arXiv subjects

Zhuoping Zhou

Publications and source records attributed to Zhuoping Zhou.

8 recordsLinked to original sources

arXiv2026

Query-Aware Flow Diffusion for Graph-Based RAG with Retrieval Guarantees

Graph-based Retrieval-Augmented Generation (RAG) systems leverage interconnected knowledge structures to capture complex relationships that flat retrieval struggles with, enabling multi-hop reasoning. Yet most existing graph-based methods suffer from (i) heuristic designs lacking theoretical guarantees for subgraph quality or relevance and/or (ii) the use of static exploration strategies that ignore the query's holistic meaning, retrieving neighborhoods or communities regardless of intent. We propose Query-Aware Flow Diffusion RAG (QAFD-RAG), a training-free framework that dynamically adapts graph traversal to each query's holistic semantics. The central innovation is query-aware traversal: during graph exploration, edges are dynamically weighted by how well their endpoints align with the query's embedding, guiding flow along semantically relevant paths while avoiding structurally connected but irrelevant regions. These query-specific reasoning subgraphs enable the first statistical guarantees for query-aware graph retrieval, showing that QAFD-RAG recovers relevant subgraphs with high probability under mild signal-to-noise conditions. The algorithm converges exponentially fast, with complexity scaling with the retrieved subgraph size rather than the full graph. Experiments on question answering and text-to-SQL tasks demonstrate consistent improvements over state-of-the-art graph-based RAG methods.

cs.IR↗

arXiv2026

Generative Cross-Entropy: A Strictly Proper Loss for Data-Efficient Classification

Cross-entropy (CE) is the default training loss for supervised classification, but its sample efficiency is limited when labels are scarce. Existing remedies primarily act on the data side, via augmentation, synthesis, or transfer from pretrained models; the training objective itself is rarely revisited. We revisit it here. Drawing on the classical observation that generative classifiers reach their asymptotic error with fewer samples than discriminative ones, we propose Generative Cross-Entropy (GenCE), a drop-in replacement for CE that introduces a generative learning principle into a standard discriminative network without altering the architecture or fitting a separate density model. GenCE follows from a Bayesian rewrite of the class-conditional likelihood and, in the mini-batch approximation, reduces to normalizing each sample's softmax score against the model's predictions on the batch, coupling the training signal across examples sharing a class. We extend the proper-scoring-rule framework to such non-local losses and prove that GenCE is strictly proper under a mild completeness condition: its population risk is uniquely minimized at the true posterior. Across three datasets, on two architectures and in both balanced small-data and class-imbalanced regimes, GenCE outperforms CE and other widely used losses, while also producing better-calibrated probabilities and stronger out-of-distribution detection.

cs.LG↗

arXiv2026

Bi-Lipschitz Autoencoder With Injectivity Guarantee

Autoencoders are widely used for dimensionality reduction, based on the assumption that high-dimensional data lies on low-dimensional manifolds. Regularized autoencoders aim to preserve manifold geometry during dimensionality reduction, but existing approaches often suffer from non-injective mappings and overly rigid constraints that limit their effectiveness and robustness. In this work, we identify encoder non-injectivity as a core bottleneck that leads to poor convergence and distorted latent representations. To ensure robustness across data distributions, we formalize the concept of admissible regularization and provide sufficient conditions for its satisfaction. In this work, we propose the Bi-Lipschitz Autoencoder (BLAE), which introduces two key innovations: (1) an injective regularization scheme based on a separation criterion to eliminate pathological local minima, and (2) a bi-Lipschitz relaxation that preserves geometry and exhibits robustness to data distribution drift. Empirical results on diverse datasets show that BLAE consistently outperforms existing methods in preserving manifold structure while remaining resilient to sampling sparsity and distribution shifts. Code is available at https://github.com/qipengz/BLAE.

cs.LG↗

arXiv2026

PCAE: Learning Ordered Representations in Latent Space for Intrinsic Dimension Estimation via Principal Component Autoencoder

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by incorporating non-uniform $\ell_2$ regularization or by adjusting the loss function. However, these approaches become insufficient in the nonlinear setting, as the remaining variance cannot be properly captured independently of the nonlinear mapping. In this work, we propose a novel autoencoder framework that integrates non-uniform variance regularization with an isometric constraint. This design serves as a natural generalization of PCA, enabling the model to preserve key advantages, such as ordered representations and variance retention, while remaining effective for nonlinear dimensionality reduction tasks.

cs.LG↗

arXiv2025

Multi-Scale Geometric Autoencoder

Autoencoders have emerged as powerful models for visualization and dimensionality reduction based on the fundamental assumption that high-dimensional data is generated from a low-dimensional manifold. A critical challenge in autoencoder design is to preserve the geometric structure of data in the latent space, with existing approaches typically focusing on either global or local geometric properties separately. Global approaches often encounter errors in distance approximation that accumulate, while local methods frequently converge to suboptimal solutions that distort large-scale relationships. We propose Multi-Scale Geometric Autoencoder (MAE), which introduces an asymmetric architecture that simultaneously preserves both scales of the geometric structure by applying global distance constraints to the encoder and local geometric constraints to the decoder. Through theoretical analysis, we establish that this asymmetric design aligns naturally with the distinct roles of the encoder and decoder components. Our comprehensive experiments on both synthetic manifolds and real-world datasets demonstrate that MAE consistently outperforms existing methods across various evaluation metrics.

cs.LG↗

arXiv2025

Fair CCA for Fair Representation Learning: An ADNI Study

Canonical correlation analysis (CCA) is a technique for finding correlations between different data modalities and learning low-dimensional representations. As fairness becomes crucial in machine learning, fair CCA has gained attention. However, previous approaches often overlook the impact on downstream classification tasks, limiting applicability. We propose a novel fair CCA method for fair representation learning, ensuring the projected features are independent of sensitive attributes, thus enhancing fairness without compromising accuracy. We validate our method on synthetic data and real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), demonstrating its ability to maintain high correlation analysis performance while improving fairness in classification tasks. Our work enables fair machine learning in neuroimaging studies where unbiased analysis is essential. Code is available in https://github.com/ZhanliangAaronWang/FR-CCA-ADNI.

cs.LG↗

arXiv2024

Fairness-Aware Estimation of Graphical Models

This paper examines the issue of fairness in the estimation of graphical models (GMs), particularly Gaussian, Covariance, and Ising models. These models play a vital role in understanding complex relationships in high-dimensional data. However, standard GMs can result in biased outcomes, especially when the underlying data involves sensitive characteristics or protected groups. To address this, we introduce a comprehensive framework designed to reduce bias in the estimation of GMs related to protected attributes. Our approach involves the integration of the pairwise graph disparity error and a tailored loss function into a nonsmooth multi-objective optimization problem, striving to achieve fairness across different sensitive groups while maintaining the effectiveness of the GMs. Experimental evaluations on synthetic and real-world datasets demonstrate that our framework effectively mitigates bias without undermining GMs' performance.

cs.LG↗

arXiv2023

Fair Canonical Correlation Analysis

This paper investigates fairness and bias in Canonical Correlation Analysis (CCA), a widely used statistical technique for examining the relationship between two sets of variables. We present a framework that alleviates unfairness by minimizing the correlation disparity error associated with protected attributes. Our approach enables CCA to learn global projection matrices from all data points while ensuring that these matrices yield comparable correlation levels to group-specific projection matrices. Experimental evaluation on both synthetic and real-world datasets demonstrates the efficacy of our method in reducing correlation disparity error without compromising CCA accuracy.

cs.LG↗