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Jingzhi Li

Publications and source records attributed to Jingzhi Li.

At least 37 records · Page 2Linked to original sources

Generalized Semantic Contrastive Learning via Embedding Side Information for Few-Shot Object Detection

The objective of few-shot object detection (FSOD) is to detect novel objects with few training samples. The core challenge of this task is how to construct a generalized feature space for novel categories with limited data on the basis of the base category space, which could adapt the learned detection model to unknown scenarios. However, limited by insufficient samples for novel categories, two issues still exist: (1) the features of the novel category are easily implicitly represented by the features of the base category, leading to inseparable classifier boundaries, (2) novel categories with fewer data are not enough to fully represent the distribution, where the model fine-tuning is prone to overfitting. To address these issues, we introduce the side information to alleviate the negative influences derived from the feature space and sample viewpoints and formulate a novel generalized feature representation learning method for FSOD. Specifically, we first utilize embedding side information to construct a knowledge matrix to quantify the semantic relationship between the base and novel categories. Then, to strengthen the discrimination between semantically similar categories, we further develop contextual semantic supervised contrastive learning which embeds side information. Furthermore, to prevent overfitting problems caused by sparse samples, a side-information guided region-aware masked module is introduced to augment the diversity of samples, which finds and abandons biased information that discriminates between similar categories via counterfactual explanation, and refines the discriminative representation space further. Extensive experiments using ResNet and ViT backbones on PASCAL VOC, MS COCO, LVIS V1, FSOD-1K, and FSVOD-500 benchmarks demonstrate that our model outperforms the previous state-of-the-art methods, significantly improving the ability of FSOD in most shots/splits.

cs.CV↗

Interpreting Object-level Foundation Models via Visual Precision Search

Advances in multimodal pre-training have propelled object-level foundation models, such as Grounding DINO and Florence-2, in tasks like visual grounding and object detection. However, interpreting these models' decisions has grown increasingly challenging. Existing interpretable attribution methods for object-level task interpretation have notable limitations: (1) gradient-based methods lack precise localization due to visual-textual fusion in foundation models, and (2) perturbation-based methods produce noisy saliency maps, limiting fine-grained interpretability. To address these, we propose a Visual Precision Search method that generates accurate attribution maps with fewer regions. Our method bypasses internal model parameters to overcome attribution issues from multimodal fusion, dividing inputs into sparse sub-regions and using consistency and collaboration scores to accurately identify critical decision-making regions. We also conducted a theoretical analysis of the boundary guarantees and scope of applicability of our method. Experiments on RefCOCO, MS COCO, and LVIS show our approach enhances object-level task interpretability over SOTA for Grounding DINO and Florence-2 across various evaluation metrics, with faithfulness gains of 23.7%, 31.6%, and 20.1% on MS COCO, LVIS, and RefCOCO for Grounding DINO, and 102.9% and 66.9% on MS COCO and RefCOCO for Florence-2. Additionally, our method can interpret failures in visual grounding and object detection tasks, surpassing existing methods across multiple evaluation metrics. The code will be released at https://github.com/RuoyuChen10/VPS.

cs.CV↗

ReCap: Better Gaussian Relighting with Cross-Environment Captures

Accurate 3D objects relighting in diverse unseen environments is crucial for realistic virtual object placement. Due to the albedo-lighting ambiguity, existing methods often fall short in producing faithful relights. Without proper constraints, observed training views can be explained by numerous combinations of lighting and material attributes, lacking physical correspondence with the actual environment maps used for relighting. In this work, we present ReCap, treating cross-environment captures as multi-task target to provide the missing supervision that cuts through the entanglement. Specifically, ReCap jointly optimizes multiple lighting representations that share a common set of material attributes. This naturally harmonizes a coherent set of lighting representations around the mutual material attributes, exploiting commonalities and differences across varied object appearances. Such coherence enables physically sound lighting reconstruction and robust material estimation - both essential for accurate relighting. Together with a streamlined shading function and effective post-processing, ReCap outperforms all leading competitors on an expanded relighting benchmark.

cs.CV↗

Shape Taylor expansion for wave scattering problems

The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high order shape derivatives required for this expansion poses significant challenges with conventional methods. This paper addresses these difficulties by introducing elegant recurrence formulas for computing high order shape derivatives. The derivation employs tools from exterior differential forms, Lie derivatives, and material derivatives. The work establishes a unified framework for computing the high order shape perturbations in scattering problems. In particular, the recurrence formulas are applicable to both acoustic and electromagnetic scattering models under a variety of boundary conditions, including Dirichlet, Neumann, impedance, and transmission types.

math.NA↗

Convexification With the Viscocity Term for Electrical Impedance Tomography

A version of the globally convergent convexification numerical method is constructed for the problem of Electrical Impedance Tomography in the 2D case. An important element of this version is the presence of the viscosity term. Global convergence analysis is carried out. Results of numerical experiments are presented.

math.NA↗

Crank-Nicolson-type iterative decoupled algorithms for Biot's consolidation model using total pressure

In this work, we develop Crank-Nicolson-type iterative decoupled algorithms for a three-field formulation of Biot's consolidation model using total pressure. We begin by constructing an equivalent fully implicit coupled algorithm using the standard Crank-Nicolson method for the three-field formulation of Biot's model. Employing an iterative decoupled scheme to decompose the resulting coupled system, we derive two distinctive forms of Crank-Nicolson-type iterative decoupled algorithms based on the order of temporal computation and iteration: a time-stepping iterative decoupled algorithm and a global-in-time iterative decoupled algorithm. Notably, the proposed global-in-time algorithm supports a partially parallel-in-time feature. Capitalizing on the convergence properties of the iterative decoupled scheme, both algorithms exhibit second-order time accuracy and unconditional stability. Through numerical experiments, we validate theoretical predictions and demonstrate the effectiveness and efficiency of these novel approaches.

math.NA↗

Convexification for the 3D Problem of Travel Time Tomography

The travel time tomography problem is a coefficient inverse problem for the eikonal equation. This problem has well known applications in seismic. The eikonal equation is considered here in the circular cylinder, where point sources run along its axis and measurements of travel times are conductes on the whole surface of this cylinder. A new version of the globally convergent convexification numerical method for this problem is developed. Results of numerical studies are presented.

math.NA↗

Less is More: Fewer Interpretable Region via Submodular Subset Selection

Image attribution algorithms aim to identify important regions that are highly relevant to model decisions. Although existing attribution solutions can effectively assign importance to target elements, they still face the following challenges: 1) existing attribution methods generate inaccurate small regions thus misleading the direction of correct attribution, and 2) the model cannot produce good attribution results for samples with wrong predictions. To address the above challenges, this paper re-models the above image attribution problem as a submodular subset selection problem, aiming to enhance model interpretability using fewer regions. To address the lack of attention to local regions, we construct a novel submodular function to discover more accurate small interpretation regions. To enhance the attribution effect for all samples, we also impose four different constraints on the selection of sub-regions, i.e., confidence, effectiveness, consistency, and collaboration scores, to assess the importance of various subsets. Moreover, our theoretical analysis substantiates that the proposed function is in fact submodular. Extensive experiments show that the proposed method outperforms SOTA methods on two face datasets (Celeb-A and VGG-Face2) and one fine-grained dataset (CUB-200-2011). For correctly predicted samples, the proposed method improves the Deletion and Insertion scores with an average of 4.9% and 2.5% gain relative to HSIC-Attribution. For incorrectly predicted samples, our method achieves gains of 81.0% and 18.4% compared to the HSIC-Attribution algorithm in the average highest confidence and Insertion score respectively. The code is released at https://github.com/RuoyuChen10/SMDL-Attribution.

cs.CV↗

Convexification for a Coefficient Inverse Problem for a System of Two Coupled Nonlinear Parabolic Equations

A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games System" (MFGS), which is derived in the mean field games (MFG) theory. This theory has numerous applications in social sciences. The topic of Coefficient Inverse Problems (CIPs) in the MFG theory is in its infant age, both in theory and computations. A numerical method for this CIP is developed. Convergence analysis ensures the global convergence of this method. Numerical experiments are presented.

math.NA↗

Schur complement based preconditioners for twofold and block tridiagonal saddle point problems

In this paper, we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems. One type of the preconditioners are based on the nested (or recursive) Schur complement, the other is based on an additive type Schur complement after permuting the original saddle point systems. We analyze different preconditioners incorporating the exact Schur complements. We show that some of them will lead to positively stable preconditioned systems if proper signs are selected in front of the Schur complements. These positive-stable preconditioners outperform other preconditioners if the Schur complements are further approximated inexactly. Numerical experiments for a 3-field formulation of the Biot model are provided to verify our predictions.

math.NA↗

Logit Standardization in Knowledge Distillation

Knowledge distillation involves transferring soft labels from a teacher to a student using a shared temperature-based softmax function. However, the assumption of a shared temperature between teacher and student implies a mandatory exact match between their logits in terms of logit range and variance. This side-effect limits the performance of student, considering the capacity discrepancy between them and the finding that the innate logit relations of teacher are sufficient for student to learn. To address this issue, we propose setting the temperature as the weighted standard deviation of logit and performing a plug-and-play Z-score pre-process of logit standardization before applying softmax and Kullback-Leibler divergence. Our pre-process enables student to focus on essential logit relations from teacher rather than requiring a magnitude match, and can improve the performance of existing logit-based distillation methods. We also show a typical case where the conventional setting of sharing temperature between teacher and student cannot reliably yield the authentic distillation evaluation; nonetheless, this challenge is successfully alleviated by our Z-score. We extensively evaluate our method for various student and teacher models on CIFAR-100 and ImageNet, showing its significant superiority. The vanilla knowledge distillation powered by our pre-process can achieve favorable performance against state-of-the-art methods, and other distillation variants can obtain considerable gain with the assistance of our pre-process.

cs.CV↗

Towards Generalized Few-Shot Open-Set Object Detection

Open-set object detection (OSOD) aims to detect the known categories and reject unknown objects in a dynamic world, which has achieved significant attention. However, previous approaches only consider this problem in data-abundant conditions, while neglecting the few-shot scenes. In this paper, we seek a solution for the generalized few-shot open-set object detection (G-FOOD), which aims to avoid detecting unknown classes as known classes with a high confidence score while maintaining the performance of few-shot detection. The main challenge for this task is that few training samples induce the model to overfit on the known classes, resulting in a poor open-set performance. We propose a new G-FOOD algorithm to tackle this issue, named \underline{F}ew-sh\underline{O}t \underline{O}pen-set \underline{D}etector (FOOD), which contains a novel class weight sparsification classifier (CWSC) and a novel unknown decoupling learner (UDL). To prevent over-fitting, CWSC randomly sparses parts of the normalized weights for the logit prediction of all classes, and then decreases the co-adaptability between the class and its neighbors. Alongside, UDL decouples training the unknown class and enables the model to form a compact unknown decision boundary. Thus, the unknown objects can be identified with a confidence probability without any threshold, prototype, or generation. We compare our method with several state-of-the-art OSOD methods in few-shot scenes and observe that our method improves the F-score of unknown classes by 4.80\%-9.08\% across all shots in VOC-COCO dataset settings \footnote[1]{The source code is available at \url{https://github.com/binyisu/food}}.

cs.CV↗

An Inverse Problem With the Final Overdetermination for the Mean Field Games System

The mean field games (MFG) theory has broad application in mathematical modeling of social phenomena. The Mean Field Games System (MFGS) is the key to the MFG theory. This is a system of two nonlinear parabolic partial differential equations with two opposite directions of time 0<t<T. The topic of Coefficient Inverse Problem (CIPs) for the MFGS is a newly emerging one. A CIP for the MFGS is studied. The input data are Dirichlet and Neumann boundary conditions either on a part of the lateral boundary (incomplete data) or on the whole lateral boundary (complete data). In addition to the initial conditions at t=0, terminal conditions at t=T are given. The terminal conditions mean the final overdetermination. The necessity of assigning all these input data is explained. Holder and Lipschitz stability estimates are obtained for the cases of incomplete and complete data respectively. These estimates imply uniqueness of the CIP.

math.AP↗

Exploring Inconsistent Knowledge Distillation for Object Detection with Data Augmentation

Knowledge Distillation (KD) for object detection aims to train a compact detector by transferring knowledge from a teacher model. Since the teacher model perceives data in a way different from humans, existing KD methods only distill knowledge that is consistent with labels annotated by human expert while neglecting knowledge that is not consistent with human perception, which results in insufficient distillation and sub-optimal performance. In this paper, we propose inconsistent knowledge distillation (IKD), which aims to distill knowledge inherent in the teacher model's counter-intuitive perceptions. We start by considering the teacher model's counter-intuitive perceptions of frequency and non-robust features. Unlike previous works that exploit fine-grained features or introduce additional regularizations, we extract inconsistent knowledge by providing diverse input using data augmentation. Specifically, we propose a sample-specific data augmentation to transfer the teacher model's ability in capturing distinct frequency components and suggest an adversarial feature augmentation to extract the teacher model's perceptions of non-robust features in the data. Extensive experiments demonstrate the effectiveness of our method which outperforms state-of-the-art KD baselines on one-stage, two-stage and anchor-free object detectors (at most +1.0 mAP). Our codes will be made available at \url{https://github.com/JWLiang007/IKD.git}.

cs.CV↗

Spatiotemporal Monitoring of Epidemics via Solution of a Coefficient Inverse Problem

Let S,I and R be susceptible, infected and recovered populations in a city affected by an epidemic. The SIR model of Lee, Liu, Tembine, Li and Osher, \emph{SIAM J. Appl. Math.},~81, 190--207, 2021 of the spatiotemoral spread of epidemics is considered. This model consists of a system of three nonlinear coupled parabolic Partial Differential Equations with respect to the space and time dependent functions S,I and R. For the first time, a Coefficient Inverse Problem (CIP) for this system is posed. The so-called \textquotedblleft convexification" numerical method for this inverse problem is constructed. The presence of the Carleman Weight Function (CWF) in the resulting regularization functional ensures the global convergence of the gradient descent method of the minimization of this functional to the true solution of the CIP, as long as the noise level tends to zero. The CWF is the function, which is used as the weight in the Carleman estimate for the corresponding Partial Differential Operator. Numerical studies demonstrate an accurate reconstruction of unknown coefficients as well as S,I,R functions inside of that city. As a by-product, uniqueness theorem for this CIP is proven. Since the minimal measured input data are required, then the proposed methodology has a potential of a significant decrease of the cost of monitoring of epidemics.

math.NA↗

On The Mean Field Games System With the Lateral Cauchy Data via Carleman Estimates

The second order Mean Field Games system (MFGS) in a bounded domain with the lateral Cauchy data is considered. This means that both Dirichlet and Neumann boundary data for the solution the MFGS are given. Two Hölder stability estimates for two slightly diffeent cases are derived. These estimates indicate how stable the solution of the MFGS is with respect to the possible noise in the lateral Cauchy data. Our stability estimates imply uniqueness. The key mathematical apparatus is the apparatus of two new Carleman estimates.

math.AP↗

Convexification for a Coefficient Inverse Problem of Mean Field Games

The globally convergent convexification numerical method is constructed for a Coefficient Inverse Problem for the Mean Field Games System. A coefficient characterizing the global interaction term is recovered from the single measurement data. In particular, a new Carleman estimate for the Volterra integral operator is proven, and it stronger than the previously known one. Numerical results demonstrate accurate reconstructions from noisy data.

math.NA↗