arXiv subjects

Zhiqiang Ge

Publications and source records attributed to Zhiqiang Ge.

8 recordsLinked to original sources

arXiv2026

Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks

Topological neural networks have emerged as effective tools for modeling higher-order relational structures beyond pairwise graphs, including hypergraphs, simplicial complexes, and cell complexes. However, existing Weisfeiler-Leman type expressivity analyses are typically developed on different structural domains and rely on domain-specific neighborhood systems, making their expressive powers difficult to compare within a common formalism. In this paper, we introduce the Combinatorial Complex Weisfeiler-Leman (CCWL) framework, a unified expressive power refinement defined on combinatorial complexes. By exploiting the ability of combinatorial complexes to represent both set-type relations and part-whole hierarchies, CCWL performs topological color refinement through four structural neighborhoods: boundary, co-boundary, lower adjacency, and upper adjacency. We show that, under specified lifting maps, CCWL can simulate several domain-specific WL-type refinements, thereby providing a common theoretical baseline for analyzing topological message passing. We further study the neighborhood sufficiency problem and prove that, under explicit coverage conditions, a reduced refinement using only lower- and upper-adjacent bridge information preserves the distinguishing power of the full four-neighborhood CCWL refinement. Guided by this theoretical result, we instantiate the reduced refinement as the Combinatorial Complex Isomorphism Network (CCIN). Experiments on synthetic and real-world benchmarks demonstrate that CCIN achieves competitive performance against representative graph and topological neural network baselines. Ablation studies and resource-efficiency analyses further support the effectiveness of the proposed lower/upper-neighborhood design.

cs.LG↗

arXiv2026

Parallel Complex Diffusion for Scalable Time Series Generation

Diffusion models learn data distributions indirectly through denoising, making the difficulty of generative modeling closely tied to the dependency structure of data. For time series, strong temporal dependence forces the noise / score estimator to recover highly entangled cross-time relationships, leading to the curse of entanglement. We mitigate this burden by changing the topology of the diffusion space: the Discrete Fourier Transform (DFT) decomposes temporal dependencies into spectral modes, diagonalizing second-order dependency structure and better aligning the data manifold with isotropic Gaussian noise and homogeneous diffusion dynamics. However, existing frequency-aware diffusion methods mainly use the DFT to design estimator blocks under temporal DDPM/SDE frameworks, while frequency-native diffusion paths face a mathematical barrier from complex-valued dynamics. We propose PaCoDi (Parallel Complex Diffusion), a frequency-native diffusion framework that constructs the diffusion path in the spectral domain while replacing the complex-valued estimator with parallel real-valued estimators for real and imaginary components. Theoretically, we prove the statistical orthogonality of spectral Gaussian noise, establish quadrature forward transitions and conditional reverse factorization, and extend discrete PaCoDi to continuous-time spectral SDEs through a Spectral Wiener Process. We further introduce a Mean Field Theory approximation with an Interactive Correction Branch to handle marginal coupling, and exploit Hermitian symmetry to reduce 50% attention FLOPs without information loss. Extensive experiments on unconditional and conditional time series generation demonstrate superior generative quality and computational efficiency against 5 SOTA baselines in 5 benchmarks, respectively. Code is available at https://github.com/RongyaoCai/PaCoDi.

cs.LG↗

arXiv2026

The Procrustean Bed of Time Series: The Optimization Bias in Point-wise Loss Functions

Intuitively, a more deterministic time series should be easier to forecast. However, point-wise loss functions (e.g., MSE and MAE), serving as differentiable surrogates for the ideal optimization target, score each timestamp independently and therefore disregard temporal dependence. This mismatch induces a systematic optimization bias that cannot be eliminated merely by improving model expressiveness or optimizer. To formalize this issue, we define the Expectation of Optimization Bias (EOB) as the Kullback--Leibler divergence between the true joint distribution and the factorized i.i.d. surrogate induced by the point-wise paradigm. Under covariance-stationary Gaussian assumptions, we derive closed-form expressions for the stochastic component of EOB, establishing it as an irreducible lower bound on the total bias in linear systems, and further extend it to nonlinear regimes through a Gaussian mixture model lower bound. Crucially, we prove this bias is governed intrinsically by two data properties, i.e., sequence length and Structural Signal-to-Noise Ratio (SSNR), regardless of specific model architecture, optimizer, or point-wise loss forms. This theory motivates a principled debiasing program based on sequence length reduction and structural orthogonalization, which we instantiate through DFT/DWT combined with a novel harmonized $\ell_p$ norm. Extensive experiments validate the predicted SSNR--horizon dynamics, resolve the classic trigonometric fitting failure as an objective-induced pathology, and demonstrate substantial plug-and-play gains. Notably, on iTransformer, our proposed objective reduces average MSE/MAE by 5.2%/5.0% in forecasting across 11 datasets and by 27.4%/19.4% in imputation across 9 datasets.

cs.LG↗

arXiv2025

Relaxing Probabilistic Latent Variable Models' Specification via Infinite-Horizon Optimal Control

In this paper, we address the issue of model specification in probabilistic latent variable models (PLVMs) using an infinite-horizon optimal control approach. Traditional PLVMs rely on joint distributions to model complex data, but introducing latent variables results in an ill-posed parameter learning problem. To address this issue, regularization terms are typically introduced, leading to the development of the expectation-maximization (EM) algorithm, where the latent variable distribution is restricted to a predefined normalized distribution family to facilitate the expectation step. To overcome this limitation, we propose representing the latent variable distribution as a finite set of instances perturbed via an ordinary differential equation with a control policy. This approach ensures that the instances asymptotically converge to the true latent variable distribution as time approaches infinity. By doing so, we reformulate the distribution inference problem as an optimal control policy determination problem, relaxing the model specification to an infinite-horizon path space. Building on this formulation, we derive the corresponding optimal control policy using the Pontryagin's maximum principle and provide a closed-form expression for its implementation using the reproducing kernel Hilbert space. After that, we develop a novel, convergence-guaranteed EM algorithm for PLVMs based on this infinite-horizon-optimal-control-based inference strategy. Finally, extensive experiments are conducted to validate the effectiveness and superiority of the proposed approach.

eess.SY↗

arXiv2024

IG2: Integrated Gradient on Iterative Gradient Path for Feature Attribution

Feature attribution explains Artificial Intelligence (AI) at the instance level by providing importance scores of input features' contributions to model prediction. Integrated Gradients (IG) is a prominent path attribution method for deep neural networks, involving the integration of gradients along a path from the explained input (explicand) to a counterfactual instance (baseline). Current IG variants primarily focus on the gradient of explicand's output. However, our research indicates that the gradient of the counterfactual output significantly affects feature attribution as well. To achieve this, we propose Iterative Gradient path Integrated Gradients (IG2), considering both gradients. IG2 incorporates the counterfactual gradient iteratively into the integration path, generating a novel path (GradPath) and a novel baseline (GradCF). These two novel IG components effectively address the issues of attribution noise and arbitrary baseline choice in earlier IG methods. IG2, as a path method, satisfies many desirable axioms, which are theoretically justified in the paper. Experimental results on XAI benchmark, ImageNet, MNIST, TREC questions answering, wafer-map failure patterns, and CelebA face attributes validate that IG2 delivers superior feature attributions compared to the state-of-the-art techniques. The code is released at: https://github.com/JoeZhuo-ZY/IG2.

cs.CV↗

arXiv2023

ABIGX: A Unified Framework for eXplainable Fault Detection and Classification

For explainable fault detection and classification (FDC), this paper proposes a unified framework, ABIGX (Adversarial fault reconstruction-Based Integrated Gradient eXplanation). ABIGX is derived from the essentials of previous successful fault diagnosis methods, contribution plots (CP) and reconstruction-based contribution (RBC). It is the first explanation framework that provides variable contributions for the general FDC models. The core part of ABIGX is the adversarial fault reconstruction (AFR) method, which rethinks the FR from the perspective of adversarial attack and generalizes to fault classification models with a new fault index. For fault classification, we put forward a new problem of fault class smearing, which intrinsically hinders the correct explanation. We prove that ABIGX effectively mitigates this problem and outperforms the existing gradient-based explanation methods. For fault detection, we theoretically bridge ABIGX with conventional fault diagnosis methods by proving that CP and RBC are the linear specifications of ABIGX. The experiments evaluate the explanations of FDC by quantitative metrics and intuitive illustrations, the results of which show the general superiority of ABIGX to other advanced explanation methods.

cs.LG↗

arXiv2023

Directed Acyclic Graphs With Tears

Bayesian network is a frequently-used method for fault detection and diagnosis in industrial processes. The basis of Bayesian network is structure learning which learns a directed acyclic graph (DAG) from data. However, the search space will scale super-exponentially with the increase of process variables, which makes the data-driven structure learning a challenging problem. To this end, the DAGs with NOTEARs methods are being well studied not only for their conversion of the discrete optimization into continuous optimization problem but also their compatibility with deep learning framework. Nevertheless, there still remain challenges for NOTEAR-based methods: 1) the infeasible solution results from the gradient descent-based optimization paradigm; 2) the truncation operation to promise the learned graph acyclic. In this work, the reason for challenge 1) is analyzed theoretically, and a novel method named DAGs with Tears method is proposed based on mix-integer programming to alleviate challenge 2). In addition, prior knowledge is able to incorporate into the new proposed method, making structure learning more practical and useful in industrial processes. Finally, a numerical example and an industrial example are adopted as case studies to demonstrate the superiority of the developed method.

cs.AI↗

arXiv2022

Latent Variable Models in the Era of Industrial Big Data: Extension and Beyond

A rich supply of data and innovative algorithms have made data-driven modeling a popular technique in modern industry. Among various data-driven methods, latent variable models (LVMs) and their counterparts account for a major share and play a vital role in many industrial modeling areas. LVM can be generally divided into statistical learning-based classic LVM and neural networks-based deep LVM (DLVM). We first discuss the definitions, theories and applications of classic LVMs in detail, which serves as both a comprehensive tutorial and a brief application survey on classic LVMs. Then we present a thorough introduction to current mainstream DLVMs with emphasis on their theories and model architectures, soon afterwards provide a detailed survey on industrial applications of DLVMs. The aforementioned two types of LVM have obvious advantages and disadvantages. Specifically, classic LVMs have concise principles and good interpretability, but their model capacity cannot address complicated tasks. Neural networks-based DLVMs have sufficient model capacity to achieve satisfactory performance in complex scenarios, but it comes at sacrifices in model interpretability and efficiency. Aiming at combining the virtues and mitigating the drawbacks of these two types of LVMs, as well as exploring non-neural-network manners to build deep models, we propose a novel concept called lightweight deep LVM (LDLVM). After proposing this new idea, the article first elaborates the motivation and connotation of LDLVM, then provides two novel LDLVMs, along with thorough descriptions on their principles, architectures and merits. Finally, outlooks and opportunities are discussed, including important open questions and possible research directions.

eess.SY↗