with a clear objective, constraints, and evaluation metrics. We then establish the first systematic LLM-based code evolution framework, EvoEngineer, that provides guidance for designing and adapting optimization strategies to achieve a balance between performance and correctness. Finally, we implement a kernel optimization system based on this framework and conduct extensive experiments on 91 real-world CUDA kernels. Our results demonstrate that EvoEngineer achieves a principled balance between performance and correctness, with the highest averaged median speedup of \textbf{2.72}$\times$ over baseline CUDA kernels and a code validity rate of \textbf{69.8}\%, outperforming existing methods on both dimensions. Our method achieves a maximum speedup of \textbf{36.75}$\times$ among all operations over PyTorch kernels and delivers the highest speedup on \textbf{28} (\textbf{56.0\%}) of 50 operations that achieve over \textbf{2$\times$} acceleration.

Siyuan Chen, Zhichao Lu, Qingfu Zhang

Automated kernel design is critical for overcoming software ecosystem barriers in emerging hardware platforms like RISC-V. While large language models (LLMs) have shown promise for automated kernel optimization, demonstrating success in CUDA domains with comprehensive technical documents and mature codebases, their effectiveness remains unproven for reference-scarce domains like RISC-V. We present Evolution of Kernels (EoK), a novel LLM-based evolutionary program search framework that automates kernel design for domains with limited reference material. EoK mitigates reference scarcity by mining and formalizing reusable optimization ideas (general design principles + actionable thoughts) from established kernel libraries' development histories; it then guides parallel LLM explorations using these ideas, enriched via Retrieval-Augmented Generation (RAG) with RISC-V-specific context, prioritizing historically effective techniques. Empirically, EoK achieves a median 1.27x speedup, surpassing human experts on all 80 evaluated kernel design tasks and improving upon prior LLM-based automated kernel design methods by 20%. These results underscore the viability of incorporating human experience into emerging domains and highlight the immense potential of LLM-based automated kernel optimization.

Han Li, Fei Liu, Zhenkun Wang et al.

Vehicle routing problems (VRPs) are central to combinatorial optimization with significant practical implications. Recent advancements in neural combinatorial optimization (NCO) have demonstrated promising results by leveraging neural networks to solve VRPs, yet the exploration of model scaling within this domain remains underexplored. Inspired by the success of model scaling in large language models (LLMs), this study introduces a Large Routing Model with 1 billion parameters (LRM-1B), designed to address diverse VRP scenarios. We present a comprehensive evaluation of LRM-1B across multiple problem variants, distributions, and sizes, establishing state-of-the-art results. Our findings reveal that LRM-1B not only adapts to different VRP challenges but also showcases superior performance, outperforming existing models. Additionally, we explore the scaling behavior of neural routing models from 1M to 1B parameters. Our analysis confirms power-law between multiple model factors and performance, offering critical insights into the optimal configurations for foundation neural routing solvers.

Ping Guo, Yiting Wang, Wanghao Ye et al.

Large Language Models (LLMs) have demonstrated great potential in automating the generation of Verilog hardware description language code for hardware design. This automation is critical to reducing human effort in the complex and error-prone process of hardware design. However, existing approaches predominantly rely on human intervention and fine-tuning using curated datasets, limiting their scalability in automated design workflows. Although recent iterative search techniques have emerged, they often fail to explore diverse design solutions and may underperform simpler approaches such as repeated prompting. To address these limitations, we introduce EvoVerilog, a novel framework that combines the reasoning capabilities of LLMs with evolutionary algorithms to automatically generate and refine Verilog code. EvoVerilog utilizes a multiobjective, population-based search strategy to explore a wide range of design possibilities without requiring human intervention. Extensive experiments demonstrate that EvoVerilog achieves state-of-the-art performance, with pass@10 scores of 89.1 and 80.2 on the VerilogEval-Machine and VerilogEval-Human benchmarks, respectively. Furthermore, the framework showcases its ability to explore diverse designs by simultaneously generating a variety of functional Verilog code while optimizing resource utilization.

Dake Bu, Wei Huang, Taiji Suzuki et al.

Neural Network-based active learning (NAL) is a cost-effective data selection technique that utilizes neural networks to select and train on a small subset of samples. While existing work successfully develops various effective or theory-justified NAL algorithms, the understanding of the two commonly used query criteria of NAL: uncertainty-based and diversity-based, remains in its infancy. In this work, we try to move one step forward by offering a unified explanation for the success of both query criteria-based NAL from a feature learning view. Specifically, we consider a feature-noise data model comprising easy-to-learn or hard-to-learn features disrupted by noise, and conduct analysis over 2-layer NN-based NALs in the pool-based scenario. We provably show that both uncertainty-based and diversity-based NAL are inherently amenable to one and the same principle, i.e., striving to prioritize samples that contain yet-to-be-learned features. We further prove that this shared principle is the key to their success-achieve small test error within a small labeled set. Contrastingly, the strategy-free passive learning exhibits a large test error due to the inadequate learning of yet-to-be-learned features, necessitating resort to a significantly larger label complexity for a sufficient test error reduction. Experimental results validate our findings.