arXiv subjects

Wei-Hao Wu

Publications and source records attributed to Wei-Hao Wu.

5 recordsLinked to original sources

arXiv2026

Tensor Decomposition Structure Search Framework from an Interaction Perspective

Recently, tensor decompositions have attracted increasing attention. Fundamentally, different interactions among factors induce distinct tensor decomposition structures (i.e., tensor decomposition). Identifying an appropriate interaction-induced tensor decomposition structure for given data is a fundamental yet challenging problem in tensor modeling, and remains largely under-explored. Existing tensor decomposition structure search methods are typically restricted to a predefined interaction family, such as tensor contraction. To address this problem, we suggest a tensor decomposition structure search framework (I-TSS) from an interaction perspective that can identify either a single structure beyond a predefined interaction family or a mixture of structures involving heterogeneous interaction families. Specifically, we first systematically review existing tensor decomposition structures from an interaction perspective and construct a heterogeneous interaction-induced candidate structure set. Based on it, we propose a unified energy-based rank estimation scheme for heterogeneous interaction-induced candidate structure set. We then introduce the top-$k$ gating mechanism with learnable gating scores to dynamically select a suitable single-candidate structure or combine suitable multi-candidate structures, thereby identifying the tensor decomposition structure in a data-adaptive manner. Theoretically, we derive an approximation error bound for I-TSS, thereby establishing its approximation capability. Extensive experiments on synthetic and real-world datasets demonstrate that I-TSS consistently outperforms state-of-the-art tensor decomposition methods.

cs.CV↗

arXiv2026

Neural Approximation and Its Applications

Multivariate function approximation is a fundamental problem in machine learning. Classic multivariate function approximations rely on hand-crafted basis functions (e.g., polynomial basis and Fourier basis), which limits their approximation ability and data adaptation ability, resulting in unsatisfactory performance. To address these challenges, we introduce the neural basis function by leveraging an untrained neural network as the basis function. Equipped with the proposed neural basis function, we suggest the neural approximation (NeuApprox) paradigm for multivariate function approximation. Specifically, the underlying multivariate function behind the multi-dimensional data is decomposed into a sum of block terms. The clear physically-interpreted block term is the product of expressive neural basis functions and their corresponding learnable coefficients, which allows us to faithfully capture distinct components of the underlying data and also flexibly adapt to new data by readily fine-tuning the neural basis functions. Attributed to the elaborately designed block terms, the suggested NeuApprox enjoys strong approximation ability and flexible data adaptation ability over the hand-crafted basis function-based methods. We also theoretically prove that NeuApprox can approximate any multivariate continuous function to arbitrary accuracy. Extensive experiments on diverse multi-dimensional datasets (including multispectral images, light field data, videos, traffic data, and point cloud data) demonstrate the promising performance of NeuApprox in terms of both approximation capability and adaptability.

cs.LG↗

arXiv2026

Neural Operator-Grounded Continuous Tensor Function Representation and Its Applications

Recently, continuous tensor functions have attracted increasing attention, because they can unifiedly represent data both on mesh grids and beyond mesh grids. However, since mode-$n$ product is essentially discrete and linear, the potential of current continuous tensor function representations is still locked. To break this bottleneck, we suggest neural operator-grounded mode-$n$ operators as a continuous and nonlinear alternative of discrete and linear mode-$n$ product. Instead of mapping the discrete core tensor to the discrete target tensor, proposed mode-$n$ operator directly maps the continuous core tensor function to the continuous target tensor function, which provides a genuine continuous representation of real-world data and can ameliorate discretization artifacts. Empowering with continuous and nonlinear mode-$n$ operators, we propose a neural operator-grounded continuous tensor function representation (abbreviated as NO-CTR), which can more faithfully represent complex real-world data compared with classic discrete tensor representations and continuous tensor function representations. Theoretically, we also prove that any continuous tensor function can be approximated by NO-CTR. To examine the capability of NO-CTR, we suggest an NO-CTR-based multi-dimensional data completion model. Extensive experiments across various data on regular mesh grids (multi-spectral images and color videos), on mesh girds with different resolutions (Sentinel-2 images) and beyond mesh grids (point clouds) demonstrate the superiority of NO-CTR.

cs.CV↗

arXiv2025

Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recovery

Tensor singular value decomposition (t-SVD) is a promising tool for multi-dimensional image representation, which decomposes a multi-dimensional image into a latent tensor and an accompanying transform matrix. However, two critical limitations of t-SVD methods persist: (1) the approximation of the latent tensor (e.g., tensor factorizations) is coarse and fails to accurately capture spatial local high-frequency information; (2) The transform matrix is composed of fixed basis atoms (e.g., complex exponential atoms in DFT and cosine atoms in DCT) and cannot precisely capture local high-frequency information along the mode-3 fibers. To address these two limitations, we propose a Gaussian Splatting-based Low-rank tensor Representation (GSLR) framework, which compactly and continuously represents multi-dimensional images. Specifically, we leverage tailored 2D Gaussian splatting and 1D Gaussian splatting to generate the latent tensor and transform matrix, respectively. The 2D and 1D Gaussian splatting are indispensable and complementary under this representation framework, which enjoys a powerful representation capability, especially for local high-frequency information. To evaluate the representation ability of the proposed GSLR, we develop an unsupervised GSLR-based multi-dimensional image recovery model. Extensive experiments on multi-dimensional image recovery demonstrate that GSLR consistently outperforms state-of-the-art methods, particularly in capturing local high-frequency information.

cs.CV↗

arXiv2024

DarkSHINE Baseline Design Report: Physics Prospects and Detector Technologies

DarkSHINE is a newly proposed fixed-target experiment initiative to search for the invisible decay of Dark Photon via missing energy/momentum signatures, based on the high repetition rate electron beam to be deployed/delivered by the Shanghai High repetition rate XFEL and Extreme light facility (SHINE). This report elaborates the baseline design of DarkSHINE experiment by introducing the physics goals, experimental setups, details of each sub-detector system technical designs, signal and backgground modelings, expected search sensitivities and future prospects, which mark an important step towards the further prototyping and technical demonstrations.

physics.ins-det↗