Hanzhen Zhao

Pengyun Yue, Hanzhen Zhao, Cong Fang et al.

With distributed machine learning being a prominent technique for large-scale machine learning tasks, communication complexity has become a major bottleneck for speeding up training and scaling up machine numbers. In this paper, we propose a new technique named Common randOm REconstruction(CORE), which can be used to compress the information transmitted between machines in order to reduce communication complexity without other strict conditions. Especially, our technique CORE projects the vector-valued information to a low-dimensional one through common random vectors and reconstructs the information with the same random noises after communication. We apply CORE to two distributed tasks, respectively convex optimization on linear models and generic non-convex optimization, and design new distributed algorithms, which achieve provably lower communication complexities. For example, we show for linear models CORE-based algorithm can encode the gradient vector to $\mathcal{O}(1)$-bits (against $\mathcal{O}(d)$), with the convergence rate not worse, preceding the existing results.

Xiaomin Yu, Yi Xin, Yuhui Zhang et al.

Despite the success of multimodal contrastive learning in aligning visual and linguistic representations, a persistent geometric anomaly, the Modality Gap, remains: embeddings of distinct modalities expressing identical semantics occupy systematically offset regions. Prior approaches to bridge this gap are largely limited by oversimplified isotropic assumptions, hindering their application in large-scale scenarios. In this paper, we address these limitations by precisely characterizing the geometric shape of the modality gap and leveraging it for efficient model scaling. First, we propose the Fixed-frame Modality Gap Theory, which decomposes the modality gap within a frozen reference frame into stable biases and anisotropic residuals. Guided by this precise modeling, we introduce ReAlign, a training-free modality alignment strategy. Utilizing statistics from massive unpaired data, ReAlign aligns text representation into the image representation distribution via a three-step process comprising Anchor, Trace, and Centroid Alignment, thereby explicitly rectifying geometric misalignment. Building on ReAlign, we propose ReVision, a scalable training paradigm for Multimodal Large Language Models~(MLLMs). ReVision integrates ReAlign into the pretraining stage, enabling the model to learn the distribution of visual representations from unpaired text before visual instruction tuning, without the need for large-scale, high-quality image-text pairs. Our framework demonstrates that statistically aligned unpaired data can effectively substitute for expensive image-text pairs, offering a robust path for the efficient scaling of MLLMs.

Xiaomin Yu, Yijiang Li, Yuhui Zhang et al.

Training multimodal large language models has long been limited by the scarcity of high-quality paired multimodal data. Recent studies show that the shared representation space of pretrained multimodal contrastive models can serve as a bridge, enabling models to perform multimodal training with unimodal data. However, the key premise of this paradigm remains insufficiently understood: can representations from different modalities be reliably interchanged? The core obstacle lies in the persistent Modality Gap in the shared space. In this work, we revisit the geometric nature of the modality gap. We find that modality representations already share compatible dominant semantic geometry. What truly hinders modality interchangeability is not a simple global shift, but an anisotropic residual structure concentrated along a small number of dominant directions. Based on this finding, we further propose the principle of anisotropic modality gap alignment: effective modality alignment should align with the target-modality distribution while preserving the semantic structure of the source modality. Guided by this principle, we propose an anisotropic geometric correction framework, AnisoAlign, for unpaired modality alignment. This framework leverages the internal geometric prior of the target modality and performs bounded correction on source-modality representations, thereby constructing substitute representations in the target modality. Experiments confirm its benefits in both geometric diagnostics and text-only MLLM training. Overall, this work recasts the modality gap from an empirical observation into a correctable, structured geometric phenomenon and provides a new representation alignment perspective for training multimodal models with unimodal data.

Yuanshi Liu, Hanzhen Zhao, Yang Xu et al.

Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/μ})$ gradient complexity for minimizing an $L$-smooth $μ$-strongly convex objective. However, an ideal algorithm would adapt to the explicit complexity of a particular objective function and incur faster rates for simpler problems, triggering our reconsideration of two defeats of existing optimization modeling and analysis. (i) The worst-case optimality is neither the instance optimality nor such one in reality. (ii) Traditional $L$-smoothness condition may not be the primary abstraction/characterization for modern practical problems. In this paper, we open up a new way to design and analyze gradient-based algorithms with direct applications in machine learning, including linear regression and beyond. We introduce two factors $(α, τ_α)$ to refine the description of the degenerated condition of the optimization problems based on the observation that the singular values of Hessian often drop sharply. We design adaptive algorithms that solve simpler problems without pre-known knowledge with reduced gradient or analogous oracle accesses. The algorithms also improve the state-of-art complexities for several problems in machine learning, thereby solving the open problem of how to design faster algorithms in light of the known complexity lower bounds. Specially, with the $\mathcal{O}(1)$-nuclear norm bounded, we achieve an optimal $\tilde{\mathcal{O}}(μ^{-1/3})$ (v.s. $\tilde{\mathcal{O}}(μ^{-1/2})$) gradient complexity for linear regression. We hope this work could invoke the rethinking for understanding the difficulty of modern problems in optimization.

Shihong Ding, Haihan Zhang, Hanzhen Zhao et al.

In machine learning, the scaling law describes how the model performance improves with the model and data size scaling up. From a learning theory perspective, this class of results establishes upper and lower generalization bounds for a specific learning algorithm. Here, the exact algorithm running using a specific model parameterization often offers a crucial implicit regularization effect, leading to good generalization. To characterize the scaling law, previous theoretical studies mainly focus on linear models, whereas, feature learning, a notable process that contributes to the remarkable empirical success of neural networks, is regretfully vacant. This paper studies the scaling law over a linear regression with the model being quadratically parameterized. We consider infinitely dimensional data and slope ground truth, both signals exhibiting certain power-law decay rates. We study convergence rates for Stochastic Gradient Descent and demonstrate the learning rates for variables will automatically adapt to the ground truth. As a result, in the canonical linear regression, we provide explicit separations for generalization curves between SGD with and without feature learning, and the information-theoretical lower bound that is agnostic to parametrization method and the algorithm. Our analysis for decaying ground truth provides a new characterization for the learning dynamic of the model.

Zhennan Chen, Junwei Zhu, Xu Chen et al.

Diffusion models face a fundamental trade-off between generation quality and computational efficiency. Latent Diffusion Models (LDMs) offer an efficient solution but suffer from potential information loss and non-end-to-end training. In contrast, existing pixel space models bypass VAEs but are computationally prohibitive for high-resolution synthesis. To resolve this dilemma, we propose DiP, an efficient pixel space diffusion framework. DiP decouples generation into a global and a local stage: a Diffusion Transformer (DiT) backbone operates on large patches for efficient global structure construction, while a co-trained lightweight Patch Detailer Head leverages contextual features to restore fine-grained local details. This synergistic design achieves computational efficiency comparable to LDMs without relying on a VAE. DiP is accomplished with up to 10$\times$ faster inference speeds than previous method while increasing the total number of parameters by only 0.3%, and achieves an 1.79 FID score on ImageNet 256$\times$256.