arXiv subjects

Ji Li

Publications and source records attributed to Ji Li.

At least 55 records · Page 3Linked to original sources

arXiv2026

Haar bases for multi-parameter twisted structures

Motivated by the Cauchy--Szegő projections on a broad class of Siegel domains and the geometric quotient structures of nilpotent Lie groups observed by Nagel, Ricci, and Stein, we develop a martingale and Haar wavelet framework for twisted multi-parameter geometries. We introduce twisted dyadic filtrations and construct adapted Haar bases on Euclidean spaces $\mathbb{R}^{2m}$. Each of the resulting dyadic systems forms a complete orthonormal basis of $L^2(\mathbb R^{2m})$, and their union yields a tight frame with frame bound $3$. We establish $L^p$-equivalences for the associated discrete twisted Littlewood--Paley square functions. Furthermore, we extend this discrete real-variable theory to the non-abelian setting of a nilpotent Lie group of step two, $\mathscr{N}$, which serves as the Shilov boundary of certain fundamental Siegel domains. By projecting product fractal tiles from a lifting group of Heisenberg products, we define twisted dyadic shards and construct twisted nilpotent Haar frames. More precisely, we first introduce raw projected shards that reflect the quotient geometry, and then pass to analytic dyadic shards which are exactly rectifiable and remain uniformly comparable to the raw quotient structure in the relevant scale regimes. This yields a discrete framework adapted to twisted quotient geometries in both the Euclidean and nilpotent settings, providing a basic dyadic infrastructure for further developments in twisted real-variable theory.

math.CA↗

arXiv2026

Maximal functions with twisted structures, distribution inequality and applications

Motivated by the geometric reduction of Cauchy--Szegő projections on quadratic surfaces of higher codimension (Nagel--Ricci--Stein, 2001) and recent developments on the real-variable theory adapted to twisted multiparameter structures (arXiv:2603.26119), we establish the Fefferman--Stein type distribution inequality relating the twisted area function and the twisted non-tangential maximal function over $\mathbb{R}^{2m}$. By deploying a recursive integration-by-parts argument involving the twisted gradient and Laplacian, and constructing smooth, compactly supported weight functions to absorb cross-derivative errors, we obtain the required estimate. As an application, we prove the uniform $L^1$ boundedness of the twisted maximal function on the twisted atoms and complete the maximal function characterization of the twisted Hardy space.

math.CA↗

arXiv2026

Twisted Multiparameter singular integrals -- real variable methods and applications, I

In this paper, we introduce a class of twisted multiparameter singular integrals on $\mathbb{R}^{2m}$, motivated by the Cauchy--Szegő projections and the solving operators for $\bar{\partial}_b$ on a broad family of quadratic surfaces of higher codimension in $\mathbb{C}^n$. These surfaces are represented as suitable quotients of products of Heisenberg groups, a framework illustrated by Stein (Notices Amer. Math. Soc., 1998). While classical multiparameter product and flag theories are well-developed, Nagel, Ricci, and Stein observed a critical limitation: the class of product operators is not closed under passage to a quotient subgroup. To handle the geometric reduction that models these quotient structures, we take the first step in developing an adapted real-variable theory. We achieve this by introducing twisted tube systems and tube maximal functions, establishing a reproducing formula, Littlewood--Paley theory, a Journé-type covering lemma, and atomic decompositions. As particular examples, we obtain twisted Fourier multipliers -- which emerge as novel, direction-sensitive, and anisotropic phase-shift converters with potential applications in signal and image processing.

math.CA↗

arXiv2026

BizGenEval: A Systematic Benchmark for Commercial Visual Content Generation

Recent advances in image generation models have expanded their applications beyond aesthetic imagery toward practical visual content creation. However, existing benchmarks mainly focus on natural image synthesis and fail to systematically evaluate models under the structured and multi-constraint requirements of real-world commercial design tasks. In this work, we introduce BizGenEval, a systematic benchmark for commercial visual content generation. The benchmark spans five representative document types: slides, charts, webpages, posters, and scientific figures, and evaluates four key capability dimensions: text rendering, layout control, attribute binding, and knowledge-based reasoning, forming 20 diverse evaluation tasks. BizGenEval contains 400 carefully curated prompts and 8000 human-verified checklist questions to rigorously assess whether generated images satisfy complex visual and semantic constraints. We conduct large-scale benchmarking on 26 popular image generation systems, including state-of-the-art commercial APIs and leading open-source models. The results reveal substantial capability gaps between current generative models and the requirements of professional visual content creation. We hope BizGenEval serves as a standardized benchmark for real-world commercial visual content generation.

cs.CV↗

arXiv2026

SpecForge: A Flexible and Efficient Open-Source Training Framework for Speculative Decoding

Large language models incur high inference latency due to sequential autoregressive decoding. Speculative decoding alleviates this bottleneck by using a lightweight draft model to propose multiple tokens for batched verification. However, its adoption has been limited by the lack of high-quality draft models and scalable training infrastructure. We introduce SpecForge, an open-source, production-oriented framework for training speculative decoding models with full support for EAGLE-3. SpecForge incorporates target-draft decoupling, hybrid parallelism, optimized training kernels, and integration with production-grade inference engines, enabling up to 9.9x faster EAGLE-3 training for Qwen3-235B-A22B. In addition, we release SpecBundle, a suite of production-grade EAGLE-3 draft models trained with SpecForge for mainstream open-source LLMs. Through a systematic study of speculative decoding training recipes, SpecBundle addresses the scarcity of high-quality drafts in the community, and our draft models achieve up to 4.48x end-to-end inference speedup on SGLang, establishing SpecForge as a practical foundation for real-world speculative decoding deployment.

cs.LG↗

arXiv2026

Just-in-Time: Training-Free Spatial Acceleration for Diffusion Transformers

Diffusion Transformers have established a new state-of-the-art in image synthesis, but the high computational cost of iterative sampling severely hampers their practical deployment. While existing acceleration methods often focus on the temporal domain, they overlook the substantial spatial redundancy inherent in the generative process, where global structures emerge long before fine-grained details are formed. The uniform computational treatment of all spatial regions represents a critical inefficiency. In this paper, we introduce Just-in-Time (JiT), a novel training-free framework that addresses this challenge by acceleration in the spatial domain. JiT formulates a spatially approximated generative ordinary differential equation (ODE) that drives the full latent state evolution based on computations from a dynamically selected, sparse subset of anchor tokens. To ensure seamless transitions as new tokens are incorporated to expand the dimensions of the latent state, we propose a deterministic micro-flow, a simple and effective finite-time ODE that maintains both structural coherence and statistical correctness. Extensive experiments on the state-of-the-art FLUX.1-dev model demonstrate that JiT achieves up to a 7x speedup with nearly lossless performance, significantly outperforming existing acceleration methods and establishing a new and superior trade-off between inference speed and generation fidelity.

cs.CV↗

arXiv2026

HIMM: Human-Inspired Long-Term Memory Modeling for Embodied Exploration and Question Answering

Deploying Multimodal Large Language Models as the brain of embodied agents remains challenging, particularly under long-horizon observations and limited context budgets. Existing memory assisted methods often rely on textual summaries, which discard rich visual and spatial details and remain brittle in non-stationary environments. In this work, we propose a non-parametric memory framework that explicitly disentangles episodic and semantic memory for embodied exploration and question answering. Our retrieval-first, reasoning-assisted paradigm recalls episodic experiences via semantic similarity and verifies them through visual reasoning, enabling robust reuse of past observations without rigid geometric alignment. In parallel, we introduce a program-style rule extraction mechanism that converts experiences into structured, reusable semantic memory, facilitating cross-environment generalization. Extensive experiments demonstrate state-of-the-art performance on embodied question answering and exploration benchmarks, yielding a 7.3% gain in LLM-Match and an 11.4% gain in LLM MatchXSPL on A-EQA, as well as +7.7% success rate and +6.8% SPL on GOAT-Bench. Analyses reveal that our episodic memory primarily improves exploration efficiency, while semantic memory strengthens complex reasoning of embodied agents.

cs.RO↗

arXiv2026

Can Vision Language Models Assess Graphic Design Aesthetics? A Benchmark, Evaluation, and Dataset Perspective

Assessing the aesthetic quality of graphic design is central to visual communication, yet remains underexplored in vision language models (VLMs). We investigate whether VLMs can evaluate design aesthetics in ways comparable to humans. Prior work faces three key limitations: benchmarks restricted to narrow principles and coarse evaluation protocols, a lack of systematic VLM comparisons, and limited training data for model improvement. In this work, we introduce AesEval-Bench, a comprehensive benchmark spanning four dimensions, twelve indicators, and three fully quantifiable tasks: aesthetic judgment, region selection, and precise localization. Then, we systematically evaluate proprietary, open-source, and reasoning-augmented VLMs, revealing clear performance gaps against the nuanced demands of aesthetic assessment. Moreover, we construct a training dataset to fine-tune VLMs for this domain, leveraging human-guided VLM labeling to produce task labels at scale and indicator-grounded reasoning to tie abstract indicators to concrete design regions.Together, our work establishes the first systematic framework for aesthetic quality assessment in graphic design. Our code and dataset will be released at: \href{https://github.com/arctanxarc/AesEval-Bench}{https://github.com/arctanxarc/AesEval-Bench}

cs.CV↗

arXiv2026

DiffPlace: Street View Generation via Place-Controllable Diffusion Model Enhancing Place Recognition

Generative models have advanced significantly in realistic image synthesis, with diffusion models excelling in quality and stability. Recent multi-view diffusion models improve 3D-aware street view generation, but they struggle to produce place-aware and background-consistent urban scenes from text, BEV maps, and object bounding boxes. This limits their effectiveness in generating realistic samples for place recognition tasks. To address these challenges, we propose DiffPlace, a novel framework that introduces a place-ID controller to enable place-controllable multi-view image generation. The place-ID controller employs linear projection, perceiver transformer, and contrastive learning to map place-ID embeddings into a fixed CLIP space, allowing the model to synthesize images with consistent background buildings while flexibly modifying foreground objects and weather conditions. Extensive experiments, including quantitative comparisons and augmented training evaluations, demonstrate that DiffPlace outperforms existing methods in both generation quality and training support for visual place recognition. Our results highlight the potential of generative models in enhancing scene-level and place-aware synthesis, providing a valuable approach for improving place recognition in autonomous driving

cs.CV↗

arXiv2026

The Brascamp--Lieb inequality on compact Lie groups and its extinction on homogeneous Lie groups

We study the Brascamp--Lieb inequalities on locally compact nonabelian groups and the Brascamp--Lieb constants $\mathbf{BL}(G, \boldsymbolσ, \boldsymbol{p})$ associated to a Brascamp--Lieb datum: locally compact groups $G$ and $G_j$, a family of homomorphisms $σ_j: G \to G_j$ and Lebesgue indices $p_j$. We focus on homogeneous Lie groups and compact Lie groups. For homogeneous Lie groups $G$, we show that the constant $\mathbf{BL}(G, \boldsymbolσ, \boldsymbol{p})$ is equal to the constant $\mathbf{BL}(\mathfrak{g}, \boldsymbol{\mathrm{d}σ}, \boldsymbol{p})$, where $\mathfrak{g}$ is the Lie algebra of $G$ and $\mathrm{d}σ_j$ is the differential of $σ_j$. For Heisenberg-like groups $G$, we show that the only inequalities that can occur are multilinear Hölder inequalities. For compact Lie groups, we find necessary and sufficient conditions for finiteness of the constant $\mathbf{BL}(G, \boldsymbolσ, \boldsymbol{p})$ in terms of $\boldsymbolσ$ and $\boldsymbol{p}$ and find an explicit expression for the constant, similar to those found by Bennett and Jeong in the abelian case.

math.GR↗

arXiv2026

On Rubio de Francia's maximal theorem

In his influential 1986 paper, Rubio de Francia established $L^p$ bounds for the maximal function generated by dilations of measures $μ$ whose Fourier transforms $\widehatμ$ satisfy specific decay condition. In the present work, we obtain results that complement his work in several directions. In particular, we obtain restricted weak-type endpoint bound on the maximal function and $L^p$--$L^q$ bounds on its local variant. We also investigate how Frostman's growth condition on the measure influences those maximal bounds. While a key feature of Rubio de Francia's result is that $L^p$ boundedness is determined solely by the decay order of $\widehatμ$, we show that the Frostman condition plays a significant role when the growth order exceeds $d-1$ or when $L^p$--$L^q$ estimates are considered.

math.CA↗

arXiv2026

ReLayout: Versatile and Structure-Preserving Design Layout Editing via Relation-Aware Design Reconstruction

Automated redesign without manual adjustments marks a key step forward in the design workflow. In this work, we focus on a foundational redesign task termed design layout editing, which seeks to autonomously modify the geometric composition of a design based on user intents. To overcome the ambiguity of user needs expressed in natural language, we introduce four basic and important editing actions and standardize the format of editing operations. The underexplored task presents a unique challenge: satisfying specified editing operations while simultaneously preserving the layout structure of unedited elements. Besides, the scarcity of triplet (original design, editing operation, edited design) samples poses another formidable challenge. To this end, we present ReLayout, a novel framework for versatile and structure-preserving design layout editing that operates without triplet data. Specifically, ReLayout first introduces the relation graph, which contains the position and size relationships among unedited elements, as the constraint for layout structure preservation. Then, relation-aware design reconstruction (RADR) is proposed to bypass the data challenge. By learning to reconstruct a design from its elements, a relation graph, and a synthesized editing operation, RADR effectively emulates the editing process in a self-supervised manner. A multi-modal large language model serves as the backbone for RADR, unifying multiple editing actions within a single model and thus achieving versatile editing after fine-tuning. Qualitative, quantitative results and user studies show that ReLayout significantly outperforms the baseline models in terms of editing quality, accuracy, and layout structure preservation.

cs.CV↗

arXiv2025

Boundedness and compactness of Bergman projection commutators in two-weight setting

The goal of this paper is to study the boundedness and compactness of the Bergman projection commutators in two weighted settings via the weighted BMO and VMO spaces, respectively. The novelty of our work lies in the distinct treatment of the symbol b in the commutator, depending on whether it is analytic or not, which turns out to be quite different. In particular, we show that an additional weight condition due to Aleman, Pott, and Reguera is necessary to study the commutators when b is not analytic, while it can be relaxed when b is analytic. In the analytic setting, we completely characterize boundedness and compactness, while in the non-analytic setting, we provide a sufficient condition which generalizes the Euclidean case and is also necessary in many cases of interest. Our work initiates a study of the commutators acting on complex function spaces with different symbols.

math.CA↗

arXiv2025

Experimental Witness of Quantum Jump Induced High-Order Liouvillian Exceptional Points

The exceptional point has presented considerably interesting and counterintuitive phenomena associated with nonreciprocity, precision measurement, and topological dynamics. The Liouvillian exceptional point (LEP), involving the interplay of energy loss and decoherence inherently relevant to quantum jumps, has recently drawn much attention due to capability to fully capture quantum system dynamics and naturally facilitate non-Hermitian quantum investigations. It was also predicted that quantum jumps could give rise to third-order LEPs in two-level quantum systems for its high dimensional Liouvillian superoperator, which, however, has never been experimentally confirmed until now. Here we report the first observation of the third-order LEPs emerging from quantum jumps in an ultracold two-level trapped-ion system. Moreover, by combining decay with dephasing processes, we present the first experimental exploration of LEPs involving combinatorial effect of decay and dephasing. In particular, due to non-commutativity between the Lindblad superoperators governing LEPs for decay and dephasing, we witness the movement of LEPs driven by the competition between decay and dephasing occurring in an open quantum system. This unique feature of non-Hermitian quantum systems paves a new avenue for modifying nonreciprocity, enhancing precision measurement, and manipulating topological dynamics by tuning the LEPs.

quant-ph↗

arXiv2025

Multi-Agent Deep Research: Training Multi-Agent Systems with M-GRPO

Multi-agent systems perform well on general reasoning tasks. However, the lack of training in specialized areas hinders their accuracy. Current training methods train a unified large language model (LLM) for all agents in the system. This may limit the performances due to different distributions underlying for different agents. Therefore, training multi-agent systems with distinct LLMs should be the next step to solve. However, this approach introduces optimization challenges. For example, agents operate at different frequencies, rollouts involve varying sub-agent invocations, and agents are often deployed across separate servers, disrupting end-to-end gradient flow. To address these issues, we propose M-GRPO, a hierarchical extension of Group Relative Policy Optimization designed for vertical Multi-agent systems with a main agent (planner) and multiple sub-agents (multi-turn tool executors). M-GRPO computes group-relative advantages for both main and sub-agents, maintaining hierarchical credit assignment. It also introduces a trajectory-alignment scheme that generates fixed-size batches despite variable sub-agent invocations. We deploy a decoupled training pipeline in which agents run on separate servers and exchange minimal statistics via a shared store. This enables scalable training without cross-server backpropagation. In experiments on real-world benchmarks (e.g., GAIA, XBench-DeepSearch, and WebWalkerQA), M-GRPO consistently outperforms both single-agent GRPO and multi-agent GRPO with frozen sub-agents, demonstrating improved stability and sample efficiency. These results show that aligning heterogeneous trajectories and decoupling optimization across specialized agents enhances tool-augmented reasoning tasks.

cs.AI↗

arXiv2025

Image Restoration via Primal Dual Hybrid Gradient and Flow Generative Model

Regularized optimization has been a classical approach to solving imaging inverse problems, where the regularization term enforces desirable properties of the unknown image. Recently, the integration of flow matching generative models into image restoration has garnered significant attention, owing to their powerful prior modeling capabilities. In this work, we incorporate such generative priors into a Plug-and-Play (PnP) framework based on proximal splitting, where the proximal operator associated with the regularizer is replaced by a time-dependent denoiser derived from the generative model. While existing PnP methods have achieved notable success in inverse problems with smooth squared $\ell_2$ data fidelity--typically associated with Gaussian noise--their applicability to more general data fidelity terms remains underexplored. To address this, we propose a general and efficient PnP algorithm inspired by the primal-dual hybrid gradient (PDHG) method. Our approach is computationally efficient, memory-friendly, and accommodates a wide range of fidelity terms. In particular, it supports both $\ell_1$ and $\ell_2$ norm-based losses, enabling robustness to non-Gaussian noise types such as Poisson and impulse noise. We validate our method on several image restoration tasks, including denoising, super-resolution, deblurring, and inpainting, and demonstrate that $\ell_1$ and $\ell_2$ fidelity terms outperform the conventional squared $\ell_2$ loss in the presence of non-Gaussian noise.

cs.CV↗

arXiv2025

Integrating Reweighted Least Squares with Plug-and-Play Diffusion Priors for Noisy Image Restoration

Existing plug-and-play image restoration methods typically employ off-the-shelf Gaussian denoisers as proximal operators within classical optimization frameworks based on variable splitting. Recently, denoisers induced by generative priors have been successfully integrated into regularized optimization methods for image restoration under Gaussian noise. However, their application to non-Gaussian noise--such as impulse noise--remains largely unexplored. In this paper, we propose a plug-and-play image restoration framework based on generative diffusion priors for robust removal of general noise types, including impulse noise. Within the maximum a posteriori (MAP) estimation framework, the data fidelity term is adapted to the specific noise model. Departing from the conventional least-squares loss used for Gaussian noise, we introduce a generalized Gaussian scale mixture-based loss, which approximates a wide range of noise distributions and leads to an $\ell_q$-norm ($0<q\leq2$) fidelity term. This optimization problem is addressed using an iteratively reweighted least squares (IRLS) approach, wherein the proximal step involving the generative prior is efficiently performed via a diffusion-based denoiser. Experimental results on benchmark datasets demonstrate that the proposed method effectively removes non-Gaussian impulse noise and achieves superior restoration performance.

cs.CV↗

arXiv2025

Lattice design of a storage-ring-based light source for generating high-power fully coherent EUV radiation

We present the physical design and systematic optimization of a high-performance storage ring tailored for the generation of high-power coherent radiation, with particular emphasis on the extreme ultraviolet (EUV) regime. The proposed ring adopts a Double Bend Achromat (DBA) lattice configuration and integrates 12 superconducting wigglers to significantly enhance radiation damping and minimize the natural emittance. And a bypass line is adopted to generate high power coherent radiation. Comprehensive linear and nonlinear beam dynamics analyses have been conducted to ensure beam stability and robustness across the operational parameter space. The optimized design achieves a natural emittance of approximately 0.8 nm and a longitudinal damping time of around 1.4 ms, enabling the efficient buildup of coherent radiation. Three-dimensional numerical simulations, incorporating the previously proposed angular dispersion-induced microbunching (ADM) mechanism, further confirm the system's capability to generate high-power EUV coherent radiation, with output powers reaching the order of several hundred watts. These results underscore the strong potential of the proposed design for applications in coherent photon science and EUV lithography.

physics.acc-ph↗