arXiv subjects

Runzhe Zhang

Publications and source records attributed to Runzhe Zhang.

4 recordsLinked to original sources

arXiv2026

FlowLM: Few-Step Language Modeling via Diffusion-to-Flow Adaptation

We present FlowLM, a flow matching language model transformed from pre-trained diffusion language models via efficient fine-tuning. By re-aligning the curved sampling trajectories of diffusion models into straight-line flows, FlowLM enables high quality few-step generation that rivals or even outperforms the quality of 2,000-step diffusion sampling with very few training epochs. Remarkably, finetuned FlowLM reaches performance saturation with only half as many training epochs as training from scratch, both approaches greatly outperforming the original diffusion model, thereby validating our method. Furthermore, we validate a more effective training objective for flow matching: predicting clean data to consistently guide the sampling process towards the true data distribution. Empirical results demonstrate that our approach is highly effective for high-quality, few-step text generation.

cs.CL↗

arXiv2025

Boundedness of multilinear Littlewood--Paley operators with convolution type kernels on products of BMO spaces

In this paper, the authors establish the existence and boundedness of multilinear Littlewood--Paley operators on products of BMO spaces, including the multilinear $g$-function, multilinear Lusin's area integral and multilinear $g^{\ast}_{\lambda}$-function. The authors prove that if the above multilinear operators are finite for a single point, then they are finite almost everywhere. Moreover, it is shown that these multilinear operators are bounded from $\mathrm{BMO}(\mathbb R^n)\times\cdots\times \mathrm{BMO}(\mathbb R^n)$ into $\mathrm{BLO}(\mathbb R^n)$ (the space of functions with bounded lower oscillation), which is a proper subspace of $\mathrm{BMO}(\mathbb R^n)$ (the space of functions with bounded mean oscillation). The corresponding estimates for multilinear Littlewood--Paley operators with non-convolution type kernels are also discussed.

math.CA↗

arXiv2025

MambaFlow: A Mamba-Centric Architecture for End-to-End Optical Flow Estimation

Recently, the Mamba architecture has demonstrated significant successes in various computer vision tasks, such as classification and segmentation. However, its application to optical flow estimation remains unexplored. In this paper, we introduce MambaFlow, a novel framework designed to leverage the high accuracy and efficiency of the Mamba architecture for capturing locally correlated features while preserving global information in end-to-end optical flow estimation. To our knowledge, MambaFlow is the first architecture centered around the Mamba design tailored specifically for optical flow estimation. It comprises two key components: (1) PolyMamba, which enhances feature representation through a dual-Mamba architecture, incorporating a Self-Mamba module for intra-token modeling and a Cross-Mamba module for inter-modality interaction, enabling both deep contextualization and effective feature fusion; and (2) PulseMamba, which leverages an Attention Guidance Aggregator (AGA) to adaptively integrate features with dynamically learned weights in contrast to naive concatenation, and then employs the intrinsic recurrent mechanism of Mamba to perform autoregressive flow decoding, facilitating efficient flow information dissemination. Extensive experiments demonstrate that MambaFlow achieves remarkable results comparable to mainstream methods on benchmark datasets. Compared to SEA-RAFT, MambaFlow attains higher accuracy on the Sintel benchmark, demonstrating stronger potential for real-world deployment on resource-constrained devices. The source code will be made publicly available upon acceptance of the paper.

cs.CV↗

arXiv2023

Several inequalities concerning interpolation in classical Fourier analysis

In this note, we establish several interpolation inequalities in $\mathbb R^n$ in the Lebesgue spaces and Morrey spaces. By using the classical Calderon--Zygmund decomposition, we will reprove that $L^{p}(\mathbb R^n)\cap\mathrm{BMO}(\mathbb R^n)\subset L^{q}(\mathbb R^n)$ for all $q$ with $p<q<\infty$, where $1\leq p<\infty$. We also reprove that there exists a constant $C(p,q,n)$ depending on $p,q,n$ such that the following inequality \begin{equation*} \|f\|_{L^q}\leq C(p,q,n)\cdot\big(\|f\|_{L^p}\big)^{p/q}\cdot\big(\|f\|_{\mathrm{BMO}}\big)^{1-p/q} \end{equation*} holds for all $f\in L^{p}(\mathbb R^n)\cap\mathrm{BMO}(\mathbb R^n)$ with $1\leq p<\infty$. Moreover, this embedding constant has the optimal growth order $q$ as $q\to\infty$, which was given by Chen--Zhu, and Kozono--Wadade. We will show that $L^{p,κ}(\mathbb R^n)\cap\mathrm{BMO}(\mathbb R^n)\subset L^{q,κ}(\mathbb R^n)$ for all $q$ with $p<q<\infty$, where $1\leq p<\infty$ and $0<κ<1$. Moreover, there exists a constant $\widetilde{C}(p,q,n)$ depending on $p,q,n$ such that \begin{equation*} \|f\|_{L^{q,κ}}\leq \widetilde{C}(p,q,n)\cdot\big(\|f\|_{L^{p,κ}}\big)^{p/q}\cdot\big(\|f\|_{\mathrm{BMO}}\big)^{1-p/q} \end{equation*} holds for all $f\in L^{p,κ}(\mathbb R^n)\cap\mathrm{BMO}(\mathbb R^n)$ with $1\leq p<\infty$ and $0<κ<1$. This embedding constant is shown to have the linear growth order as $q\to\infty$, that is, $\widetilde{C}(p,q,n)\leq C_n\cdot q$ with the constant $C_n$ depending only on the dimension $n$, when $q$ is large. As an application of the above results, some new bilinear estimates are also established, which can be used in the study of the global existence and regularity of weak solutions to elliptic and parabolic partial differential equations of the second order.

math.CA↗