arXiv subjects

Richard Yi Da Xu

Publications and source records attributed to Richard Yi Da Xu.

At least 19 recordsLinked to original sources

arXiv2026

Fair Multi-View Determinantal Coresets via Adaptive NEPv

Selecting a small, diverse subset from a large candidate pool often means balancing several incompatible notions of diversity. In trademark curation, for instance, a subset should cover both the language used to describe marks and the visual space of their logos. A single determinantal point process (\DPP) kernel can hide failure in one view, and averaging kernels replaces the multi-view relaxation by an ordinary single-kernel spectral problem. We formulate \emph{fair multi-view determinant selection}: maximize the weakest per-view log determinant of a size-$k$ subset. We smooth this nonsmooth objective and relax it to the Stiefel manifold. The relaxation embeds every discrete subset exactly, but unlike its single-view counterpart it has no closed-form spectral solution in general. Its stationarity condition is a gauge-invariant nonlinear eigenvalue problem with eigenvector-dependent, view-adaptive weights. We derive an adaptive self-consistent-field (\SCF) solver with damping and level shifting, and round the resulting subspace by leverage-score screening followed by fair local refinement. The solver needs only feature-map products for each view. We report conflicting-view synthetic experiments and specify a multimodal USPTO protocol; the real-data multimodal results require aligned logo embeddings and are not claimed in this version.

stat.ML↗

arXiv2026

Spectral Certificates and Projection-DPP Rounding for Determinantal MAP Selection

Selecting a fixed-size subset that maximizes the determinant of a positive semidefinite kernel is the MAP problem for a size-constrained determinantal point process and the classical maximum-entropy sampling problem. Although this discrete problem is NP-hard, a classical spectral bound gives an efficiently computable ceiling using the leading eigenvalues. The same ceiling is the exact optimum of the associated Stiefel relaxation, so the continuous problem is already solved by the leading eigenspace. We study what this eigenspace implies for discrete rounding. The leading eigenvectors induce a projection determinantal point process whose probability for a subset equals its squared coordinate volume. We prove that the gap between the determinant of any subset and the spectral ceiling is at most its negative log-probability under this distribution. Consequently, the integrality gap is bounded by the min-entropy and equals it when the kernel rank matches the subset size. Projection-DPP rounding also has an expected gap bounded by the Shannon entropy and admits a high-probability additive guarantee. These results identify leading-subspace localization, rather than eigenvalue decay alone, as the geometry controlling roundability. This analysis yields CertDPP, a matrix-free pipeline that computes the leading eigenspace, draws projection-DPP samples, optionally improves them by determinant-increasing swaps, and reports the gap from a verified spectral ceiling. Controlled experiments validate the entropy identities, compare with exact MAP on small instances, and demonstrate linear scaling in the ground-set size for the rounding stage.

cs.LG↗

arXiv2026

Hierarchical Copula-Gumbel-Top-K Routing: Two-Sided Dependence Control for Frozen Mixture-of-Experts at Fixed Per-Token Routing Laws

A stochastic Gumbel-Top-K router defines, for every token of a mixture-of-experts (MoE) model, a routing law: a distribution over ordered expert lists and mixture weights. We ask which joint distributions over the routing choices of different tokens are reachable while every individual token's complete routing law is held exactly fixed. We give a two-sided construction, Hierarchical Copula-Gumbel-Top-K (CGA). Within a group of related tokens, an exchangeable Gaussian copula positively correlates the Gumbel perturbations at each expert coordinate, which can increase within-group expert-set coherence. Across disjoint pairs of groups, a tunable antithetic construction introduces a selectable amount of negative dependence. We prove that both operations leave each token's ordered Top-K sample, mixture weights, and inclusion probabilities identical in distribution to independent routing at a routing layer conditioned on its pre-routing logits; conditional expected expert traffic is preserved as a consequence. We characterize the resulting trade-off: positive within-group coupling can only inflate the variance of realized expert loads relative to independent routing, while nonnegative cross-group opposition can only reduce it relative to flat coupling at the same within-group strength. Coherence and load dispersion are thus controlled by two complementary dependence dials on the invariance constraint surface. Because the base model is untouched, the dials can be driven by a small controller over frozen features, trainable with a score-function estimator: the frozen network is evaluated only in the forward direction, and gradients are confined to the controller. An initial small-scale pilot validates the mechanism and the training route, but does not establish task-level fine-tuning gains.

cs.LG↗

arXiv2026

Rethinking Generalization in Graph Neural Networks: A Structural Complexity Perspective

Graph neural networks (GNNs) have emerged as a fundamental tool for learning from graph-structured data, achieving strong performance across a wide range of applications. However, understanding their generalization capabilities remains challenging due to the complex structural dependencies inherent in such data. Existing generalization analyses largely follow the classical machine learning paradigm, focusing primarily on model complexity while overlooking the fundamental role of graph structure. Therefore, in this work, we systematically investigate this role by asking: does the graph structure actually influence generalization, and if so, by how much? To answer the first question and validate our intuition, we theoretically prove that incorporating more edges into the prediction process transforms the input representations to be overly accommodating to the output model, thereby inducing overfitting. To address the second question, we formulate a structural complexity measure based on the number of effective edges and derive a Rademacher complexity-based generalization bound. In doing so, we demonstrate that GNN generalization depends explicitly on structural complexity, alongside traditional parameter-dependent factors. Motivated by these theoretical findings, we propose a structural entropy regularization method. This approach controls structural complexity by regulating effective edges to balance underfitting and overfitting, ultimately improving the generalization performance of GNNs.

cs.LG↗

arXiv2025

Deep Sparse Latent Feature Models for Knowledge Graph Completion

Recent advances in knowledge graph completion (KGC) have emphasized text-based approaches to navigate the inherent complexities of large-scale knowledge graphs (KGs). While these methods have achieved notable progress, they frequently struggle to fully incorporate the global structural properties of the graph. Stochastic blockmodels (SBMs), especially the latent feature relational model (LFRM), offer robust probabilistic frameworks for identifying latent community structures and improving link prediction. This paper presents a novel probabilistic KGC framework utilizing sparse latent feature models, optimized via a deep variational autoencoder (VAE). Our proposed method dynamically integrates global clustering information with local textual features to effectively complete missing triples, while also providing enhanced interpretability of the underlying latent structures. Extensive experiments on four benchmark datasets with varying scales demonstrate the significant performance gains achieved by our method.

cs.CL↗

arXiv2025

KERMIT: Knowledge Graph Completion of Enhanced Relation Modeling with Inverse Transformation

Knowledge graph completion (KGC) revolves around populating missing triples in a knowledge graph using available information. Text-based methods, which depend on textual descriptions of triples, often encounter difficulties when these descriptions lack sufficient information for accurate prediction-an issue inherent to the datasets and not easily resolved through modeling alone. To address this and ensure data consistency, we first use large language models (LLMs) to generate coherent descriptions, bridging the semantic gap between queries and answers. Secondly, we utilize inverse relations to create a symmetric graph, thereby providing augmented training samples for KGC. Additionally, we employ the label information inherent in knowledge graphs (KGs) to enhance the existing contrastive framework, making it fully supervised. These efforts have led to significant performance improvements on the WN18RR and FB15k-237 datasets. According to standard evaluation metrics, our approach achieves a 4.2% improvement in Hit@1 on WN18RR and a 3.4% improvement in Hit@3 on FB15k-237, demonstrating superior performance.

cs.CL↗

arXiv2025

TsCA: On the Semantic Consistency Alignment via Conditional Transport for Compositional Zero-Shot Learning

Compositional Zero-Shot Learning (CZSL) aims to recognize novel state-object compositions by leveraging the shared knowledge of their primitive components. Despite considerable progress, effectively calibrating the bias between semantically similar multimodal representations, as well as generalizing pre-trained knowledge to novel compositional contexts, remains an enduring challenge. In this paper, our interest is to revisit the conditional transport (CT) theory and its homology to the visual-semantics interaction in CZSL and further, propose a novel Trisets Consistency Alignment framework (dubbed TsCA) that well-addresses these issues. Concretely, we utilize three distinct yet semantically homologous sets, i.e., patches, primitives, and compositions, to construct pairwise CT costs to minimize their semantic discrepancies. To further ensure the consistency transfer within these sets, we implement a cycle-consistency constraint that refines the learning by guaranteeing the feature consistency of the self-mapping during transport flow, regardless of modality. Moreover, we extend the CT plans to an open-world setting, which enables the model to effectively filter out unfeasible pairs, thereby speeding up the inference as well as increasing the accuracy. Extensive experiments are conducted to verify the effectiveness of the proposed method.

cs.CV↗

arXiv2024

Nonlinear Eigen-approach ADMM for Sparse Optimization on Stiefel Manifold

With the growing interest and applications in machine learning and data science, finding an efficient method to sparse analysis the high-dimensional data and optimizing a dimension reduction model to extract lower dimensional features has becoming more and more important. Orthogonal constraints (Stiefel manifold) is a commonly met constraint in these applications, and the sparsity is usually enforced through the element-wise L1 norm. Many applications can be found on optimization over Stiefel manifold within the area of physics and machine learning. In this paper, we propose a novel idea by tackling the Stiefel manifold through an nonlinear eigen-approach by first using ADMM to split the problem into smooth optimization over manifold and convex non-smooth optimization, and then transforming the former into the form of nonlinear eigenvalue problem with eigenvector dependency (NEPv) which is solved by self-consistent field (SCF) iteration, and the latter can be found to have an closed-form solution through proximal gradient. Compared with existing methods, our proposed algorithm takes the advantage of specific structure of the objective function, and has efficient convergence results under mild assumptions.

math.OC↗

arXiv2024

Free Lunch for Generating Effective Outlier Supervision

When deployed in practical applications, computer vision systems will encounter numerous unexpected images (\emph{i.e.}, out-of-distribution data). Due to the potentially raised safety risks, these aforementioned unseen data should be carefully identified and handled. Generally, existing approaches in dealing with out-of-distribution (OOD) detection mainly focus on the statistical difference between the features of OOD and in-distribution (ID) data extracted by the classifiers. Although many of these schemes have brought considerable performance improvements, reducing the false positive rate (FPR) when processing open-set images, they necessarily lack reliable theoretical analysis and generalization guarantees. Unlike the observed ways, in this paper, we investigate the OOD detection problem based on the Bayes rule and present a convincing description of the reason for failures encountered by conventional classifiers. Concretely, our analysis reveals that refining the probability distribution yielded by the vanilla neural networks is necessary for OOD detection, alleviating the issues of assigning high confidence to OOD data. To achieve this effortlessly, we propose an ultra-effective method to generate near-realistic outlier supervision. Extensive experiments on large-scale benchmarks reveal that our proposed \texttt{BayesAug} significantly reduces the FPR95 over 12.50\% compared with the previous schemes, boosting the reliability of machine learning systems. The code will be made publicly available.

cs.CV↗

arXiv2023

A variational autoencoder-based nonnegative matrix factorisation model for deep dictionary learning

Construction of dictionaries using nonnegative matrix factorisation (NMF) has extensive applications in signal processing and machine learning. With the advances in deep learning, training compact and robust dictionaries using deep neural networks, i.e., dictionaries of deep features, has been proposed. In this study, we propose a probabilistic generative model which employs a variational autoencoder (VAE) to perform nonnegative dictionary learning. In contrast to the existing VAE models, we cast the model under a statistical framework with latent variables obeying a Gamma distribution and design a new loss function to guarantee the nonnegative dictionaries. We adopt an acceptance-rejection sampling reparameterization trick to update the latent variables iteratively. We apply the dictionaries learned from VAE-NMF to two signal processing tasks, i.e., enhancement of speech and extraction of muscle synergies. Experimental results demonstrate that VAE-NMF performs better in learning the latent nonnegative dictionaries in comparison with state-of-the-art methods.

cs.LG↗

arXiv2022

Domain Decorrelation with Potential Energy Ranking

Machine learning systems, especially the methods based on deep learning, enjoy great success in modern computer vision tasks under experimental settings. Generally, these classic deep learning methods are built on the \emph{i.i.d.} assumption, supposing the training and test data are drawn from a similar distribution independently and identically. However, the aforementioned \emph{i.i.d.} assumption is in general unavailable in the real-world scenario, and as a result, leads to sharp performance decay of deep learning algorithms. Behind this, domain shift is one of the primary factors to be blamed. In order to tackle this problem, we propose using \textbf{Po}tential \textbf{E}nergy \textbf{R}anking (PoER) to decouple the object feature and the domain feature (\emph{i.e.,} appearance feature) in given images, promoting the learning of label-discriminative features while filtering out the irrelevant correlations between the objects and the background. PoER helps the neural networks to capture label-related features which contain the domain information first in shallow layers and then distills the label-discriminative representations out progressively, enforcing the neural networks to be aware of the characteristic of objects and background which is vital to the generation of domain-invariant features. PoER reports superior performance on domain generalization benchmarks, improving the average top-1 accuracy by at least 1.20\% compared to the existing methods. Moreover, we use PoER in the ECCV 2022 NICO Challenge\footnote{https://nicochallenge.com}, achieving top place with only a vanilla ResNet-18. The code has been made available at https://github.com/ForeverPs/PoER.

cs.CV↗

arXiv2022

Towards Deepening Graph Neural Networks: A GNTK-based Optimization Perspective

Graph convolutional networks (GCNs) and their variants have achieved great success in dealing with graph-structured data. Nevertheless, it is well known that deep GCNs suffer from the over-smoothing problem, where node representations tend to be indistinguishable as more layers are stacked up. The theoretical research to date on deep GCNs has focused primarily on expressive power rather than trainability, an optimization perspective. Compared to expressivity, trainability attempts to address a more fundamental question: Given a sufficiently expressive space of models, can we successfully find a good solution via gradient descent-based optimizers? This work fills this gap by exploiting the Graph Neural Tangent Kernel (GNTK), which governs the optimization trajectory under gradient descent for wide GCNs. We formulate the asymptotic behaviors of GNTK in the large depth, which enables us to reveal the dropping trainability of wide and deep GCNs at an exponential rate in the optimization process. Additionally, we extend our theoretical framework to analyze residual connection-based techniques, which are found to be merely able to mitigate the exponential decay of trainability mildly. Inspired by our theoretical insights on trainability, we propose Critical DropEdge, a connectivity-aware and graph-adaptive sampling method, to alleviate the exponential decay problem more fundamentally. Experimental evaluation consistently confirms using our proposed method can achieve better results compared to relevant counterparts with both infinite-width and finite-width.

cs.LG↗

arXiv2022

Demystify Optimization and Generalization of Over-parameterized PAC-Bayesian Learning

PAC-Bayesian is an analysis framework where the training error can be expressed as the weighted average of the hypotheses in the posterior distribution whilst incorporating the prior knowledge. In addition to being a pure generalization bound analysis tool, PAC-Bayesian bound can also be incorporated into an objective function to train a probabilistic neural network, making them a powerful and relevant framework that can numerically provide a tight generalization bound for supervised learning. For simplicity, we call probabilistic neural network learned using training objectives derived from PAC-Bayesian bounds as {\it PAC-Bayesian learning}. Despite their empirical success, the theoretical analysis of PAC-Bayesian learning for neural networks is rarely explored. This paper proposes a new class of convergence and generalization analysis for PAC-Bayes learning when it is used to train the over-parameterized neural networks by the gradient descent method. For a wide probabilistic neural network, we show that when PAC-Bayes learning is applied, the convergence result corresponds to solving a kernel ridge regression when the probabilistic neural tangent kernel (PNTK) is used as its kernel. Based on this finding, we further characterize the uniform PAC-Bayesian generalization bound which improves over the Rademacher complexity-based bound for non-probabilistic neural network. Finally, drawing the insight from our theoretical results, we propose a proxy measure for efficient hyperparameters selection, which is proven to be time-saving.

cs.LG↗

arXiv2021

Bayesian data assimilation for estimating epidemic evolution: a COVID-19 study

The evolution of epidemiological parameters, such as instantaneous reproduction number Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to Rt estimation, resulting in the state-of-the-art DARt system. With DARt, time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is overcome by instantaneously updating upon new observations and developing a model selection mechanism that captures abrupt changes; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt and demonstrate its power in revealing the transmission dynamics of COVID-19. The proposed approach provides a promising solution for accurate and timely estimating transmission dynamics from reported data.

stat.AP↗

arXiv2021

Greedy UnMixing for Q-Learning in Multi-Agent Reinforcement Learning

This paper introduces Greedy UnMix (GUM) for cooperative multi-agent reinforcement learning (MARL). Greedy UnMix aims to avoid scenarios where MARL methods fail due to overestimation of values as part of the large joint state-action space. It aims to address this through a conservative Q-learning approach through restricting the state-marginal in the dataset to avoid unobserved joint state action spaces, whilst concurrently attempting to unmix or simplify the problem space under the centralized training with decentralized execution paradigm. We demonstrate the adherence to Q-function lower bounds in the Q-learning for MARL scenarios, and demonstrate superior performance to existing Q-learning MARL approaches as well as more general MARL algorithms over a set of benchmark MARL tasks, despite its relative simplicity compared with state-of-the-art approaches.

cs.LG↗

arXiv2021

Dual Behavior Regularized Reinforcement Learning

Reinforcement learning has been shown to perform a range of complex tasks through interaction with an environment or collected leveraging experience. However, many of these approaches presume optimal or near optimal experiences or the presence of a consistent environment. In this work we propose dual, advantage-based behavior policy based on counterfactual regret minimization. We demonstrate the flexibility of this approach and how it can be adapted to online contexts where the environment is available to collect experiences and a variety of other contexts. We demonstrate this new algorithm can outperform several strong baseline models in different contexts based on a range of continuous environments. Additional ablations provide insights into how our dual behavior regularized reinforcement learning approach is designed compared with other plausible modifications and demonstrates its ability to generalize.

cs.LG↗

arXiv2021

Regularize! Don't Mix: Multi-Agent Reinforcement Learning without Explicit Centralized Structures

We propose using regularization for Multi-Agent Reinforcement Learning rather than learning explicit cooperative structures called {\em Multi-Agent Regularized Q-learning} (MARQ). Many MARL approaches leverage centralized structures in order to exploit global state information or removing communication constraints when the agents act in a decentralized manner. Instead of learning redundant structures which is removed during agent execution, we propose instead to leverage shared experiences of the agents to regularize the individual policies in order to promote structured exploration. We examine several different approaches to how MARQ can either explicitly or implicitly regularize our policies in a multi-agent setting. MARQ aims to address these limitations in the MARL context through applying regularization constraints which can correct bias in off-policy out-of-distribution agent experiences and promote diverse exploration. Our algorithm is evaluated on several benchmark multi-agent environments and we show that MARQ consistently outperforms several baselines and state-of-the-art algorithms; learning in fewer steps and converging to higher returns.

cs.LG↗

arXiv2021

Alleviating Mode Collapse in GAN via Diversity Penalty Module

The vanilla GAN (Goodfellow et al. 2014) suffers from mode collapse deeply, which usually manifests as that the images generated by generators tend to have a high similarity amongst them, even though their corresponding latent vectors have been very different. In this paper, we introduce a pluggable diversity penalty module (DPM) to alleviate mode collapse of GANs. It reduces the similarity of image pairs in feature space, i.e., if two latent vectors are different, then we enforce the generator to generate two images with different features. The normalized Gram matrix is used to measure the similarity. We compare the proposed method with Unrolled GAN (Metz et al. 2016), BourGAN (Xiao, Zhong, and Zheng 2018), PacGAN (Lin et al. 2018), VEEGAN (Srivastava et al. 2017) and ALI (Dumoulin et al. 2016) on 2D synthetic dataset, and results show that the diversity penalty module can help GAN capture much more modes of the data distribution. Further, in classification tasks, we apply this method as image data augmentation on MNIST, Fashion- MNIST and CIFAR-10, and the classification testing accuracy is improved by 0.24%, 1.34% and 0.52% compared with WGAN GP (Gulrajani et al. 2017), respectively. In domain translation, diversity penalty module can help StarGAN (Choi et al. 2018) generate more accurate attention masks and accelarate the convergence process. Finally, we quantitatively evaluate the proposed method with IS and FID on CelebA, CIFAR-10, MNIST and Fashion-MNIST, and the results suggest GAN with diversity penalty module gets much higher IS and lower FID compared with some SOTA GAN architectures.

cs.CV↗