EXPLORE THE ARCHIVE

Yuan Yuan

Publications and source records attributed to Yuan Yuan.

4 recordsLinked to original sources

arXiv2026

Doubly Stochastic Adaptive Neighbors Clustering via the Marcus Mapping

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.

cs.LG↗

arXiv2026

Achieving More with Less: A Tensor-Optimization-Powered Ensemble Method

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.

cs.LG↗

arXiv2026

A Unified Rate-Distortion Perspective on Vector, Product, and Scalar Quantization

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.

cs.LG↗

arXiv2026

Cultural Bias Without a Cultural Self:A Disassociation Study of LLM's Persona and Bias

Language models prompted with cultural personas increasingly stand in for human respondents in cross-cultural research. Their responses separate personas cleanly, and that separation is read as evidence of a cultural point of view. We show that the separation is real, that the point of view is not, and that one criterion tells them apart. A trait is structure internal to one respondent that survives a change of measurement frame; a bias needs only group-specific item means. To test for the first, we represent a single response set as an Item--Dimension matrix and treat its correlation matrix as a point on the manifold of symmetric positive definite matrices. In humans this carries what a trait should: it reproduces across test--retest sessions sharing no items, order or context ($r=0.77$, $N=89$); on public NEO-PI-R data it identifies individuals at up to $76\%$ against a $0.4\%$ chance level ($N=263$); and it predicts GPA ($R^2=0.281$, $p=0.003$) where BigFive aggregates from the same responses predict nothing ($R^2=0.018$). In four frontier LLMs it returns nothing. Persona structure is readable only while every instance shares one item order: give each its own order and separation falls from $94.7\%$ to chance, while realigning instances to \emph{any} shared random order restores it to $82$--$84\%$. Responses generated independently item by item, with no latent structure, reproduce the entire pattern. The cultural signal is a group template, not a property of any instance, and alignment regimes differ only in which stereotype survives on the surface.

stat.ML↗