arXiv subjects

Jian Ding

Publications and source records attributed to Jian Ding.

At least 73 records · Page 4Linked to original sources

arXiv2023

Uniqueness of the critical long-range percolation metrics

In this work, we study the random metric for the critical long-range percolation on $\mathbb{Z}^d$. A recent work by Bäumler [3] implies the subsequential scaling limit, and our main contribution is to prove that the subsequential limit is uniquely characterized by a natural list of axioms. Our proof method is hugely inspired by recent works of Gwynne and Miller [42], and Ding and Gwynne [25] on the uniqueness of Liouville quantum gravity metrics.

math.PR↗

arXiv2023

Towards Generic and Controllable Attacks Against Object Detection

Existing adversarial attacks against Object Detectors (ODs) suffer from two inherent limitations. Firstly, ODs have complicated meta-structure designs, hence most advanced attacks for ODs concentrate on attacking specific detector-intrinsic structures, which makes it hard for them to work on other detectors and motivates us to design a generic attack against ODs. Secondly, most works against ODs make Adversarial Examples (AEs) by generalizing image-level attacks from classification to detection, which brings redundant computations and perturbations in semantically meaningless areas (e.g., backgrounds) and leads to an emergency for seeking controllable attacks for ODs. To this end, we propose a generic white-box attack, LGP (local perturbations with adaptively global attacks), to blind mainstream object detectors with controllable perturbations. For a detector-agnostic attack, LGP tracks high-quality proposals and optimizes three heterogeneous losses simultaneously. In this way, we can fool the crucial components of ODs with a part of their outputs without the limitations of specific structures. Regarding controllability, we establish an object-wise constraint that exploits foreground-background separation adaptively to induce the attachment of perturbations to foregrounds. Experimentally, the proposed LGP successfully attacked sixteen state-of-the-art object detectors on MS-COCO and DOTA datasets, with promising imperceptibility and transferability obtained. Codes are publicly released in https://github.com/liguopeng0923/LGP.git

cs.CV↗

arXiv2023

One-arm exponent of critical level-set for metric graph Gaussian free field in high dimensions

In this paper, we study the critical level-set of Gaussian free field (GFF) on the metric graph $\widetilde{\mathbb{Z}}^d,d>6$. We prove that the one-arm probability (i.e. the probability of the event that the origin is connected to the boundary of the box $B(N)$) is proportional to $N^{-2}$, where $B(N)$ is centered at the origin and has side length $2\lfloor N \rfloor$. Our proof is hugely inspired by Kozma and Nachmias [29] which proves the analogous result of the critical bond percolation for $d\geq 11$, and by Werner [51] which conjectures the similarity between the GFF level-set and the bond percolation in general and proves this connection for various geometric aspects.

math.PR↗

arXiv2023

HGFormer: Hierarchical Grouping Transformer for Domain Generalized Semantic Segmentation

Current semantic segmentation models have achieved great success under the independent and identically distributed (i.i.d.) condition. However, in real-world applications, test data might come from a different domain than training data. Therefore, it is important to improve model robustness against domain differences. This work studies semantic segmentation under the domain generalization setting, where a model is trained only on the source domain and tested on the unseen target domain. Existing works show that Vision Transformers are more robust than CNNs and show that this is related to the visual grouping property of self-attention. In this work, we propose a novel hierarchical grouping transformer (HGFormer) to explicitly group pixels to form part-level masks and then whole-level masks. The masks at different scales aim to segment out both parts and a whole of classes. HGFormer combines mask classification results at both scales for class label prediction. We assemble multiple interesting cross-domain settings by using seven public semantic segmentation datasets. Experiments show that HGFormer yields more robust semantic segmentation results than per-pixel classification methods and flat grouping transformers, and outperforms previous methods significantly. Code will be available at https://github.com/dingjiansw101/HGFormer.

cs.CV↗

arXiv2023

Dynamic Coarse-to-Fine Learning for Oriented Tiny Object Detection

Detecting arbitrarily oriented tiny objects poses intense challenges to existing detectors, especially for label assignment. Despite the exploration of adaptive label assignment in recent oriented object detectors, the extreme geometry shape and limited feature of oriented tiny objects still induce severe mismatch and imbalance issues. Specifically, the position prior, positive sample feature, and instance are mismatched, and the learning of extreme-shaped objects is biased and unbalanced due to little proper feature supervision. To tackle these issues, we propose a dynamic prior along with the coarse-to-fine assigner, dubbed DCFL. For one thing, we model the prior, label assignment, and object representation all in a dynamic manner to alleviate the mismatch issue. For another, we leverage the coarse prior matching and finer posterior constraint to dynamically assign labels, providing appropriate and relatively balanced supervision for diverse instances. Extensive experiments on six datasets show substantial improvements to the baseline. Notably, we obtain the state-of-the-art performance for one-stage detectors on the DOTA-v1.5, DOTA-v2.0, and DIOR-R datasets under single-scale training and testing. Codes are available at https://github.com/Chasel-Tsui/mmrotate-dcfl.

cs.CV↗

arXiv2023

Introduction to the Liouville quantum gravity metric

Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal surfaces which first appeared in the physics literature in the 1980s. Recent works have constructed a metric (distance function) on an LQG surface. We give an overview of the construction of this metric and discuss some of its most important properties, such as the behavior of geodesics and the KPZ formula. We also discuss some of the main techniques for proving statements about the LQG metric, give examples of their use, and discuss some open problems.

math.PR↗

arXiv2023

Few-Shot Object Detection via Variational Feature Aggregation

As few-shot object detectors are often trained with abundant base samples and fine-tuned on few-shot novel examples,the learned models are usually biased to base classes and sensitive to the variance of novel examples. To address this issue, we propose a meta-learning framework with two novel feature aggregation schemes. More precisely, we first present a Class-Agnostic Aggregation (CAA) method, where the query and support features can be aggregated regardless of their categories. The interactions between different classes encourage class-agnostic representations and reduce confusion between base and novel classes. Based on the CAA, we then propose a Variational Feature Aggregation (VFA) method, which encodes support examples into class-level support features for robust feature aggregation. We use a variational autoencoder to estimate class distributions and sample variational features from distributions that are more robust to the variance of support examples. Besides, we decouple classification and regression tasks so that VFA is performed on the classification branch without affecting object localization. Extensive experiments on PASCAL VOC and COCO demonstrate that our method significantly outperforms a strong baseline (up to 16\%) and previous state-of-the-art methods (4\% in average). Code will be available at: \url{https://github.com/csuhan/VFA}

cs.CV↗

arXiv2023

Detecting Building Changes with Off-Nadir Aerial Images

The tilted viewing nature of the off-nadir aerial images brings severe challenges to the building change detection (BCD) problem: the mismatch of the nearby buildings and the semantic ambiguity of the building facades. To tackle these challenges, we present a multi-task guided change detection network model, named as MTGCD-Net. The proposed model approaches the specific BCD problem by designing three auxiliary tasks, including: (1) a pixel-wise classification task to predict the roofs and facades of buildings; (2) an auxiliary task for learning the roof-to-footprint offsets of each building to account for the misalignment between building roof instances; and (3) an auxiliary task for learning the identical roof matching flow between bi-temporal aerial images to tackle the building roof mismatch problem. These auxiliary tasks provide indispensable and complementary building parsing and matching information. The predictions of the auxiliary tasks are finally fused to the main building change detection branch with a multi-modal distillation module. To train and test models for the BCD problem with off-nadir aerial images, we create a new benchmark dataset, named BANDON. Extensive experiments demonstrate that our model achieves superior performance over the previous state-of-the-art competitors.

cs.CV↗

arXiv2022

A polynomial time iterative algorithm for matching Gaussian matrices with non-vanishing correlation

Motivated by the problem of matching vertices in two correlated Erdős-Rényi graphs, we study the problem of matching two correlated Gaussian Wigner matrices. We propose an iterative matching algorithm, which succeeds in polynomial time as long as the correlation between the two Gaussian matrices does not vanish. Our result is the first polynomial time algorithm that solves a graph matching type of problem when the correlation is an arbitrarily small constant.

cs.DS↗

arXiv2022

A polynomial-time approximation scheme for the maximal overlap of two independent Erdős-Rényi graphs

For two independent Erdős-Rényi graphs $\mathbf G(n,p)$, we study the maximal overlap (i.e., the number of common edges) of these two graphs over all possible vertex correspondence. We present a polynomial-time algorithm which finds a vertex correspondence whose overlap approximates the maximal overlap up to a multiplicative factor that is arbitrarily close to 1. As a by-product, we prove that the maximal overlap is asymptotically $\frac{n}{2α-1}$ for $p=n^{-α}$ with some constant $α\in (1/2,1)$.

math.PR↗

arXiv2022

Long range order for three-dimensional random field Ising model throughout the entire low temperature regime

For $d\geq 3$, we study the Ising model on $\mathbb Z^d$ with random field given by $\{εh_v: v\in \mathbb Z^d\}$ where $h_v$'s are independent normal variables with mean 0 and variance 1. We show that for any $T < T_c$ (here $T_c$ is the critical temperature without disorder), long range order exists as long as $ε$ is sufficiently small depending on $T$. Our work extends previous results of Imbrie (1985) and Bricmont--Kupiainen (1988) from the very low temperature regime to the entire low temperature regime.

math.PR↗

arXiv2022

Shotgun threshold for sparse Erdős-Rényi graphs

In the shotgun assembly problem for a graph, we are given the empirical profile for rooted neighborhoods of depth $r$ (up to isomorphism) for some $r\geq 1$ and we wish to recover the underlying graph up to isomorphism. When the underlying graph is an Erdős-Rényi $\mathcal G(n, \fracλ{n})$, we show that the shotgun assembly threshold $r_* \approx \frac{ \log n}{\log (λ^2 γ_λ)^{-1}}$ where $γ_λ$ is the probability for two independent Poisson-Galton-Watson trees with parameter $λ$ to be rooted isomorphic with each other. Our result sharpens a constant factor in a previous work by Mossel and Ross (2019) and thus solves a question therein.

math.PR↗

arXiv2022

Uniqueness of the critical and supercritical Liouville quantum gravity metrics

We show that for each ${\mathbf c}_{\mathrm M} \in [1,25)$, there is a unique metric associated with Liouville quantum gravity (LQG) with matter central charge ${\mathbf c}_{\mathrm M}$. An earlier series of works by Ding-Dubédat-Dunlap-Falconet, Gwynne-Miller, and others showed that such a metric exists and is unique in the subcritical case ${\mathbf c}_{\mathrm M} \in (-\infty,1)$, which corresponds to coupling constant $γ\in (0,2)$. The critical case ${\mathbf c}_{\mathrm M} = 1$ corresponds to $γ=2$ and the supercritical case ${\mathbf c}_{\mathrm M} \in (1,25)$ corresponds to $γ\in \mathbb C$ with $|γ| = 2$. Our metric is constructed as the limit of an approximation procedure called Liouville first passage percolation, which was previously shown to be tight for $\mathbf c_{\mathrm M} \in [1,25)$ by Ding and Gwynne (2020). In this paper, we show that the subsequential limit is uniquely characterized by a natural list of axioms. This extends the characterization of the LQG metric proven by Gwynne and Miller (2019) for $\mathbf c_{\mathrm M} \in (-\infty,1)$ to the full parameter range $\mathbf c_{\mathrm M} \in (-\infty,25)$. Our argument is substantially different from the proof of the characterization of the LQG metric for $\mathbf c_{\mathrm M} \in (-\infty,1)$. In particular, the core part of the argument is simpler and does not use confluence of geodesics.

math.PR↗

arXiv2022

Correlation length of the two-dimensional random field Ising model via greedy lattice animal

For the two-dimensional random field Ising model where the random field is given by i.i.d.\ mean zero Gaussian variables with variance $ε^2$, we study (one natural notion of) the correlation length, which is the critical size of a box at which the influences of the random field and of the boundary condition on the spin magnetization are comparable. We show that as $ε\to 0$, at zero temperature the correlation length scales as $e^{Θ(ε^{-4/3})}$ (and our upper bound applies for all positive temperatures).

math.PR↗

arXiv2022

Detection threshold for correlated Erdős-Rényi graphs via densest subgraphs

The problem of detecting edge correlation between two Erdős-Rényi random graphs on $n$ unlabeled nodes can be formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are sampled independently; under the alternative, the two graphs are independently sub-sampled from a parent graph which is Erdős-Rényi $\mathbf{G}(n, p)$ (so that their marginal distributions are the same as the null). We establish a sharp information-theoretic threshold when $p = n^{-α+o(1)}$ for $α\in (0, 1]$ which sharpens a constant factor in a recent work by Wu, Xu and Yu. A key novelty in our work is an interesting connection between the detection problem and the densest subgraph of an Erdős-Rényi graph.

math.PR↗

arXiv2022

Matching recovery threshold for correlated random graphs

For two correlated graphs which are independently sub-sampled from a common Erdős-Rényi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}. When $p = n^{-α+o(1)}$ for $α\in (0, 1]$, we establish a sharp information-theoretic threshold for whether it is possible to correctly match a positive fraction of vertices. Our result sharpens a constant factor in a recent work by Wu, Xu and Yu.

math.ST↗

arXiv2022

Expanding Low-Density Latent Regions for Open-Set Object Detection

Modern object detectors have achieved impressive progress under the close-set setup. However, open-set object detection (OSOD) remains challenging since objects of unknown categories are often misclassified to existing known classes. In this work, we propose to identify unknown objects by separating high/low-density regions in the latent space, based on the consensus that unknown objects are usually distributed in low-density latent regions. As traditional threshold-based methods only maintain limited low-density regions, which cannot cover all unknown objects, we present a novel Open-set Detector (OpenDet) with expanded low-density regions. To this aim, we equip OpenDet with two learners, Contrastive Feature Learner (CFL) and Unknown Probability Learner (UPL). CFL performs instance-level contrastive learning to encourage compact features of known classes, leaving more low-density regions for unknown classes; UPL optimizes unknown probability based on the uncertainty of predictions, which further divides more low-density regions around the cluster of known classes. Thus, unknown objects in low-density regions can be easily identified with the learned unknown probability. Extensive experiments demonstrate that our method can significantly improve the OSOD performance, e.g., OpenDet reduces the Absolute Open-Set Errors by 25%-35% on six OSOD benchmarks. Code is available at: https://github.com/csuhan/opendet2.

cs.CV↗

arXiv2022

Shotgun assembly threshold for lattice labeling model

We study the shotgun assembly problem for the lattice labeling model, where i.i.d. uniform labels are assigned to each vertex in a $d$-dimensional box of side length $n$. We wish to recover the labeling configuration on the whole box given empirical profile of labeling configurations on all boxes of side length $r$. We determine the threshold around which there is a sharp transition from impossible to recover with probability tending to 1, to possible to recover with an efficient algorithm with probability tending to 1. Our result sharpens a constant factor in a previous work of Mossel and Ross (2019) and thus solves a question therein.

math.PR↗