arXiv subjects
Publications and source records attributed to Yuan Yuan.
On a connected compact Kähler manifold without boundary, we derive a uniform upper bound for each Laplace eigenvalue over all Kähler metrics in a given Kähler class. This provides an affirmative answer to a question of Yau.
This paper investigates a two-machine permutation flow shop in which the second machine is unavailable during one fixed interval $[s,t]$. We consider the non-resumable setting: an operation interrupted by the interval must restart from the beginning after the machine becomes available. The objective is to minimize the makespan. We establish three results. First, we give a polynomial-time $10/7$-approximation algorithm. Second, we develop a pseudopolynomial-time exact dynamic program. Third, we prove that the problem does not admit a fully polynomial-time approximation scheme (FPTAS) unless $\mathrm{P}=\mathrm{NP}$, even when the non-availability interval has unit length. Together, these results characterize a distinctive complexity profile: exact optimization is possible in pseudopolynomial time, whereas the usual route from such an algorithm to an FPTAS is impossible unless $\mathrm{P}=\mathrm{NP}$. They also reveal an approximability separation from the corresponding non-resumable problem with the interval on the first machine.
We consider the two-machine open-shop scheduling problem in which one machine is unavailable during a fixed interval. We study the resumable setting: an operation interrupted by the unavailability interval may resume, without penalty, when the machine becomes available. The objective is to minimize the makespan. Although the problem is NP-hard and several approximation algorithms are known, whether it admits a fully polynomial-time approximation scheme (FPTAS) has remained open for two decades. We resolve this question affirmatively by giving the first FPTAS, thereby strengthening the previously known polynomial-time approximation scheme (PTAS). As an intermediate result, we develop a new pseudo-polynomial dynamic program with seven state dimensions, improving on the ten-dimensional formulation in the literature.
Solving repository-level code tasks requires LLM-based agents to use code search tools to navigate large codebases and identify a small set of relevant files and functions. However, current retrieval tools typically return flat lists of isolated code snippets: such lists can surface relevant files, but provide insufficient structure for agents to distinguish the target function from semantically similar alternatives in the same file. We introduce RepoNav, a lightweight post-retrieval interface that reorganizes retrieved snippets into a file-centered navigation scaffold. By presenting compact structural cues and candidate targets, this scaffold guides on-demand file-structure browsing, helping agents compare sibling symbols before selecting a target function. Across diverse models on LocBench, RepoNav improves function-level localization and narrows the file-to-function gap. Controlled ablations demonstrate that these gains come from structured evidence organization rather than simply exposing additional file structure, and the approach also improves performance on a repository-level question-answering benchmark.
Clustering is a fundamental task in machine learning and data science, and similarity graph-based clustering is an important approach within this domain. Doubly stochastic symmetric similarity graphs provide numerous benefits for clustering problems and downstream tasks, yet learning such graphs remains a significant challenge. Marcus theorem states that a strictly positive symmetric matrix can be transformed into a doubly stochastic symmetric matrix by diagonal matrices. However, in clustering, learning sparse matrices is crucial for computational efficiency. We extend Marcus theorem by proposing the Marcus mapping, which indicates that certain sparse matrices can also be transformed into doubly stochastic symmetric matrices via diagonal matrices. Additionally, we introduce rank constraints into the clustering problem and propose the Doubly Stochastic Adaptive Neighbors Clustering algorithm based on the Marcus Mapping (ANCMM). This ensures that the learned graph naturally divides into the desired number of clusters. We validate the effectiveness of our algorithm through extensive comparisons with state-of-the-art algorithms. Finally, we explore the relationship between the Marcus mapping and optimal transport. We prove that the Marcus mapping solves a specific type of optimal transport problem.
Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to achieve the performance typically obtained with many base learners using only a few. We argue that to achieve this, it is essential to enhance both classification performance and generalization ability during the ensemble process. To increase model accuracy, each weak base learner needs to be more efficiently integrated. It is observed that different base learners exhibit varying levels of accuracy in predicting different classes. To capitalize on this, we introduce confidence tensors $\tilde{\mathbfΘ}$, where $\tilde{\mathbfΘ}_{rst}$ signifies the degree of confidence that the $t$-th base classifier assigns the sample to class $r$ while it actually belongs to class $s$. To the best of our knowledge, this is the first time an evaluation of the performance of base classifiers across different classes has been proposed. The proposed confidence tensor compensates for the strengths and weaknesses of each base classifier in different classes, enabling the method to achieve superior results with a smaller number of base learners. To enhance generalization performance, we design a smooth and partially convex objective function that leverages the concept of margin, making the strong learner more discriminative. Furthermore, it is proved that in the gradient matrix of the loss function, the sum of each column's elements is zero, allowing us to solve a constrained optimization problem using gradient-based methods.
Discrete visual tokenization, predominantly driven by vector, scalar, and product quantization, lacks a unified conceptual framework for understanding quantization tradeoffs. In this paper, we propose a unified rate--distortion perspective on modern discrete visual tokenization. By viewing quantization as lossy compression, we characterize the nominal fixed-length coding rate through token count and codebook size, and quantization error as the distortion. Within this framework, we resolve three central questions. First, we theoretically and empirically show that minimizing distortion, rather than maximizing codebook utilization, is the primary intrinsic objective for reconstruction fidelity, with a direct connection to the STE-induced gradient discrepancy. Second, we establish two critical fairness conditions for intrinsic quantization comparison: controlling latent feature statistics and enforcing identical coding rates. Third, under these conditions, we recover the VQ--PQ--SQ distortion hierarchy in modern visual tokenization and show empirically that modern VQ methods achieve the lowest distortion. This work provides a foundational rate--distortion reframing of modern discrete visual tokenization, resolves ambiguities in quantizer evaluation, and provides a controlled framework for isolating intrinsic quantization effectiveness under fixed-rate constraints.
We construct a bounded pseudoconvex complete Reinhardt domain $Ω$ with smooth boundary in $\mathbb{C}^3$ such that the $\bar\partial$-Neumann operator $N_1$ is compact although $bΩ$ contains an analytic disc and thus also fails Catlin's Property $(P)$ and McNeal's Property $(\tilde P)$. This example solves an open problem on compactness of the $\bar\partial$-Neumann operator in the negative.
Let $U$ be a connected open subset of the complex unit ball $B^n$, $n\geq2$, and let $F_i: U \to Ω_i$ be non-constant holomorphic maps into irreducible bounded symmetric domains. We prove that if $F=(F_1, \cdots, F_m)$ is a holomorphic isometric map from $U$ to the product of $Ω_i$, then every $F_i$ extends to a proper holomorphic isometric embedding up to a positive constant from $B^n$ into $Ω_i$.
This paper is devoted to studying the strong solutions to the vacuum free boundary problem for the isentropic compressible Navier-Stokes equations with density-dependent viscosities under spherical symmetry, which models the motions of isentropic compressible viscous flows surrounded by vacuum. We construct a class of expanding global solutions when the initial data is a small perturbation of the expanding affine solutions for the adiabatic exponent $γ>1$ and the viscosity coefficients proportional to $ρ^γ$, with $ρ$ being the fluid density. In addition, when the viscosity coefficients tend to zero, the perturbed solutions are proved to converge to the solutions to the compressible Euler equations with an explicit converging rate of viscosity coefficients.
Preserving safety alignment during large language models fine-tuning is critical, however, recent studies have demonstrated that even benign fine-tuning data may contain safety-degrading samples that silently undermine safety alignment. Existing approaches typically identify such samples using representations from a single safety-sensitive layer. While this assumption has shown effectiveness in monolingual settings, its validity for multilingual models remains unclear due to potential cross-lingual differences in representation patterns. Through a cross-lingual analysis, we show that sensitive layers are only partially shared across languages, with safety-relevant signals often distributed across multiple layers. Motivated by these observations, we propose MMSAFE, a multi-layer framework for multilingual safety-degrading data identification that captures both shared and language-specific safety signals. Extensive experiments across multiple models, languages, and safety benchmarks demonstrate that MMSAFE reduces the average harmful-response ratio by 60% compared with random filtering and achieves stronger average performance than the strongest single-layer baseline, demonstrating the effectiveness of multi-layer modeling for robust multilingual safety alignment.
Hybrid III-V/silicon quantum-dot microring lasers are compact, energy-efficient O-band sources, but their whispering-gallery cavities are inherently multimode and bidirectional, producing unstable mode hopping that is incompatible with dense wavelength-division multiplexing. We show that an azimuthal grating patterned into the silicon ring - a single lithographic degree of freedom - converts this multimode cavity into a wavelength-addressed, single-mode source. A coupled-mode analysis derives the angular-momentum selection rule from first principles and shows that the inner-wall corrugation replaces the degenerate counter-propagating pair with symmetric and anti-symmetric standing-wave supermodes of unequal radiative loss. At the second-order Bragg condition the anti-symmetric mode is symmetry-protected, yielding a high-quality-factor state at exactly one azimuthal order; finite-element simulations confirm this and identify grating depth as the primary loss-engineering handle. Devices fabricated in-house on a 100 mm silicon-on-insulator platform hold a single longitudinal order with a side-mode suppression ratio of 37.9 dB and continuous, hop-free tuning, while the emission wavelength stays fixed across a factor-of-two change in cavity loading, set lithographically rather than by the gain peak. Because the grating decouples the lasing wavelength from the quantum-dot gain, the detuning becomes a mask-level design variable that sets the temperature of minimum threshold current, reaching 1.95 mA near 50 °C. Combined with side-mode suppression beyond 37 dB and multi-gigahertz direct modulation, these lasers are practical building blocks for cascaded, wavelength-addressed transmitter arrays in data communication and co-packaged optics.
We prove that a possibly unbounded Reinhardt domain in $\mathbb{C}^n$ with smooth boundary and a complete Bergman-Einstein metric is biholomorphic to the complex unit ball. In particular, no unbounded smooth Reinhardt domain admits a complete Bergman-Einstein metric.
Vector Quantization (VQ) underpins modern discrete visual tokenization. However, training quantization modules for state-of-the-art VQ-based models requires significant computational resources which, in practice, all but prevents the development of novel, cutting-edge VQ techniques under resource constraints. To address this limitation, we propose {\bf VQ-Transplant}, a simple framework that enables plug-and-play integration of new VQ modules into frozen, pre-trained tokenizers by replacing their native VQ modules. Crucially, the proposed transplantation process preserves all encoder-decoder parameters, obviating the need for costly end-to-end retraining when modifying the quantization method. To mitigate decoder-quantization mismatch, we introduce a lightweight decoder adaptation strategy (trained for only 5 epochs on ImageNet-1k) to align feature priors with the new quantization space. In our empirical evaluation, we find that VQ-Transplant allows obtaining near state-of-the-art reconstruction fidelity for industry-level models like VAR while reducing the training cost by 95\%. VQ-Transplant democratizes quantization research by enabling resource-efficient integration of novel VQ techniques while matching industry-level reconstruction performance.
Intra-tumoural heterogeneity (ITH) reflects spatial variation in tumour biology and is an important determinant of tumour behaviour, prognosis, and treatment response. Radiomics and deep learning have shown promise for tumour classification from multiparametric MRI (mp-MRI), but radiomics relies on handcrafted features, while most deep learning methods use whole-tumour representations or manually defined sub-regions, limiting scalable modelling of tumour heterogeneity. We propose a Heterogeneity-Aware Deep Learning Classification (HA-DLC) framework that explicitly models imaging-derived tumour sub-regions for lesion-type diagnosis and molecular-status prediction. HA-DLC consists of: (1) a Heterogeneous Sub-region Generation (HSG) module that produces initial pseudo-labelled sub-regions via unsupervised clustering, followed by Cross-Patient Sub-region Alignment (CPSA), which maps cluster-derived regions to a shared label space using soft assignments; and (2) a Dual-Stream Feature Extraction (DSFE) module that integrates local heterogeneity-aware features with global tumour representations. Given the initial clustering masks, CPSA, segmentation, feature extraction, and classification are jointly optimized end-to-end using soft-target segmentation and classification objectives. We evaluate HA-DLC on the LLD-MMRI2023 liver lesion dataset and the RSNA-ASNR-MICCAI 2021 Radiogenomic Brain Tumour dataset. HA-DLC consistently outperforms state-of-the-art radiomics and deep learning baselines, demonstrating the value of cross-patient sub-region alignment and dual-stream heterogeneity modelling for tumour classification from mp-MRI.
We study holomorphic maps between complex manifolds that preserve the Bergman metric up to a positive constant. In the equal dimensional case, either the source is a Stein manifold and the target is a bounded domain in the complex Euclidean space, or the source is a bounded pseudoconvex domain and the target is a complex manifold, holomorphic Bergman isometry is a biholomorphism onto the complement of a relatively closed locally pluripolar set, and the constant is necessarily one. These include the bounded domains in the complex Euclidean space as special cases. Some applications to curvature-preserving maps are obtained. We further prove the rigidity result for local holomorphic Bergman isometries into Cartesian product of strongly pseudoconvex domains, with applications to finite analytic and modular correspondences.
Large Language Models (LLMs) have achieved remarkable progress in code generation, yet ensuring correctness in complex, repository-level tasks remains challenging. Existing approaches often use generated tests as static post-hoc validators, which limits their ability to guide implementation and may introduce misleading feedback when the tests themselves are incomplete or incorrect. In this paper, we introduce TDD-Agent, which operationalizes the test-driven development paradigm for code generation. TDD-Agent first prompts the model to generate executable tests, encouraging it to clarify expected behaviors before implementation, and then performs iterative dual-track refinement over both the generated code and tests using execution feedback. We first isolate the effect of test-first reasoning through a prompt variant TDD-prompt on LiveCodeBench, where it consistently improves upon reasoning-based prompting baselines. Building on this finding, we evaluate the full TDD-Agent framework on RepoEval, a repository-level benchmark, and show that it consistently outperforms retrieval-based and agent-based baselines. Additional analyses show that iterative refinement improves not only code correctness but also the effectiveness of the generated tests, yielding higher pass rates, coverage, and mutation scores, suggesting that tests can serve as evolving reasoning artifacts rather than fixed validators. Our source code is available at https://anonymous.4open.science/r/TDD-Agent-Framework-6370/.
The effectiveness of modern visual representation learning and autoregressive models critically depends on vector quantization (VQ), which discretizes continuous feature representations using a learnable codebook. Despite its widespread use, existing VQ methods often suffer from training instability and codebook collapse, arising from gradient mismatch induced by the straight-through estimator and the under-utilization of code vectors. In this work, we show that both issues can be traced to a fundamental mismatch between the distributions of feature vectors and code vectors, leading to inefficient representation and information loss. Building on this observation, we propose a distributional matching framework for vector quantization. We introduce principled criteria for desirable VQ behavior and demonstrate through theoretical analysis and empirical evaluation that aligning feature and code vector distributions provides a unifying mechanism for mitigating training instability and codebook collapse. We instantiate this framework using a Wasserstein-based objective with an efficient closed-form under a mild Gaussian approximation, and further show that a nonparametric alternative based on maximum mean discrepancy yields comparable performance. Extensive experiments on visual tokenization benchmarks support the effectiveness and robustness of the proposed approach.