Wenxuan Zhong

Luyang Fang, Yongkai Chen, Jiazhang Cai et al.

Knowledge distillation is a powerful method for model compression, enabling the efficient deployment of complex deep learning models (teachers), including large language models. However, its underlying statistical mechanisms remain unclear, and uncertainty evaluation is often overlooked, especially in real-world scenarios requiring diverse teacher expertise. To address these challenges, we introduce \textit{Multi-Teacher Bayesian Knowledge Distillation} (MT-BKD), where a distilled student model learns from multiple teachers within the Bayesian framework. Our approach leverages Bayesian inference to capture inherent uncertainty in the distillation process. We introduce a teacher-informed prior, integrating external knowledge from teacher models and task-specific training data, offering better generalization, robustness, and scalability. Additionally, an entropy-based weighting mechanism adaptively adjusts each teacher's influence, allowing the student to combine multiple sources of expertise effectively. MT-BKD enhances the interpretability of the student model's learning process, improves predictive accuracy, and provides uncertainty quantification. We validate MT-BKD on both synthetic and real-world tasks, including protein subcellular location prediction and image classification. Our experiments show improved performance and robust uncertainty quantification, highlighting the strengths of our MT-BKD framework.

Yongkai Chen, Wenxuan Zhong, Ping Ma

Deep learning excels at prediction but often lacks finite-sample guarantees and calibrated uncertainty; RKHS (Reproducing Kernel Hilbert Space)-based methods provide those guarantees but struggle to adapt in high dimensions. We propose Wahkon, a deep RKHS superposition network that unifies Kolmogorov's superposition principle with RKHS regularization in the smoothing-spline tradition of Wahba. This yields a finite-dimensional deep representer theorem that makes training tractable and provides explicit layerwise complexity control. We show the penalized estimator is exactly the MAP (maximum a posteriori) estimate under a hierarchical Gaussian-process prior, extending the spline/GP duality to deep compositions. Using metric-entropy arguments, we establish minimax-optimal convergence rates under mild smoothness and clarify how depth and width trade off with regularity. Empirically, Wahkon outperforms multilayer perceptrons, Neural Tangent Kernels, and Kolmogorov--Arnold Networks across simulation benchmarks and a single-cell CITE-seq study. By unifying Kolmogorov's superposition principle with RKHS regularization, Wahkon delivers accuracy, interpretability, and statistical rigor in a single framework.

Huimin Cheng, Xiaowei Yu, Shushan Wu et al.

Medical images exhibit latent anatomical groupings, such as organs, tissues, and pathological regions, that standard Vision Transformers (ViTs) fail to exploit. While recent work like SBM-Transformer attempts to incorporate such structures through stochastic binary masking, they suffer from non-differentiability, training instability, and the inability to model complex community structure. We present DCMM-Transformer, a novel ViT architecture for medical image analysis that incorporates a Degree-Corrected Mixed-Membership (DCMM) model as an additive bias in self-attention. Unlike prior approaches that rely on multiplicative masking and binary sampling, our method introduces community structure and degree heterogeneity in a fully differentiable and interpretable manner. Comprehensive experiments across diverse medical imaging datasets, including brain, chest, breast, and ocular modalities, demonstrate the superior performance and generalizability of the proposed approach. Furthermore, the learned group structure and structured attention modulation substantially enhance interpretability by yielding attention maps that are anatomically meaningful and semantically coherent.

Luyang Fang, Haoran Lu, Yongkai Chen et al.

As machine learning models and datasets continue to grow, developing complex models has become increasingly computationally demanding. Knowledge distillation reduces deployment cost by compressing a large, well-trained teacher model into a compact student model, but it does not address settings where constructing the teacher itself is the bottleneck. Motivated by this challenge, we introduce Knowledge Cascade (KCas), a reverse knowledge distillation framework that uses information from a small, inexpensive student model to guide the development of a more complex teacher model. Although this direction is counterintuitive because the teacher typically has greater representational capacity, we show that student-to-teacher transfer can be principled when supported by statistical scaling relationships. We first develop KCas for nonparametric multivariate functional estimation in reproducing kernel Hilbert spaces via smoothing splines, where selecting multiple smoothing parameters is a major computational bottleneck. KCas transfers student-selected smoothing parameters to the full-sample regime through asymptotic scaling laws, substantially reducing computational cost for high-dimensional and large-scale datasets while retaining theoretical guarantees. Beyond smoothing splines, we illustrate the same principle through kernel density estimation and deep learning hyperparameter transfer. Simulations and real-data experiments show that KCas achieves substantial computational savings while maintaining strong statistical performance, and can sometimes outperform the corresponding full-sample procedure.

Yingchuan Zhang, Terry Ma, Wenxuan Zhong et al.

Large language models (LLMs) achieve higher accuracy on challenging reasoning tasks by scaling test-time compute through multiple trajectory sampling. However, standard aggregation methods like majority voting or individual confidence-based filtering face a fundamental "blind spot": they evaluate each trace in isolation. As problems scale in difficulty, models often generate hallucinated paths that exhibit misleadingly high confidence, causing the true solution to be suppressed by a narrow margin in traditional voting. We ask: can we enable traces to "peer-review" each other to resolve these near-miss errors? We introduce Packet-Conditioned Revision (PACER), a training-free, inference-only framework that enables reasoning traces to revise their conclusions through a structured coordination step. After a preliminary screening of generated traces, PACER constructs a compact consensus packet containing (i) unique candidate answers, (ii) their aggregated confidence scores, and (iii) representative reasoning summaries for each candidate answer. Individual traces then perform a targeted self-review conditioned on this packet, allowing them to identify specific logical junctions where they diverged from the broader consensus and pivot if their original reasoning is found to be flawed. Final predictions are obtained via confidence-weighted voting over these revised trajectories. On challenging competitive math benchmarks such as AIME and BRUMO, PACER matches or exceeds the accuracy of 256-sample majority voting, significantly outperforming raw ensemble baselines by transforming simple consensus into a collaborative logical refinement process.

Cheng Meng, Yuan Ke, Jingyi Zhang et al.

This paper studies the estimation of large-scale optimal transport maps (OTM), which is a well-known challenging problem owing to the curse of dimensionality. Existing literature approximates the large-scale OTM by a series of one-dimensional OTM problems through iterative random projection. Such methods, however, suffer from slow or none convergence in practice due to the nature of randomly selected projection directions. Instead, we propose an estimation method of large-scale OTM by combining the idea of projection pursuit regression and sufficient dimension reduction. The proposed method, named projection pursuit Monge map (PPMM), adaptively selects the most ``informative'' projection direction in each iteration. We theoretically show the proposed dimension reduction method can consistently estimate the most ``informative'' projection direction in each iteration. Furthermore, the PPMM algorithm weakly convergences to the target large-scale OTM in a reasonable number of steps. Empirically, PPMM is computationally easy and converges fast. We assess its finite sample performance through the applications of Wasserstein distance estimation and generative models.

Jingyi Zhang, Huolan Zhu, Yongkai Chen et al.

Background: Extensive clinical evidence suggests that a preventive screening of coronary heart disease (CHD) at an earlier stage can greatly reduce the mortality rate. We use 64 two-dimensional speckle tracking echocardiography (2D-STE) features and seven clinical features to predict whether one has CHD. Methods: We develop a machine learning approach that integrates a number of popular classification methods together by model stacking, and generalize the traditional stacking method to a two-step stacking method to improve the diagnostic performance. Results: By borrowing strengths from multiple classification models through the proposed method, we improve the CHD classification accuracy from around 70% to 87.7% on the testing set. The sensitivity of the proposed method is 0.903 and the specificity is 0.843, with an AUC of 0.904, which is significantly higher than those of the individual classification models. Conclusions: Our work lays a foundation for the deployment of speckle tracking echocardiography-based screening tools for coronary heart disease.

Cheng Meng, Jun Yu, Jingyi Zhang et al.

Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory performance for the categorical response, especially for the binary-response. To address this issue, we propose a novel estimation method of sufficient dimension reduction subspace (SDR subspace) using optimal transport. The proposed method, named principal optimal transport direction (POTD), estimates the basis of the SDR subspace using the principal directions of the optimal transport coupling between the data respecting different response categories. The proposed method also reveals the relationship among three seemingly irrelevant topics, i.e., sufficient dimension reduction, support vector machine, and optimal transport. We study the asymptotic properties of POTD and show that in the cases when the class labels contain no error, POTD estimates the SDR subspace exclusively. Empirical studies show POTD outperforms most of the state-of-the-art linear dimension reduction methods.

Jingyi Zhang, Wenxuan Zhong, Ping Ma

Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a remarkable proliferation of modern data science applications. To meet the big data challenges, various computational tools have been developed in the recent decade to accelerate the computation for optimal transport methods. In this review, we present some cutting-edge computational optimal transport methods with a focus on the regularization-based methods and the projection-based methods. We discuss their real-world applications in biomedical research.

Xin Xing, Zuofeng Shang, Pang Du et al.

We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability density comparison is equivalent to testing the presence/absence of interactions. We propose a penalized likelihood ratio test for such interaction testing and show that the test statistic is asymptotically chi-square distributed under the null hypothesis. Furthermore, we derive a sharp minimax testing rate based on the Bernstein width for nonparametric two-sample tests and show that our proposed test statistics is minimax optimal. In addition, a data-adaptive tuning criterion is developed to choose the penalty parameter. Simulations and real applications demonstrate that the proposed test outperforms the conventional approaches under various scenarios.