arXiv subjects

Wenlong Lyu

Publications and source records attributed to Wenlong Lyu.

11 recordsLinked to original sources

arXiv2026

Learning Design-Score Manifold to Guide Diffusion Models for Offline Optimization

Optimizing complex systems, from discovering therapeutic drugs to designing high-performance materials, remains a fundamental challenge across science and engineering, as the underlying rules are often unknown and costly to evaluate. Offline optimization aims to optimize designs for target scores using pre-collected datasets without system interaction. However, conventional approaches may fail beyond training data, predicting inaccurate scores and generating inferior designs. This paper introduces ManGO, a diffusion-based framework that learns the design-score manifold, capturing the design-score interdependencies holistically. Unlike existing methods that treat design and score spaces in isolation, ManGO unifies forward prediction and backward generation, attaining generalization beyond training data. Key to this is its derivative-free guidance for conditional generation, coupled with adaptive inference-time scaling that dynamically optimizes denoising paths. Extensive evaluations demonstrate that ManGO outperforms 24 single- and 10 multi-objective optimization methods across diverse domains, including synthetic tasks, robot control, material design, DNA sequence, and real-world engineering optimization.

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arXiv2025

Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective

The well-known graph-based clustering methods, including spectral clustering, symmetric non-negative matrix factorization, and doubly stochastic normalization, can be viewed as relaxations of the kernel $k$-means approach. However, we posit that these methods excessively relax their inherent low-rank, nonnegative, doubly stochastic, and orthonormal constraints to ensure numerical feasibility, potentially limiting their clustering efficacy. In this paper, guided by our theoretical analyses, we propose \textbf{Lo}w-\textbf{R}ank \textbf{D}oubly stochastic clustering (\textbf{LoRD}), a model that only relaxes the orthonormal constraint to derive a probabilistic clustering results. Furthermore, we theoretically establish the equivalence between orthogonality and block diagonality under the doubly stochastic constraint. By integrating \textbf{B}lock diagonal regularization into LoRD, expressed as the maximization of the Frobenius norm, we propose \textbf{B-LoRD}, which further enhances the clustering performance. To ensure numerical solvability, we transform the non-convex doubly stochastic constraint into a linear convex constraint through the introduction of a class probability parameter. We further theoretically demonstrate the gradient Lipschitz continuity of our LoRD and B-LoRD enables the proposal of a globally convergent projected gradient descent algorithm for their optimization. Extensive experiments validate the effectiveness of our approaches. The code is publicly available at https://github.com/lwl-learning/LoRD.

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arXiv2024

Learnable Similarity and Dissimilarity Guided Symmetric Non-Negative Matrix Factorization

Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for clustering, which typically uses the $k$-nearest neighbor ($k$-NN) method to construct similarity matrix. However, $k$-NN may mislead clustering since the neighbors may belong to different clusters, and its reliability generally decreases as $k$ grows. In this paper, we construct the similarity matrix as a weighted $k$-NN graph with learnable weight that reflects the reliability of each $k$-th NN. This approach reduces the search space of the similarity matrix learning to $n - 1$ dimension, as opposed to the $\mathcal{O}(n^2)$ dimension of existing methods, where $n$ represents the number of samples. Moreover, to obtain a discriminative similarity matrix, we introduce a dissimilarity matrix with a dual structure of the similarity matrix, and propose a new form of orthogonality regularization with discussions on its geometric interpretation and numerical stability. An efficient alternative optimization algorithm is designed to solve the proposed model, with theoretically guarantee that the variables converge to a stationary point that satisfies the KKT conditions. The advantage of the proposed model is demonstrated by the comparison with nine state-of-the-art clustering methods on eight datasets. The code is available at \url{https://github.com/lwl-learning/LSDGSymNMF}.

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arXiv2023

Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs

Bayesian Optimization (BO) is a sample-efficient optimization algorithm widely employed across various applications. In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such as machining errors, execution noise, or contextual variability. This uncertainty deviates the input from the intended value before evaluation, resulting in significant performance fluctuations in the final result. In this paper, we introduce a novel robust Bayesian Optimization algorithm, AIRBO, which can effectively identify a robust optimum that performs consistently well under arbitrary input uncertainty. Our method directly models the uncertain inputs of arbitrary distributions by empowering the Gaussian Process with the Maximum Mean Discrepancy (MMD) and further accelerates the posterior inference via Nystrom approximation. Rigorous theoretical regret bound is established under MMD estimation error and extensive experiments on synthetic functions and real problems demonstrate that our approach can handle various input uncertainties and achieve state-of-the-art performance.

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arXiv2023

Efficient Bayesian Optimization with Deep Kernel Learning and Transformer Pre-trained on Multiple Heterogeneous Datasets

Bayesian optimization (BO) is widely adopted in black-box optimization problems and it relies on a surrogate model to approximate the black-box response function. With the increasing number of black-box optimization tasks solved and even more to solve, the ability to learn from multiple prior tasks to jointly pre-train a surrogate model is long-awaited to further boost optimization efficiency. In this paper, we propose a simple approach to pre-train a surrogate, which is a Gaussian process (GP) with a kernel defined on deep features learned from a Transformer-based encoder, using datasets from prior tasks with possibly heterogeneous input spaces. In addition, we provide a simple yet effective mix-up initialization strategy for input tokens corresponding to unseen input variables and therefore accelerate new tasks' convergence. Experiments on both synthetic and real benchmark problems demonstrate the effectiveness of our proposed pre-training and transfer BO strategy over existing methods.

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arXiv2023

Exploring Effective Mask Sampling Modeling for Neural Image Compression

Image compression aims to reduce the information redundancy in images. Most existing neural image compression methods rely on side information from hyperprior or context models to eliminate spatial redundancy, but rarely address the channel redundancy. Inspired by the mask sampling modeling in recent self-supervised learning methods for natural language processing and high-level vision, we propose a novel pretraining strategy for neural image compression. Specifically, Cube Mask Sampling Module (CMSM) is proposed to apply both spatial and channel mask sampling modeling to image compression in the pre-training stage. Moreover, to further reduce channel redundancy, we propose the Learnable Channel Mask Module (LCMM) and the Learnable Channel Completion Module (LCCM). Our plug-and-play CMSM, LCMM, LCCM modules can apply to both CNN-based and Transformer-based architectures, significantly reduce the computational cost, and improve the quality of images. Experiments on the public Kodak and Tecnick datasets demonstrate that our method achieves competitive performance with lower computational complexity compared to state-of-the-art image compression methods.

cs.CV↗

arXiv2023

Reweighted Interacting Langevin Diffusions: an Accelerated Sampling Methodfor Optimization

We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and then we propose an interacting particle scheme that approximates a Reweighted Interacting Langevin Diffusion system (RILD). The underlying system is designed by adding a multiplicative source term into the classical Langevin operator, leading to a higher convergence rate and a more concentrated invariant measure. We analyze the convergence rate of our algorithm and the improvement compared to existing results in the asymptotic situation. We also design various tests to verify our theoretical results, showing the advantages of accelerating convergence and breaking through barriers of suspicious local minimums, especially in high-dimensional non-convex settings. Our algorithms and analysis shed some light on combining gradient and genetic algorithms using Partial Differential Equations (PDEs) with provable guarantees.

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arXiv2022

HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation

In this work we rigorously analyse assumptions inherent to black-box optimisation hyper-parameter tuning tasks. Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box optimisers. Based on these findings, we propose a Heteroscedastic and Evolutionary Bayesian Optimisation solver (HEBO). HEBO performs non-linear input and output warping, admits exact marginal log-likelihood optimisation and is robust to the values of learned parameters. We demonstrate HEBO's empirical efficacy on the NeurIPS 2020 Black-Box Optimisation challenge, where HEBO placed first. Upon further analysis, we observe that HEBO significantly outperforms existing black-box optimisers on 108 machine learning hyperparameter tuning tasks comprising the Bayesmark benchmark. Our findings indicate that the majority of hyper-parameter tuning tasks exhibit heteroscedasticity and non-stationarity, multi-objective acquisition ensembles with Pareto front solutions improve queried configurations, and robust acquisition maximisers afford empirical advantages relative to their non-robust counterparts. We hope these findings may serve as guiding principles for practitioners of Bayesian optimisation. All code is made available at https://github.com/huawei-noah/HEBO.

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arXiv2021

High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning

We introduce a method combining variational autoencoders (VAEs) and deep metric learning to perform Bayesian optimisation (BO) over high-dimensional and structured input spaces. By adapting ideas from deep metric learning, we use label guidance from the blackbox function to structure the VAE latent space, facilitating the Gaussian process fit and yielding improved BO performance. Importantly for BO problem settings, our method operates in semi-supervised regimes where only few labelled data points are available. We run experiments on three real-world tasks, achieving state-of-the-art results on the penalised logP molecule generation benchmark using just 3% of the labelled data required by previous approaches. As a theoretical contribution, we present a proof of vanishing regret for VAE BO.

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arXiv2019

An Efficient Multi-fidelity Bayesian Optimization Approach for Analog Circuit Synthesis

This paper presents an efficient multi-fidelity Bayesian optimization approach for analog circuit synthesis. The proposed method can significantly reduce the overall computational cost by fusing the simple but potentially inaccurate low-fidelity model and a few accurate but expensive high-fidelity data. Gaussian Process (GP) models are employed to model the low- and high-fidelity black-box functions separately. The nonlinear map between the low-fidelity model and high-fidelity model is also modelled as a Gaussian process. A fusing GP model which combines the low- and high-fidelity models can thus be built. An acquisition function based on the fusing GP model is used to balance the exploitation and exploration. The fusing GP model is evolved gradually as new data points are selected sequentially by maximizing the acquisition function. Experimental results show that our proposed method reduces up to 65.5\% of the simulation time compared with the state-of-the-art single-fidelity Bayesian optimization method, while exhibiting more stable performance and a more promising practical prospect.

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arXiv2019

Bayesian Optimization Approach for Analog Circuit Synthesis Using Neural Network

Bayesian optimization with Gaussian process as surrogate model has been successfully applied to analog circuit synthesis. In the traditional Gaussian process regression model, the kernel functions are defined explicitly. The computational complexity of training is O(N 3 ), and the computation complexity of prediction is O(N 2 ), where N is the number of training data. Gaussian process model can also be derived from a weight space view, where the original data are mapped to feature space, and the kernel function is defined as the inner product of nonlinear features. In this paper, we propose a Bayesian optimization approach for analog circuit synthesis using neural network. We use deep neural network to extract good feature representations, and then define Gaussian process using the extracted features. Model averaging method is applied to improve the quality of uncertainty prediction. Compared to Gaussian process model with explicitly defined kernel functions, the neural-network-based Gaussian process model can automatically learn a kernel function from data, which makes it possible to provide more accurate predictions and thus accelerate the follow-up optimization procedure. Also, the neural-network-based model has O(N) training time and constant prediction time. The efficiency of the proposed method has been verified by two real-world analog circuits.

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