Zexuan Wang

Qipeng Zhan, Zhuoping Zhou, Zexuan Wang et al.

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.

Zexuan Wang, Chenghao Yang, Yingqi Que et al.

Real-world autonomous planning requires coordinating tightly coupled constraints where a single decision dictates the feasibility of all subsequent actions. However, existing benchmarks predominantly feature loosely coupled constraints solvable through local greedy decisions and rely on idealized data, failing to capture the complexity of extracting parameters from dynamic web environments. We introduce \textbf{WorldTravel}, a benchmark comprising 150 real-world travel scenarios across 5 cities that demand navigating an average of 15+ interdependent temporal and logical constraints. To evaluate agents in realistic deployments, we develop \textbf{WorldTravel-Webscape}, a multi-modal environment featuring over 2,000 rendered webpages where agents must perceive constraint parameters directly from visual layouts to inform their planning. Our evaluation of 10 frontier models reveals a significant performance collapse: even the state-of-the-art GPT-5.2 achieves only 32.67\% feasibility in text-only settings, which plummets to 19.33\% in multi-modal environments. We identify a critical Perception-Action Gap and a Planning Horizon threshold at approximately 10 constraints where model reasoning consistently fails, suggesting that perception and reasoning remain independent bottlenecks. These findings underscore the need for next-generation agents that unify high-fidelity visual perception with long-horizon reasoning to handle brittle real-world logistics.

Bojian Hou, Zhanliang Wang, Zhuoping Zhou et al.

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.

Qipeng Zhan, Zhuoping Zhou, Zexuan Wang et al.

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.

Qipeng Zhan, Zhuoping Zhou, Zexuan Wang et al.

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.

Songyang Chen, Yu Liu, Lei Zou et al.

Unsupervised graph alignment finds the node correspondence between a pair of attributed graphs by only exploiting graph structure and node features. One category of recent studies first computes the node representation and then matches nodes with the largest embedding-based similarity, while the other category reduces the problem to optimal transport (OT) via Gromov-Wasserstein learning. However, it remains largely unexplored in the model expressiveness, as well as how theoretical expressivity impacts prediction accuracy. We investigate the model expressiveness from two aspects. First, we characterize the model's discriminative power in distinguishing matched and unmatched node pairs across two graphs. Second, we study the model's capability of guaranteeing node matching properties such as one-to-one matching and mutual alignment. Motivated by our theoretical analysis, we put forward a hybrid approach named CombAlign with stronger expressive power. Specifically, we enable cross-dimensional feature interaction for OT-based learning and propose an embedding-based method inspired by the Weisfeiler-Lehman test. We also apply non-uniform marginals obtained from the embedding-based modules to OT as priors for more expressiveness. Based on that, we propose a traditional algorithm-based refinement, which combines our OT and embedding-based predictions using the ensemble learning strategy and reduces the problem to maximum weight matching. With carefully designed edge weights, we ensure those matching properties and further enhance prediction accuracy. By extensive experiments, we demonstrate a significant improvement of 14.5% in alignment accuracy compared to state-of-the-art approaches and confirm the soundness of our theoretical analysis.