Hao Wang

André H. Deutz, Michael T. M. Emmerich, Hao Wang

The problem of approximating the Pareto front of a multiobjective optimization problem can be reformulated as the problem of finding a set that maximizes the hypervolume indicator. This paper establishes the analytical expression of the Hessian matrix of the mapping from a (fixed size) collection of $n$ points in the $d$-dimensional decision space (or $m$ dimensional objective space) to the scalar hypervolume indicator value. To define the Hessian matrix, the input set is vectorized, and the matrix is derived by analytical differentiation of the mapping from a vectorized set to the hypervolume indicator. The Hessian matrix plays a crucial role in second-order methods, such as the Newton-Raphson optimization method, and it can be used for the verification of local optimal sets. So far, the full analytical expression was only established and analyzed for the relatively simple bi-objective case. This paper will derive the full expression for arbitrary dimensions ($m\geq2$ objective functions). For the practically important three-dimensional case, we also provide an asymptotically efficient algorithm with time complexity in $O(n\log n)$ for the exact computation of the Hessian Matrix' non-zero entries. We establish a sharp bound of $12m-6$ for the number of non-zero entries. Also, for the general $m$-dimensional case, a compact recursive analytical expression is established, and its algorithmic implementation is discussed. Also, for the general case, some sparsity results can be established; these results are implied by the recursive expression. To validate and illustrate the analytically derived algorithms and results, we provide a few numerical examples using Python and Mathematica implementations. Open-source implementations of the algorithms and testing data are made available as a supplement to this paper.

Yu Huang, Min Zhou, Menglin Yang et al.

Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations, have become a popular paradigm. With these models being usually characterized by intuition-driven design or highly intricate components, placing them within the theoretical analysis framework to distill the core concepts, helps understand the key principles that drive the functionality better and guide further development. Given this surge in interest, this article provides a comprehensive summary of the theoretical foundations and breakthroughs concerning the approximation and learning behaviors intrinsic to prevalent graph learning models. Encompassing discussions on fundamental aspects such as expressiveness power, generalization, optimization, and unique phenomena such as over-smoothing and over-squashing, this piece delves into the theoretical foundations and frontier driving the evolution of graph learning. In addition, this article also presents several challenges and further initiates discussions on possible solutions.

Tingjia Shen, Hao Wang, Jiaqing Zhang et al.

Cross-Domain Sequential Recommendation (CDSR) aims to mine and transfer users' sequential preferences across different domains to alleviate the long-standing cold-start issue. Traditional CDSR models capture collaborative information through user and item modeling while overlooking valuable semantic information. Recently, Large Language Model (LLM) has demonstrated powerful semantic reasoning capabilities, motivating us to introduce them to better capture semantic information. However, introducing LLMs to CDSR is non-trivial due to two crucial issues: seamless information integration and domain-specific generation. To this end, we propose a novel framework named URLLM, which aims to improve the CDSR performance by exploring the User Retrieval approach and domain grounding on LLM simultaneously. Specifically, we first present a novel dual-graph sequential model to capture the diverse information, along with an alignment and contrastive learning method to facilitate domain knowledge transfer. Subsequently, a user retrieve-generation model is adopted to seamlessly integrate the structural information into LLM, fully harnessing its emergent inferencing ability. Furthermore, we propose a domain-specific strategy and a refinement module to prevent out-of-domain generation. Extensive experiments on Amazon demonstrated the information integration and domain-specific generation ability of URLLM in comparison to state-of-the-art baselines. Our code is available at https://github.com/TingJShen/URLLM

Tiange Li, Xiangyu Yang, Hao Wang

In this paper, we develop a simple yet effective screening rule strategy to improve the computational efficiency in solving structured optimization involving nonconvex $\ell_{q,p}$ regularization. Based on an iteratively reweighted $\ell_1$ (IRL1) framework, the proposed screening rule works like a preprocessing module that potentially removes the inactive groups before starting the subproblem solver, thereby reducing the computational time in total. This is mainly achieved by heuristically exploiting the dual subproblem information during each iteration.Moreover, we prove that our screening rule can remove all inactive variables in a finite number of iterations of the IRL1 method. Numerical experiments illustrate the efficiency of our screening rule strategy compared with several state-of-the-art algorithms.

HyperAI Team, Yuchen Liu, Kaiyang Han et al.

Current multimodal large lanauge models possess strong perceptual and reasoning capabilities, however high computational and memory requirements make them difficult to deploy directly on on-device environments. While small-parameter models are progressively endowed with strong general capabilities, standard Vision Transformer (ViT) encoders remain a critical bottleneck, suffering from excessive latency and memory consumption when processing high-resolution inputs.To address these challenges, we introduce HyperVL, an efficient multimodal large language model tailored for on-device inference. HyperVL adopts an image-tiling strategy to cap peak memory usage and incorporates two novel techniques: (1) a Visual Resolution Compressor (VRC) that adaptively predicts optimal encoding resolutions to eliminate redundant computation, and (2) Dual Consistency Learning (DCL), which aligns multi-scale ViT encoders within a unified framework, enabling dynamic switching between visual branches under a shared LLM. Extensive experiments demonstrate that HyperVL achieves state-of-the-art performance among models of comparable size across multiple benchmarks. Furthermore, it significantly significantly reduces latency and power consumption on real mobile devices, demonstrating its practicality for on-device multimodal inference.

Qiankun Shi, Xiao Wang, Hao Wang

In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems, for which we have access to exact information of constraints and noisy function values of the objective. We propose a Bregman linearized augmented Lagrangian method that utilizes stochastic zeroth-order gradient estimators combined with a variance reduction technique. We analyze its oracle complexity, in terms of the total number of stochastic function value evaluations required to achieve an \(ε\)-KKT point in \(\ell_p\)-norm metrics with \(p \ge 2\), where \(p\) is a parameter associated with the selected Bregman distance. In particular, starting from a near-feasible initial point and using Rademacher smoothing, the oracle complexity is in order \(O(p d^{2/p} ε^{-3})\) for \(p \in [2, 2 \ln d]\), and \(O(\ln d \cdot ε^{-3})\) for \(p > 2 \ln d\), where \(d\) denotes the problem dimension. Those results show that the complexity of the proposed method can achieve a dimensional dependency lower than \(O(d)\) without requiring additional assumptions, provided that a Bregman distance is chosen properly. This offers a significant improvement in the high-dimensional setting over existing work, and matches the lowest complexity order with respect to the tolerance \(ε\) reported in the literature. Numerical experiments on constrained Lasso and black-box adversarial attack problems highlight the promising performances of the proposed method.

Hao Wang, Yining Gao, Jiashan Wang et al.

This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the constraint. This kind of problems have strong applicability to a wide range of areas since usually the $\ell_p$ norm can promote sparse solutions. However, the nonsmooth and non-Lipschtiz nature of the $\ell_p$ norm often cause these problems difficult to analyze and solve. We provide the calculation of the subgradients of the $\ell_p$ norm and the normal cones of the $\ell_p$ ball. For both problems, we derive the first-order necessary conditions under various constraint qualifications. We also derive the sequential optimality conditions for both problems and study the conditions under which these conditions imply the first-order necessary conditions. We point out that the sequential optimality conditions can be easily satisfied for iteratively reweighted algorithms and show that the global convergence can be easily derived using sequential optimality conditions.

Hao Wang, Xiangyu Yang, Wei Jiang

This paper is intended to solve the nonconvex $\ell_{p}$-ball constrained nonlinear optimization problems. An iteratively reweighted method is proposed, which solves a sequence of weighted $\ell_{1}$-ball projection subproblems. At each iteration, the next iterate is obtained by moving along the negative gradient with a stepsize and then projecting the resulted point onto the weighted $\ell_{1}$ ball to approximate the $\ell_{p}$ ball. Specifically, if the current iterate is in the interior of the feasible set, then the weighted $\ell_{1}$ ball is formed by linearizing the $\ell_{p}$ norm at the current iterate. If the current iterate is on the boundary of the feasible set, then the weighted $\ell_{1}$ ball is formed differently by keeping those zero components in the current iterate still zero. In our analysis, we prove that the generated iterates converge to a first-order stationary point. Numerical experiments demonstrate the effectiveness of the proposed method.

Xiangyu Yang, Jiashan Wang, Hao Wang

This paper primarily focuses on computing the Euclidean projection of a vector onto the $\ell_{p}$ ball in which $p\in(0,1)$. Such a problem emerges as the core building block in statistical machine learning and signal processing tasks because of its ability to promote the sparsity of the desired solution. However, efficient numerical algorithms for finding the projections are still not available, particularly in large-scale optimization. To meet this challenge, we first derive the first-order necessary optimality conditions of this problem. Based on this characterization, we develop a novel numerical approach for computing the stationary point by solving a sequence of projections onto the reweighted $\ell_{1}$-balls. This method is practically simple to implement and computationally efficient. Moreover, the proposed algorithm is shown to converge uniquely under mild conditions and has a worst-case $O(1/\sqrt{k})$ convergence rate. Numerical experiments demonstrate the efficiency of our proposed algorithm.

Shengkui Zhao, Trung Hieu Nguyen, Hao Wang et al.

Recent state-of-the-art neural text-to-speech (TTS) synthesis models have dramatically improved intelligibility and naturalness of generated speech from text. However, building a good bilingual or code-switched TTS for a particular voice is still a challenge. The main reason is that it is not easy to obtain a bilingual corpus from a speaker who achieves native-level fluency in both languages. In this paper, we explore the use of Mandarin speech recordings from a Mandarin speaker, and English speech recordings from another English speaker to build high-quality bilingual and code-switched TTS for both speakers. A Tacotron2-based cross-lingual voice conversion system is employed to generate the Mandarin speaker's English speech and the English speaker's Mandarin speech, which show good naturalness and speaker similarity. The obtained bilingual data are then augmented with code-switched utterances synthesized using a Transformer model. With these data, three neural TTS models -- Tacotron2, Transformer and FastSpeech are applied for building bilingual and code-switched TTS. Subjective evaluation results show that all the three systems can produce (near-)native-level speech in both languages for each of the speaker.

Hao Wang, Hao Zeng, Jiashan Wang

We propose a general framework of iteratively reweighted l1 methods for solving lp regularization problems. We prove that after some iteration k, the iterates generated by the proposed methods have the same support and sign as the limit points, and are bounded away from 0, so that the algorithm behaves like solving a smooth problem in the reduced space. As a result, the global convergence can be easily obtained and an update strategy for the smoothing parameter is proposed which can automatically terminate the updates for zero components. We show that lp regularization problems are locally equivalent to a weighted l1 regularization problem and every optimal point corresponds to a Maximum A Posterior estimation for independently and non-identically distributed Laplace prior parameters. Numerical experiments exhibit the behaviors and the efficiency of our proposed methods.

Hao Wang, Bing Wang, Jianyong Duan et al.

Spelling error detection serves as a crucial preprocessing in many natural language processing applications. Due to the characteristics of Chinese Language, Chinese spelling error detection is more challenging than error detection in English. Existing methods are mainly under a pipeline framework, which artificially divides error detection process into two steps. Thus, these methods bring error propagation and cannot always work well due to the complexity of the language environment. Besides existing methods only adopt character or word information, and ignore the positive effect of fusing character, word, pinyin1 information together. We propose an LF-LSTM-CRF model, which is an extension of the LSTMCRF with word lattices and character-pinyin-fusion inputs. Our model takes advantage of the end-to-end framework to detect errors as a whole process, and dynamically integrates character, word and pinyin information. Experiments on the SIGHAN data show that our LF-LSTM-CRF outperforms existing methods with similar external resources consistently, and confirm the feasibility of adopting the end-to-end framework and the availability of integrating of character, word and pinyin information.

Fan Zhang, Hao Wang, Jiashan Wang et al.

In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each iteration, consequently reducing the computational cost for projections per iteration. This feature is attractive especially for solving problems where the projections are computationally not easy to calculate. Global convergence guarantee and O(1/k) ergodic convergence rate of the optimality residual are provided under loose assumptions. We apply our proposed strategy to l1-ball constrained problems. Numerical results exhibit that our inexact gradient projection methods for solving l1-ball constrained problems are more efficient than the exact methods.

Hao Wang, Fan Zhang, Yuanming Shi et al.

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a wide range of applications. We design a general algorithmic framework of iteratively reweighted algorithms for solving the proposed nonconvex and nonsmooth sparse optimization problems, which solves a sequence of weighted convex regularization problems with adaptively updated weights. First-order optimality condition is derived and global convergence results are provided under loose assumptions, making our theoretical results a practical tool for analyzing a family of various reweighted algorithms. The effectiveness and efficiency of our proposed formulation and the algorithms are demonstrated in numerical experiments on various sparse optimization problems.

Hao Wang, Ruibin Feng, Chi-Sing Leung

The aim of sparse approximation is to estimate a sparse signal according to the measurement matrix and an observation vector. It is widely used in data analytics, image processing, and communication, etc. Up to now, a lot of research has been done in this area, and many off-the-shelf algorithms have been proposed. However, most of them cannot offer a real-time solution. To some extent, this shortcoming limits its application prospects. To address this issue, we devise a novel sparse approximation algorithm based on Lagrange programming neural network (LPNN), locally competitive algorithm (LCA), and projection theorem. LPNN and LCA are both analog neural network which can help us get a real-time solution. The non-differentiable objective function can be solved by the concept of LCA. Utilizing the projection theorem, we further modify the dynamics and proposed a new system with global asymptotic stability. Simulation results show that the proposed sparse approximation method has the real-time solutions with satisfactory MSEs.