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Jian Ding

Publications and source records attributed to Jian Ding.

At least 91 records · Page 5Linked to original sources
arXiv2022

Decoupling Zero-Shot Semantic Segmentation

Zero-shot semantic segmentation (ZS3) aims to segment the novel categories that have not been seen in the training. Existing works formulate ZS3 as a pixel-level zeroshot classification problem, and transfer semantic knowledge from seen classes to unseen ones with the help of language models pre-trained only with texts. While simple, the pixel-level ZS3 formulation shows the limited capability to integrate vision-language models that are often pre-trained with image-text pairs and currently demonstrate great potential for vision tasks. Inspired by the observation that humans often perform segment-level semantic labeling, we propose to decouple the ZS3 into two sub-tasks: 1) a classagnostic grouping task to group the pixels into segments. 2) a zero-shot classification task on segments. The former task does not involve category information and can be directly transferred to group pixels for unseen classes. The latter task performs at segment-level and provides a natural way to leverage large-scale vision-language models pre-trained with image-text pairs (e.g. CLIP) for ZS3. Based on the decoupling formulation, we propose a simple and effective zero-shot semantic segmentation model, called ZegFormer, which outperforms the previous methods on ZS3 standard benchmarks by large margins, e.g., 22 points on the PASCAL VOC and 3 points on the COCO-Stuff in terms of mIoU for unseen classes. Code will be released at https://github.com/dingjiansw101/ZegFormer.

cs.CV↗
arXiv2022

Deeply Unsupervised Patch Re-Identification for Pre-training Object Detectors

Unsupervised pre-training aims at learning transferable features that are beneficial for downstream tasks. However, most state-of-the-art unsupervised methods concentrate on learning global representations for image-level classification tasks instead of discriminative local region representations, which limits their transferability to region-level downstream tasks, such as object detection. To improve the transferability of pre-trained features to object detection, we present Deeply Unsupervised Patch Re-ID (DUPR), a simple yet effective method for unsupervised visual representation learning. The patch Re-ID task treats individual patch as a pseudo-identity and contrastively learns its correspondence in two views, enabling us to obtain discriminative local features for object detection. Then the proposed patch Re-ID is performed in a deeply unsupervised manner, appealing to object detection, which usually requires multilevel feature maps. Extensive experiments demonstrate that DUPR outperforms state-of-the-art unsupervised pre-trainings and even the ImageNet supervised pre-training on various downstream tasks related to object detection.

cs.CV↗
arXiv2022

A New Correlation Inequality for Ising Models with External Fields

We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of boundary conditions on any given spin is maximised when the external field is identically $0$. One corollary is that spin-spin correlations are maximised when the external field vanishes and the boundary condition is free, which proves a conjecture of Shlosman. In particular, the random field Ising model on ${\mathbb Z}^d$, $d\geq 3$, exhibits exponential decay of correlations in the entire high temperature regime of the pure Ising model. Another corollary is that the pure Ising model in $d\geq 3$ satisfies the conjectured strong spatial mixing property in the entire high temperature regime.

math.PR↗
arXiv2021

Object Detection in Aerial Images: A Large-Scale Benchmark and Challenges

In the past decade, object detection has achieved significant progress in natural images but not in aerial images, due to the massive variations in the scale and orientation of objects caused by the bird's-eye view of aerial images. More importantly, the lack of large-scale benchmarks has become a major obstacle to the development of object detection in aerial images (ODAI). In this paper,we present a large-scale Dataset of Object deTection in Aerial images (DOTA) and comprehensive baselines for ODAI. The proposed DOTA dataset contains 1,793,658 object instances of 18 categories of oriented-bounding-box annotations collected from 11,268 aerial images. Based on this large-scale and well-annotated dataset, we build baselines covering 10 state-of-the-art algorithms with over 70 configurations, where the speed and accuracy performances of each model have been evaluated. Furthermore, we provide a code library for ODAI and build a website for evaluating different algorithms. Previous challenges run on DOTA have attracted more than 1300 teams worldwide. We believe that the expanded large-scale DOTA dataset, the extensive baselines, the code library and the challenges can facilitate the designs of robust algorithms and reproducible research on the problem of object detection in aerial images.

cs.CV↗
arXiv2021

The distance exponent for Liouville first passage percolation is positive

Discrete Liouville first passage percolation (LFPP) with parameter $ξ> 0$ is the random metric on a sub-graph of $\mathbb Z^2$ obtained by assigning each vertex $z$ a weight of $e^{ξh(z)}$, where $h$ is the discrete Gaussian free field. We show that the distance exponent for discrete LFPP is strictly positive for all $ξ> 0$. More precisely, the discrete LFPP distance between the inner and outer boundaries of a discrete annulus of size $2^n$ is typically at least $2^{αn}$ for an exponent $α> 0$ depending on $ξ$. This is a crucial input in the proof that LFPP admits non-trivial subsequential scaling limits for all $ξ> 0$ and also has theoretical implications for the study of distances in Liouville quantum gravity.

math.PR↗
arXiv2021

Long range order for random field Ising and Potts models

We present a new and simple proof for the classic results of Imbrie (1985) and Bricmont-Kupiainen (1988) that for the random field Ising model in dimension three and above there is long range order at low temperatures with presence of weak disorder. With the same method, we obtain a couple of new results: (1) we prove that long range order exists for the random field Potts model at low temperatures with presence of weak disorder in dimension three and above; (2) we obtain a lower bound on the correlation length for the random field Ising model at low temperatures in dimension two (which matches the upper bound in Ding-Wirth (2020)). Our proof is based on an extension of the Peierls argument with inputs from Chalker (1983), Fisher-Fröhlich-Spencer (1984), Ding-Wirth (2020) and Talagrand's majorizing measure theory (1980s) (and in particular, our proof does not involve the renormalization group theory).

math.PR↗
arXiv2021

LUAI Challenge 2021 on Learning to Understand Aerial Images

This report summarizes the results of Learning to Understand Aerial Images (LUAI) 2021 challenge held on ICCV 2021, which focuses on object detection and semantic segmentation in aerial images. Using DOTA-v2.0 and GID-15 datasets, this challenge proposes three tasks for oriented object detection, horizontal object detection, and semantic segmentation of common categories in aerial images. This challenge received a total of 146 registrations on the three tasks. Through the challenge, we hope to draw attention from a wide range of communities and call for more efforts on the problems of learning to understand aerial images.

cs.CV↗
arXiv2021

Up-to-constants comparison of Liouville first passage percolation and Liouville quantum gravity

Liouville first passage percolation (LFPP) with parameter $ξ> 0$ is the family of random distance functions $\{D_h^ε\}_{ε>0}$ on the plane obtained by integrating $e^{ξh_ε}$ along paths, where $\{h_ε\}_{ε>0}$ is a smooth mollification of the planar Gaussian free field. Recent works have shown that for all $ξ> 0$ the LFPP metrics, appropriately re-scaled, admit non-trivial subsequential limiting metrics. In the case when $ξ< ξ_{\mathrm{crit}} \approx 0.41$, it has been shown that the subsequential limit is unique and defines a metric on $γ$-Liouville quantum gravity $γ= γ(ξ) \in (0,2)$. We prove that for all $ξ> 0$, each possible subsequential limiting metric is nearly bi-Lipschitz equivalent to the LFPP metric $D_h^ε$ when $ε$ is small, even if $ε$ does not belong to the appropriate subsequence. Using this result, we obtain bounds for the scaling constants for LFPP which are sharp up to polylogarithmic factors. We also prove that any two subsequential limiting metrics are bi-Lipschitz equivalent. Our results are an input in subsequent work which shows that the subsequential limits of LFPP induce the same topology as the Euclidean metric when $ξ= ξ_{\mathrm{crit}}$. We expect that our results will also have several other uses, e.g., in the proof that the subsequential limit is unique when $ξ\geq ξ_{\mathrm{crit}}$.

math.PR↗
arXiv2021

The critical Liouville quantum gravity metric induces the Euclidean topology

We show that every possible metric associated with critical ($γ=2$) Liouville quantum gravity (LQG) induces the same topology on the plane as the Euclidean metric. More precisely, we show that the optimal modulus of continuity of the critical LQG metric with respect to the Euclidean metric is a power of $1/\log(1/|\cdot|)$. Our result applies to every possible subsequential limit of critical Liouville first passage percolation, a natural approximation scheme for the LQG metric which was recently shown to be tight.

math.PR↗
arXiv2021

DetCo: Unsupervised Contrastive Learning for Object Detection

Unsupervised contrastive learning achieves great success in learning image representations with CNN. Unlike most recent methods that focused on improving accuracy of image classification, we present a novel contrastive learning approach, named DetCo, which fully explores the contrasts between global image and local image patches to learn discriminative representations for object detection. DetCo has several appealing benefits. (1) It is carefully designed by investigating the weaknesses of current self-supervised methods, which discard important representations for object detection. (2) DetCo builds hierarchical intermediate contrastive losses between global image and local patches to improve object detection, while maintaining global representations for image recognition. Theoretical analysis shows that the local patches actually remove the contextual information of an image, improving the lower bound of mutual information for better contrastive learning. (3) Extensive experiments on PASCAL VOC, COCO and Cityscapes demonstrate that DetCo not only outperforms state-of-the-art methods on object detection, but also on segmentation, pose estimation, and 3D shape prediction, while it is still competitive on image classification. For example, on PASCAL VOC, DetCo-100ep achieves 57.4 mAP, which is on par with the result of MoCov2-800ep. Moreover, DetCo consistently outperforms supervised method by 1.6/1.2/1.0 AP on Mask RCNN-C4/FPN/RetinaNet with 1x schedule. Code will be released at \href{https://github.com/xieenze/DetCo}{\color{blue}{\tt github.com/xieenze/DetCo}}.

cs.CV↗
arXiv2021

Align Deep Features for Oriented Object Detection

The past decade has witnessed significant progress on detecting objects in aerial images that are often distributed with large scale variations and arbitrary orientations. However most of existing methods rely on heuristically defined anchors with different scales, angles and aspect ratios and usually suffer from severe misalignment between anchor boxes and axis-aligned convolutional features, which leads to the common inconsistency between the classification score and localization accuracy. To address this issue, we propose a Single-shot Alignment Network (S$^2$A-Net) consisting of two modules: a Feature Alignment Module (FAM) and an Oriented Detection Module (ODM). The FAM can generate high-quality anchors with an Anchor Refinement Network and adaptively align the convolutional features according to the anchor boxes with a novel Alignment Convolution. The ODM first adopts active rotating filters to encode the orientation information and then produces orientation-sensitive and orientation-invariant features to alleviate the inconsistency between classification score and localization accuracy. Besides, we further explore the approach to detect objects in large-size images, which leads to a better trade-off between speed and accuracy. Extensive experiments demonstrate that our method can achieve state-of-the-art performance on two commonly used aerial objects datasets (i.e., DOTA and HRSC2016) while keeping high efficiency. The code is available at https://github.com/csuhan/s2anet.

cs.CV↗
arXiv2021

Proof of the satisfiability conjecture for large k

We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $α_*(k)$ such that a random $k$-SAT formula of clause density $α$ is with high probability satisfiable for $α<α_*$, and unsatisfiable for $α>α_*$. We show that the threshold $α_*(k)$ is given explicitly by the one-step replica symmetry breaking prediction from statistical physics. The proof develops a new analytic method for moment calculations on random graphs, mapping a high-dimensional optimization problem to a more tractable problem of analyzing tree recursions. We believe that our method may apply to a range of random CSPs in the 1-RSB universality class.

math.PR↗
arXiv2021

Tightness of supercritical Liouville first passage percolation

Liouville first passage percolation (LFPP) with parameter $ξ>0$ is the family of random distance functions $\{D_h^ε\}_{ε>0}$ on the plane obtained by integrating $e^{ξh_ε}$ along paths, where $h_ε$ for $ε>0$ is a smooth mollification of the planar Gaussian free field. Previous work by Ding-Dubédat-Dunlap-Falconet and Gwynne-Miller has shown that there is a critical value $ξ_{\mathrm{crit}} > 0$ such that for $ξ< ξ_{\mathrm{crit}}$, LFPP converges under appropriate re-scaling to a random metric on the plane which induces the same topology as the Euclidean metric (the so-called $γ$-\emph{Liouville quantum gravity metric} for $γ= γ(ξ)\in (0,2)$). We show that for all $ξ> 0$, the LFPP metrics are tight with respect to the topology on lower semicontinuous functions. For $ξ> ξ_{\mathrm{crit}}$, every possible subsequential limit $D_h$ is a metric on the plane which does \emph{not} induce the Euclidean topology: rather, there is an uncountable, dense, Lebesgue measure-zero set of points $z\in\mathbb C $ such that $D_h(z,w) = \infty$ for every $w\in\mathbb C\setminus \{z\}$. We expect that these subsequential limiting metrics are related to Liouville quantum gravity with matter central charge in $(1,25)$.

math.PR↗
arXiv2021

The planted matching problem: Sharp threshold and infinite-order phase transition

We study the problem of reconstructing a perfect matching $M^*$ hidden in a randomly weighted $n\times n$ bipartite graph. The edge set includes every node pair in $M^*$ and each of the $n(n-1)$ node pairs not in $M^*$ independently with probability $d/n$. The weight of each edge $e$ is independently drawn from the distribution $\mathcal{P}$ if $e \in M^*$ and from $\mathcal{Q}$ if $e \notin M^*$. We show that if $\sqrt{d} B(\mathcal{P},\mathcal{Q}) \le 1$, where $B(\mathcal{P},\mathcal{Q})$ stands for the Bhattacharyya coefficient, the reconstruction error (average fraction of misclassified edges) of the maximum likelihood estimator of $M^*$ converges to $0$ as $n\to \infty$. Conversely, if $\sqrt{d} B(\mathcal{P},\mathcal{Q}) \ge 1+ε$ for an arbitrarily small constant $ε>0$, the reconstruction error for any estimator is shown to be bounded away from $0$ under both the sparse and dense model, resolving the conjecture in [Moharrami et al. 2019, Semerjian et al. 2020]. Furthermore, in the special case of complete exponentially weighted graph with $d=n$, $\mathcal{P}=\exp(λ)$, and $\mathcal{Q}=\exp(1/n)$, for which the sharp threshold simplifies to $λ=4$, we prove that when $λ\le 4-ε$, the optimal reconstruction error is $\exp\left( - Θ(1/\sqrtε) \right)$, confirming the conjectured infinite-order phase transition in [Semerjian et al. 2020].

math.ST↗
arXiv2021

ReDet: A Rotation-equivariant Detector for Aerial Object Detection

Recently, object detection in aerial images has gained much attention in computer vision. Different from objects in natural images, aerial objects are often distributed with arbitrary orientation. Therefore, the detector requires more parameters to encode the orientation information, which are often highly redundant and inefficient. Moreover, as ordinary CNNs do not explicitly model the orientation variation, large amounts of rotation augmented data is needed to train an accurate object detector. In this paper, we propose a Rotation-equivariant Detector (ReDet) to address these issues, which explicitly encodes rotation equivariance and rotation invariance. More precisely, we incorporate rotation-equivariant networks into the detector to extract rotation-equivariant features, which can accurately predict the orientation and lead to a huge reduction of model size. Based on the rotation-equivariant features, we also present Rotation-invariant RoI Align (RiRoI Align), which adaptively extracts rotation-invariant features from equivariant features according to the orientation of RoI. Extensive experiments on several challenging aerial image datasets DOTA-v1.0, DOTA-v1.5 and HRSC2016, show that our method can achieve state-of-the-art performance on the task of aerial object detection. Compared with previous best results, our ReDet gains 1.2, 3.5 and 2.6 mAP on DOTA-v1.0, DOTA-v1.5 and HRSC2016 respectively while reducing the number of parameters by 60\% (313 Mb vs. 121 Mb). The code is available at: \url{https://github.com/csuhan/ReDet}.

cs.CV↗
arXiv2020

Tightness of Liouville first passage percolation for $γ\in (0,2)$

We study Liouville first passage percolation metrics associated to a Gaussian free field $h$ mollified by the two-dimensional heat kernel $p_t$ in the bulk, and related star-scale invariant metrics. For $γ\in (0,2)$ and $ξ= \fracγ{d_γ}$, where $d_γ$ is the Liouville quantum gravity dimension defined in [Ding-Gwynne18], we show that renormalized metrics $(λ_t^{-1} e^{ξp_t * h} ds)_{t \in (0,1)}$ are tight with respect to the uniform topology. In particular, we show that subsequential limits are bi-Hölder with respect to the Euclidean topology, obtain tail estimates for side-to-side distances and derive error bounds for the normalizing constants $λ_t$.

math.PR↗
arXiv2020

Efficient random graph matching via degree profiles

Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erdős-Rényi graphs $G(n,\frac{d}{n})$. This can be viewed as an average-case and noisy version of the graph isomorphism problem. Under this model, the maximum likelihood estimator is equivalent to solving the intractable quadratic assignment problem. This work develops an $\tilde{O}(n d^2+n^2)$-time algorithm which perfectly recovers the true vertex correspondence with high probability, provided that the average degree is at least $d = Ω(\log^2 n)$ and the two graphs differ by at most $δ= O( \log^{-2}(n) )$ fraction of edges. For dense graphs and sparse graphs, this can be improved to $δ= O( \log^{-2/3}(n) )$ and $δ= O( \log^{-2}(d) )$ respectively, both in polynomial time. The methodology is based on appropriately chosen distance statistics of the degree profiles (empirical distribution of the degrees of neighbors). Before this work, the best known result achieves $δ=O(1)$ and $n^{o(1)} \leq d \leq n^c$ for some constant $c$ with an $n^{O(\log n)}$-time algorithm \cite{barak2018nearly} and $δ=\tilde O((d/n)^4)$ and $d = \tildeΩ(n^{4/5})$ with a polynomial-time algorithm \cite{dai2018performance}.

stat.ML↗