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Boyang Zhang

Boyang Zhang contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence math.OC Methodology

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preprint2026arXiv

A Qualitative Test-Risk Mechanism for Scaling Behavior in Normalized Residual Networks

The scaling behavior, in which test performance often improves as model size and data increase, is a central empirical phenomenon in modern deep learning, yet its theoretical basis remains incomplete. In this paper, we study depth expansion in normalized residual networks: starting from a trained model in an old hypothesis class, we insert a new residual block at an intermediate layer and ask when such an expansion can yield a provable improvement in test risk. We develop a unified framework that decomposes this question into representational gain, optimization gain, and generalization transfer. First, under a first-order descent condition near zero initialization, we prove that the expanded hypothesis class contains an auxiliary jumpboard model with strictly smaller population risk than the original model. Second, under norm control tailored to post-normalized residual architectures, we establish a norm-based Rademacher complexity bound for the expanded model class. These ingredients lead to two complementary test-risk guarantees: one route passes through population risk and is tighter when a positive population margin is available, while the other works directly at the train/test level, avoids Hoeffding transfer, and is more robust in degenerate regimes. Together, these results provide a theorem-driven mechanism under which residual depth expansion can improve test performance in normalized residual networks. More broadly, they suggest that scaling is inherently joint: depth creates new improving directions, width enhances the finite-sample observability of weak signals, and data determines whether the statistical cost of expansion can be controlled.

preprint2026arXiv

MoE-DisCo:Low Economy Cost Training Mixture-of-Experts Models

Training large-scale Mixture-of-Experts (MoE) models typically requires high-memory, high-bandwidth GPUs (e.g., A100), and their high cost has become a major barrier to large-model training. In contrast, affordable hardware is low-cost but constrained by memory capacity and bandwidth, making it unsuitable for direct LLM training. To address this, we propose MoE-DisCo (Mixture-of-Experts with Disentangled Clustering and Coordination), a staged training framework. MoE-DisCo decomposes the MoE model into multiple dense submodels, each consisting of a shared backbone and a single expert, and partitions the training data into subsets using unsupervised clustering. Each submodel is trained independently and in parallel on its assigned data subset using low-cost devices, without any inter-device communication. Subsequently, all experts are integrated into a complete MoE model and fine-tuned globally for a short period on high-memory, high-bandwidth GPUs. Experiments show that our method matches or even surpasses full-parameter training in performance across multiple downstream tasks, loss function, and perplexity (PPL), while reducing training cost by 47.6 percent to 69.5 percent on Qwen1.5-MoE-2.7B and Llama-MoE-3.5B across different datasets.

preprint2026arXiv

Proximal-Based Generative Modeling for Bayesian Inverse Problems

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we propose a novel proximal-based generative modeling (PGM) framework that rigorously circumvents explicit likelihood evaluation. Our framework is built upon a theoretical equivalence between Gaussian convolution in diffusion processes and Moreau-Yosida regularization in nonsmooth optimization. This enables a new sampling mechanism driven by the proposed Moreau score, which admits a closed-form expression via proximal operators. Moreover, we introduce Moreau score matching to learn the proximal operators that rely solely on samples drawn from the prior distribution. Theoretically, PGM eliminates the early-stopping bias inherent in the score-based diffusion model and achieves non-asymptotic convergence. Experiments demonstrate that PGM significantly surpasses state-of-the-art methods in reconstruction quality and sampling time.

preprint2024arXiv

Contrastive linear regression

Contrastive dimension reduction methods have been developed for case-control study data to identify variation that is enriched in the foreground (case) data X relative to the background (control) data Y. Here, we develop contrastive regression for the setting when there is a response variable r associated with each foreground observation. This situation occurs frequently when, for example, the unaffected controls do not have a disease grade or intervention dosage but the affected cases have a disease grade or intervention dosage, as in autism severity, solid tumors stages, polyp sizes, or warfarin dosages. Our contrastive regression model captures shared low-dimensional variation between the predictors in the cases and control groups, and then explains the case-specific response variables through the variance that remains in the predictors after shared variation is removed. We show that, in one single-nucleus RNA sequencing dataset on autism severity in postmortem brain samples from donors with and without autism and in another single-cell RNA sequencing dataset on cellular differentiation in chronic rhinosinusitis with and without nasal polyps, our contrastive linear regression performs feature ranking and identifies biologically-informative predictors associated with response that cannot be identified using other approaches

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