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Jian Lu

Publications and source records attributed to Jian Lu.

At least 37 records · Page 2Linked to original sources
arXiv2025

MoFu: Scale-Aware Modulation and Fourier Fusion for Multi-Subject Video Generation

Multi-subject video generation aims to synthesize videos from textual prompts and multiple reference images, ensuring that each subject preserves natural scale and visual fidelity. However, current methods face two challenges: scale inconsistency, where variations in subject size lead to unnatural generation, and permutation sensitivity, where the order of reference inputs causes subject distortion. In this paper, we propose MoFu, a unified framework that tackles both challenges. For scale inconsistency, we introduce Scale-Aware Modulation (SMO), an LLM-guided module that extracts implicit scale cues from the prompt and modulates features to ensure consistent subject sizes. To address permutation sensitivity, we present a simple yet effective Fourier Fusion strategy that processes the frequency information of reference features via the Fast Fourier Transform to produce a unified representation. Besides, we design a Scale-Permutation Stability Loss to jointly encourage scale-consistent and permutation-invariant generation. To further evaluate these challenges, we establish a dedicated benchmark with controlled variations in subject scale and reference permutation. Extensive experiments demonstrate that MoFu significantly outperforms existing methods in preserving natural scale, subject fidelity, and overall visual quality.

cs.CV↗
arXiv2025

Causal Discovery in Nonlinear Dynamical Systems using Koopman Operators

We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that causal mechanisms manifest as particular flows of observables between function subspaces. While the flow map definition is a clear generalization of the standard definition of causal mechanism given in the structural causal model framework, the flow maps are complicated objects that are not tractable to work with in practice. By contrast, the equivalent Koopman definition lends itself to a straightforward data-driven algorithm that can quantify multivariate causal relations in high-dimensional nonlinear dynamical systems. The coupled Rossler system provides examples and demonstrations throughout our exposition. We also demonstrate the utility of our data-driven Koopman causality measure by identifying causal flow in the Lorenz 96 system. We show that the causal flow identified by our data-driven algorithm agrees with the information flow identified through a perturbation propagation experiment. Our work provides new theoretical insights into causality for nonlinear dynamical systems, as well as a new toolkit for data-driven causal analysis.

math.DS↗
arXiv2025

Approximation Rates of Shallow Neural Networks: Barron Spaces, Activation Functions and Optimality Analysis

This paper investigates the approximation properties of shallow neural networks with activation functions that are powers of exponential functions. It focuses on the dependence of the approximation rate on the dimension and the smoothness of the function being approximated within the Barron function space. We examine the approximation rates of ReLU$^{k}$ activation functions, proving that the optimal rate cannot be achieved under $\ell^{1}$-bounded coefficients or insufficient smoothness conditions. We also establish optimal approximation rates in various norms for functions in Barron spaces and Sobolev spaces, confirming the curse of dimensionality. Our results clarify the limits of shallow neural networks' approximation capabilities and offer insights into the selection of activation functions and network structures.

cs.LG↗
arXiv2025

Synchrosqueezed windowed linear canonical transform: A method for mode retrieval from multicomponent signals with crossing instantaneous frequencies

In nature, signals often appear in the form of the superposition of multiple non-stationary signals. The overlap of signal components in the time-frequency domain poses a significant challenge for signal analysis. One approach to addressing this problem is to introduce an additional chirprate parameter and use the chirplet transform (CT) to elevate the two-dimensional time-frequency representation to a three-dimensional time-frequency-chirprate representation. From a certain point of view, the CT of a signal can be regarded as a windowed special linear canonical transform of that signal, undergoing a shift and a modulation. In this paper, we develop this idea to propose a novel windowed linear canonical transform (WLCT), which provides a new time-frequency-chirprate representation. We discuss four types of WLCTs. In addition, we use a special X-ray transform to further sharpen the time-frequency-chirprate representation. Furthermore, we derive the corresponding three-dimensional synchrosqueezed transform, demonstrating that the WLCTs have great potential for three-dimensional signal separation.

eess.SP↗
arXiv2025

RAGAR: Retrieval Augmented Personalized Image Generation Guided by Recommendation

Personalized image generation is crucial for improving the user experience, as it renders reference images into preferred ones according to user visual preferences. Although effective, existing methods face two main issues. First, existing methods treat all items in the user historical sequence equally when extracting user preferences, overlooking the varying semantic similarities between historical items and the reference item. Disproportionately high weights for low-similarity items distort users' visual preferences for the reference item. Second, existing methods heavily rely on consistency between generated and reference images to optimize the generation, which leads to underfitting user preferences and hinders personalization. To address these issues, we propose Retrieval Augment Personalized Image GenerAtion guided by Recommendation (RAGAR). Our approach uses a retrieval mechanism to assign different weights to historical items according to their similarities to the reference item, thereby extracting more refined users' visual preferences for the reference item. Then we introduce a novel rank task based on the multi-modal ranking model to optimize the personalization of the generated images instead of forcing depend on consistency. Extensive experiments and human evaluations on three real-world datasets demonstrate that RAGAR achieves significant improvements in both personalization and semantic metrics compared to five baselines.

cs.IR↗
arXiv2025

Orthogonal Constrained Minimization with Tensor $\ell_{2,p}$ Regularization for HSI Denoising and Destriping

Hyperspectral images~(HSIs) are often contaminated by a mixture of noise such as Gaussian noise, dead lines, stripes, and so on. In this paper, we propose a multi-scale low-rank tensor regularized $\ell_{2,p}$ (MLTL2p) approach for HSI denoising and destriping, which consists of an orthogonal constrained minimization model and an iterative algorithm with convergence guarantees. The model of the proposed MLTL2p approach is built based on a new sparsity-enhanced Multi-scale Low-rank Tensor regularization and a tensor $\ell_{2,p}$ norm with \(p\in (0,1)\). The multi-scale low-rank regularization for HSI denoising utilizes the global and local spectral correlation as well as the spatial nonlocal self-similarity priors of HSIs. The corresponding low-rank constraints are formulated based on independent higher-order singular value decomposition with sparsity enhancement on its core tensor to prompt more low-rankness. The tensor $\ell_{2,p}$ norm for HSI destriping is extended from the matrix $\ell_{2,p}$ norm. A proximal block coordinate descent algorithm is proposed in the MLTL2p approach to solve the resulting nonconvex nonsmooth minimization with orthogonal constraints. We show any accumulation point of the sequence generated by the proposed algorithm converges to a first-order stationary point, which is defined using three equalities of substationarity, symmetry, and feasibility for orthogonal constraints. In the numerical experiments, we compare the proposed method with state-of-the-art methods including a deep learning based method, and test the methods on both simulated and real HSI datasets. Our proposed MLTL2p method demonstrates outperformance in terms of metrics such as mean peak signal-to-noise ratio as well as visual quality.

math.OC↗
arXiv2025

MyGO: Make your Goals Obvious, Avoiding Semantic Confusion in Prostate Cancer Lesion Region Segmentation

Early diagnosis and accurate identification of lesion location and progression in prostate cancer (PCa) are critical for assisting clinicians in formulating effective treatment strategies. However, due to the high semantic homogeneity between lesion and non-lesion areas, existing medical image segmentation methods often struggle to accurately comprehend lesion semantics, resulting in the problem of semantic confusion. To address this challenge, we propose a novel Pixel Anchor Module, which guides the model to discover a sparse set of feature anchors that serve to capture and interpret global contextual information. This mechanism enhances the model's nonlinear representation capacity and improves segmentation accuracy within lesion regions. Moreover, we design a self-attention-based Top_k selection strategy to further refine the identification of these feature anchors, and incorporate a focal loss function to mitigate class imbalance, thereby facilitating more precise semantic interpretation across diverse regions. Our method achieves state-of-the-art performance on the PI-CAI dataset, demonstrating 69.73% IoU and 74.32% Dice scores, and significantly improving prostate cancer lesion detection.

eess.IV↗
arXiv2025

Dyna3DGR: 4D Cardiac Motion Tracking with Dynamic 3D Gaussian Representation

Accurate analysis of cardiac motion is crucial for evaluating cardiac function. While dynamic cardiac magnetic resonance imaging (CMR) can capture detailed tissue motion throughout the cardiac cycle, the fine-grained 4D cardiac motion tracking remains challenging due to the homogeneous nature of myocardial tissue and the lack of distinctive features. Existing approaches can be broadly categorized into image based and representation-based, each with its limitations. Image-based methods, including both raditional and deep learning-based registration approaches, either struggle with topological consistency or rely heavily on extensive training data. Representation-based methods, while promising, often suffer from loss of image-level details. To address these limitations, we propose Dynamic 3D Gaussian Representation (Dyna3DGR), a novel framework that combines explicit 3D Gaussian representation with implicit neural motion field modeling. Our method simultaneously optimizes cardiac structure and motion in a self-supervised manner, eliminating the need for extensive training data or point-to-point correspondences. Through differentiable volumetric rendering, Dyna3DGR efficiently bridges continuous motion representation with image-space alignment while preserving both topological and temporal consistency. Comprehensive evaluations on the ACDC dataset demonstrate that our approach surpasses state-of-the-art deep learning-based diffeomorphic registration methods in tracking accuracy. The code will be available in https://github.com/windrise/Dyna3DGR.

cs.CV↗
arXiv2025

Normalized Iterative Hard Thresholding for Tensor Recovery

Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized iterative hard thresholding (NIHT) method-have been widely used in compressed sensing (CS) and applied to matrix recovery tasks. In this paper, we propose a tensor extension of NIHT, referred to as TNIHT, for the recovery of low-rank tensors under two widely used tensor decomposition models. This extension enables the effective reconstruction of high-order low-rank tensors from a limited number of linear measurements by leveraging the inherent low-dimensional structure of multi-way data. Specifically, we consider both the CANDECOMP/PARAFAC (CP) rank and the Tucker rank to characterize tensor low-rankness within the TNIHT framework. At the same time, we establish a convergence theorem for the proposed TNIHT method under the tensor restricted isometry property (TRIP), providing theoretical support for its recovery guarantees. Finally, we evaluate the performance of TNIHT through numerical experiments on synthetic, image, and video data, and compare it with several state-of-the-art algorithms.

cs.LG↗
arXiv2024

CustomTTT: Motion and Appearance Customized Video Generation via Test-Time Training

Benefiting from large-scale pre-training of text-video pairs, current text-to-video (T2V) diffusion models can generate high-quality videos from the text description. Besides, given some reference images or videos, the parameter-efficient fine-tuning method, i.e. LoRA, can generate high-quality customized concepts, e.g., the specific subject or the motions from a reference video. However, combining the trained multiple concepts from different references into a single network shows obvious artifacts. To this end, we propose CustomTTT, where we can joint custom the appearance and the motion of the given video easily. In detail, we first analyze the prompt influence in the current video diffusion model and find the LoRAs are only needed for the specific layers for appearance and motion customization. Besides, since each LoRA is trained individually, we propose a novel test-time training technique to update parameters after combination utilizing the trained customized models. We conduct detailed experiments to verify the effectiveness of the proposed methods. Our method outperforms several state-of-the-art works in both qualitative and quantitative evaluations.

cs.CV↗
arXiv2024

Nonlocal, Pattern-aware Response and Feedback Framework for Regional Climate Change

We devise a pattern-aware feedback framework for representing the forced climate response using a suite of Green's function experiments with solar radiation perturbations. By considering the column energy balance, a comprehensive linear response function (CLRF) forimportant climate variables and feedback quantities such as moist static energy, sea surface temperature, albedo, cloud optical depth, and lapse rate is learned from Green's function data. The learned CLRF delineates the effects of the energy diffusion in both the ocean and atmosphere and the pattern-aware feedbacks from the aforementioned radiatively active processes. The CLRF can then be decomposed into forcing-response mode pairs which are in turn used to construct a reduced-order model (ROM) describing the dominant dynamics of climate responses. These mode pairs capture nonlocal effects and teleconnections in the climate and thus, make the ROM apt for capturing regional features of climate change response. A key observation is that the CLRF captures the polar amplified response as the most excitable mode of the climate system and this mode is explainable in the data-learned pattern-aware feedback framework. The ROM can be used for predicting the response for a given forcing and for reconstructing the forcing from a given response; we demonstrate these capabilities for independent forcing pattern.

physics.ao-ph↗
arXiv2024

Neuro-symbolic Learning Yielding Logical Constraints

Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural network training, symbol grounding, and logical constraint synthesis into a coherent and efficient end-to-end learning process. The capability of this framework comes from the improved interactions between the neural and the symbolic parts of the system in both the training and inference stages. Technically, to bridge the gap between the continuous neural network and the discrete logical constraint, we introduce a difference-of-convex programming technique to relax the logical constraints while maintaining their precision. We also employ cardinality constraints as the language for logical constraint learning and incorporate a trust region method to avoid the degeneracy of logical constraint in learning. Both theoretical analyses and empirical evaluations substantiate the effectiveness of the proposed framework.

cs.AI↗
arXiv2024

Revisiting Multi-Modal LLM Evaluation

With the advent of multi-modal large language models (MLLMs), datasets used for visual question answering (VQA) and referring expression comprehension have seen a resurgence. However, the most popular datasets used to evaluate MLLMs are some of the earliest ones created, and they have many known problems, including extreme bias, spurious correlations, and an inability to permit fine-grained analysis. In this paper, we pioneer evaluating recent MLLMs (LLaVA 1.5, LLaVA-NeXT, BLIP2, InstructBLIP, GPT-4V, and GPT-4o) on datasets designed to address weaknesses in earlier ones. We assess three VQA datasets: 1) TDIUC, which permits fine-grained analysis on 12 question types; 2) TallyQA, which has simple and complex counting questions; and 3) DVQA, which requires optical character recognition for chart understanding. We also study VQDv1, a dataset that requires identifying all image regions that satisfy a given query. Our experiments reveal the weaknesses of many MLLMs that have not previously been reported. Our code is integrated into the widely used LAVIS framework for MLLM evaluation, enabling the rapid assessment of future MLLMs. Project webpage: https://kevinlujian.github.io/MLLM_Evaluations/

cs.AI↗
arXiv2024

On the number of solutions to the planar dual Minkowski problem

The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the constant dual curvature case when $0 4$ is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the $L_p$-Alexandrov problem is obtained for $p<0$.

math.AP↗
arXiv2024

How optimal control of polar sea-ice depends on its tipping points

Several Earth system components are at a high risk of undergoing rapid and irreversible qualitative changes or `tipping', due to increasing climate warming. Potential tipping elements include Arctic sea-ice, Atlantic meridional overturning circulation, and tropical coral reefs. Amidst such immediate concerns, it has become necessary to investigate the feasibility of arresting or even reversing the crossing of tipping thresholds using feedback control. In this paper, we study the control of an idealized diffusive energy balance model (EBM) for the Earth's climate; this model has two tipping points due to strong co-albedo feedback. One of these tipping points is a `small icecap' instability responsible for a rapid transition to an ice-free climate state under increasing greenhouse gas (GHG) forcing. We develop an optimal control strategy for the EBM under different climate forcing scenarios with the goal of reversing sea ice loss while minimizing costs. We find that effective control is achievable for such a system, but the cost of reversing sea-ice loss nearly quadruples for an initial state that has just tipped as compared to a state before reaching the tipping point. We also show that thermal inertia may delay tipping leading to an overshoot of the critical GHG forcing threshold. This may offer a short intervention window (overshoot window) during which the control required to reverse sea-ice loss only scales linearly with intervention time. While systems with larger system inertia may have longer overshoot windows, this increased elbow room comes with a steeper rise in the requisite control once the intervention is delayed past this window. Additionally, we find that the requisite control to restore sea-ice is localized in the polar region.

physics.ao-ph↗
arXiv2024

EMBANet: A Flexible Efffcient Multi-branch Attention Network

This work presents a novel module, namely multi-branch concat (MBC), to process the input tensor and obtain the multi-scale feature map. The proposed MBC module brings new degrees of freedom (DoF) for the design of attention networks by allowing the type of transformation operators and the number of branches to be flexibly adjusted. Two important transformation operators, multiplex and split, are considered in this work, both of which can represent multi-scale features at a more granular level and increase the range of receptive fields. By integrating the MBC and attention module, a multi-branch attention (MBA) module is consequently developed to capture the channel-wise interaction of feature maps for establishing the long-range channel dependency. By substituting the 3x3 convolutions in the bottleneck blocks of the ResNet with the proposed MBA, a novel block namely efficient multi-branch attention (EMBA) is obtained, which can be easily plugged into the state-of-the-art backbone CNN models. Furthermore, a new backbone network called EMBANet is established by stacking the EMBA blocks. The proposed EMBANet is extensively evaluated on representative computer vision tasks including: classification, detection, and segmentation. And it demonstrates consistently superior performance over the popular backbones.

cs.CV↗
arXiv2024

On the equivalence of two spinodal decomposition criteria with a case study of Fe${}_{15}$Co${}_{15}$Ni${}_{35}$Cu${}_{35}$ multicomponent alloy

Spinodal decomposition in multicomponent alloys has attracted increasing attention due to its beneficial effect on their mechanical and functional properties and potential applications. Both based on the Cahn-Hillard equation, the reference element method (REM) and the projection matrix method (PMM) are the two main methods to predict the occurrence of spinodal decomposition in multicomponent alloys. In this work, it is mathematically proven that the two methods are equivalent, and therefore the advanced results based on one method can be applied to the other. Based on these methods, the $Fe{}_{15}$Co${}_{15}$Ni${}_{35}$Cu${}_{35}$ multicomponent alloy is designed as a case study. Experimental results confirm the spinodal decomposition in the heat-treated alloy, and its strength and ductility are simultaneously enhanced. This work can be the pavement for further theoretical and experimental studies on the spinodal decomposition in multicomponent alloys.

cond-mat.mtrl-sci↗