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Suppose $0 < p \le \infty$. For a simple graph $G$ with a vertex-degree sequence $d_1, \dots, d_n$ satisfying $(d_1^p + \dots + d_n^p)^{1/p} \le C$, we prove asymptotically sharp upper bounds on the number of $t$-cliques in $G$. This result bridges the $p = 1$ case, which is the notable Kruskal--Katona theorem, and the $p = \infty$ case, known as the Gan--Loh--Sudakov conjecture, and resolved by Chase. In particular, we demonstrate that the extremal construction exhibits a dichotomy between a single clique and multiple cliques at $p_0 = t - 1$. Our proof employs the entropy method., Comment: 15 pages

Let $P$ be a $2n$-point set in the plane that is in general position. We prove that every red-blue bipartition of $P$ into $R$ and $B$ with $|R| = |B| = n$ generates $\Omega(n^{3/2})$ red-red-blue empty triangles., Comment: 9 pages, 3 figures

We introduce a novel MV-DETR pipeline which is effective while efficient transformer based detection method. Given input RGBD data, we notice that there are super strong pretraining weights for RGB data while less effective works for depth related data. First and foremost , we argue that geometry and texture cues are both of vital importance while could be encoded separately. Secondly, we find that visual texture feature is relatively hard to extract compared with geometry feature in 3d space. Unfortunately, single RGBD dataset with thousands of data is not enough for training an discriminating filter for visual texture feature extraction. Last but certainly not the least, we designed a lightweight VG module consists of a visual textual encoder, a geometry encoder and a VG connector. Compared with previous state of the art works like V-DETR, gains from pretrained visual encoder could be seen. Extensive experiments on ScanNetV2 dataset shows the effectiveness of our method. It is worth mentioned that our method achieve 78\% AP which create new state of the art on ScanNetv2 benchmark.

Multi-modality fusion is proven an effective method for 3d perception for autonomous driving. However, most current multi-modality fusion pipelines for LiDAR semantic segmentation have complicated fusion mechanisms. Point painting is a quite straight forward method which directly bind LiDAR points with visual information. Unfortunately, previous point painting like methods suffer from projection error between camera and LiDAR. In our experiments, we find that this projection error is the devil in point painting. As a result of that, we propose a depth aware point painting mechanism, which significantly boosts the multi-modality fusion. Apart from that, we take a deeper look at the desired visual feature for LiDAR to operate semantic segmentation. By Lifting Visual Information as Cue, LVIC ranks 1st on nuScenes LiDAR semantic segmentation benchmark. Our experiments show the robustness and effectiveness. Codes would be make publicly available soon.

In this paper, we consider saturation problems related to the celebrated Erd\H{o}s--Szekeres convex polygon problem. For each $n \ge 7$, we construct a planar point set of size $(7/8) \cdot 2^{n-2}$ which is saturated for convex $n$-gons. That is, the set contains no $n$ points in convex position while the addition of any new point creates such a configuration. This demonstrates that the saturation number is smaller than the Ramsey number for the Erd\H{o}s--Szekeres problem. The proof also shows that the original Erd\H{o}s--Szekeres construction is indeed saturated. Our construction is based on a similar improvement for the saturation version of the cups-versus-caps theorem. Moreover, we consider the generalization of the cups-versus-caps theorem to monotone paths in ordered hypergraphs. In contrast to the geometric setting, we show that this abstract saturation number is always equal to the corresponding Ramsey number., Comment: Minor revisions

Point encoder is of vital importance for point cloud recognition. As the very beginning step of whole model pipeline, adding features from diverse sources and providing stronger feature encoding mechanism would provide better input for downstream modules. In our work, we proposed a novel PeP module to tackle above issue. PeP contains two main parts, a refined point painting method and a LM-based point encoder. Experiments results on the nuScenes and KITTI datasets validate the superior performance of our PeP. The advantages leads to strong performance on both semantic segmentation and object detection, in both lidar and multi-modal settings. Notably, our PeP module is model agnostic and plug-and-play. Our code will be publicly available soon.

Human robot interaction is an exciting task, which aimed to guide robots following instructions from human. Since huge gap lies between human natural language and machine codes, end to end human robot interaction models is fair challenging. Further, visual information receiving from sensors of robot is also a hard language for robot to perceive. In this work, HuBo-VLM is proposed to tackle perception tasks associated with human robot interaction including object detection and visual grounding by a unified transformer based vision language model. Extensive experiments on the Talk2Car benchmark demonstrate the effectiveness of our approach. Code would be publicly available in https://github.com/dzcgaara/HuBo-VLM.

Occupancy prediction tasks focus on the inference of both geometry and semantic labels for each voxel, which is an important perception mission. However, it is still a semantic segmentation task without distinguishing various instances. Further, although some existing works, such as Open-Vocabulary Occupancy (OVO), have already solved the problem of open vocabulary detection, visual grounding in occupancy has not been solved to the best of our knowledge. To tackle the above two limitations, this paper proposes Occupancy Grounding (OG), a novel method that equips vanilla occupancy instance segmentation ability and could operate visual grounding in a voxel manner with the help of grounded-SAM. Keys to our approach are (1) affinity field prediction for instance clustering and (2) association strategy for aligning 2D instance masks and 3D occupancy instances. Extensive experiments have been conducted whose visualization results and analysis are shown below. Our code will be publicly released soon.

Semantic occupancy prediction aims to infer dense geometry and semantics of surroundings for an autonomous agent to operate safely in the 3D environment. Existing occupancy prediction methods are almost entirely trained on human-annotated volumetric data. Although of high quality, the generation of such 3D annotations is laborious and costly, restricting them to a few specific object categories in the training dataset. To address this limitation, this paper proposes Open Vocabulary Occupancy (OVO), a novel approach that allows semantic occupancy prediction of arbitrary classes but without the need for 3D annotations during training. Keys to our approach are (1) knowledge distillation from a pre-trained 2D open-vocabulary segmentation model to the 3D occupancy network, and (2) pixel-voxel filtering for high-quality training data generation. The resulting framework is simple, compact, and compatible with most state-of-the-art semantic occupancy prediction models. On NYUv2 and SemanticKITTI datasets, OVO achieves competitive performance compared to supervised semantic occupancy prediction approaches. Furthermore, we conduct extensive analyses and ablation studies to offer insights into the design of the proposed framework. Our code is publicly available at https://github.com/dzcgaara/OVO.

We prove that every family of (not necessarily distinct) even cycles $D_1, \dotsc, D_{\lfloor 1.2(n-1) \rfloor+1}$ on some fixed $n$-vertex set has a rainbow even cycle (that is, a set of edges from distinct $D_i$'s, forming an even cycle). This resolves an open problem of Aharoni, Briggs, Holzman and Jiang. Moreover, the result is best possible for every positive integer $n$., Comment: 20 pages, 10 figures

For a finite point set $P \subset \mathbb{R}^d$, denote by $\text{diam}(P)$ the ratio of the largest to the smallest distances between pairs of points in $P$. Let $c_{d, \alpha}(n)$ be the largest integer $c$ such that any $n$-point set $P \subset \mathbb{R}^d$ in general position, satisfying $\text{diam}(P) < \alpha\sqrt[d]{n}$, contains an $c$-point convex independent subset. We determine the asymptotics of $c_{d, \alpha}(n)$ as $n \to \infty$ by showing the existence of positive constants $\beta = \beta(d, \alpha)$ and $\gamma = \gamma(d)$ such that $\beta n^{\frac{d-1}{d+1}} \le c_{d, \alpha}(n) \le \gamma n^{\frac{d-1}{d+1}}$ for $\alpha\geq 2$., Comment: 30 pages, 2 figures; added more detailed explanations throughout the paper

We give a new unified proof that any simple graph on $n$ vertices with maximum degree at most $\Delta$ has no more than $a\binom{\Delta+1}{t}+\binom{b}{t}$ cliques of size $t \ (t \ge 3)$, where $n = a(\Delta+1)+b \ (0 \le b \le \Delta)$., Comment: 4 pages

Long-range and short-range temporal modeling are two complementary and crucial aspects of video recognition. Most of the state-of-the-arts focus on short-range spatio-temporal modeling and then average multiple snippet-level predictions to yield the final video-level prediction. Thus, their video-level prediction does not consider spatio-temporal features of how video evolves along the temporal dimension. In this paper, we introduce a novel Dynamic Segment Aggregation (DSA) module to capture relationship among snippets. To be more specific, we attempt to generate a dynamic kernel for a convolutional operation to aggregate long-range temporal information among adjacent snippets adaptively. The DSA module is an efficient plug-and-play module and can be combined with the off-the-shelf clip-based models (i.e., TSM, I3D) to perform powerful long-range modeling with minimal overhead. The final video architecture, coined as DSANet. We conduct extensive experiments on several video recognition benchmarks (i.e., Mini-Kinetics-200, Kinetics-400, Something-Something V1 and ActivityNet) to show its superiority. Our proposed DSA module is shown to benefit various video recognition models significantly. For example, equipped with DSA modules, the top-1 accuracy of I3D ResNet-50 is improved from 74.9% to 78.2% on Kinetics-400. Codes are available at https://github.com/whwu95/DSANet., Comment: Accepted to ACMMM2021

Let $G$ be a graph on $n$ vertices of independence number $\alpha(G)$ such that every induced subgraph of $G$ on $n-k$ vertices has an independent set of size at least $\alpha(G) - \ell$. What is the largest possible $\alpha(G)$ in terms of $n$ for fixed $k$ and $\ell$? We show that $\alpha(G) \le n/2 + C_{k, \ell}$, which is sharp for $k-\ell \le 2$. We also use this result to determine new values of the Erd\H{o}s--Rogers function., Comment: 16 pages, 2 figures

We consider the expected length of the longest common subsequence between two random words of lengths $n$ and $(1-\varepsilon)kn$ over $k$-symbol alphabet. It is well-known that this quantity is asymptotic to $\gamma_{k,\varepsilon} n$ for some constant $\gamma_{k,\varepsilon}$. We show that $\gamma_{k,\varepsilon}$ is of the order $1-c\varepsilon^2$ uniformly in $k$ and $\varepsilon$. In addition, for large $k$, we give evidence that $\gamma_{k,\varepsilon}$ approaches $1-\tfrac{1}{4}\varepsilon^2$, and prove a matching lower bound., Comment: 38 pages

Fine-grained image classification is a challenging problem, since the difficulty of finding discriminative features. To handle this circumstance, basically, there are two ways to go. One is use attention based method to focus on informative areas, while the other one aims to find high order between features. Further, for attention based method there are two directions, activation based and detection based, which are proved effective by scholars. However ,rare work focus on fusing two types of attention with high order feature. In this paper, we propose a novel DAF method which fuse two types of attention and use them to as PAF(part attention filter) in deep bilinear transformation module to mine the relationship between separate parts of an object. Briefly, our network constructed by a student net who attempt to output two attention maps and a teacher net uses these two maps as empirical information to refine the result. The experiment result shows that only student net could get 87.6% accuracy in CUB dataset while cooperating with teacher net could achieve 89.1% accuracy., Comment: arXiv admin note: text overlap with arXiv:1809.00287 by other authors