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For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory, tropical geometry, and the theory of total positivity. Bloch and Karp furthermore characterized the (type A) partial flag varieties for which the two notions of positivity similarly coincide. We characterize the symplectic (type C) and odd-orthogonal (type B) partial flag varieties for which Lusztig's total positivity coincides with Plucker positivity., Comment: 36 pages; comments welcome. v2: minor revisions

We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of giving a description of the correctable erasure patterns in a maximally recoverable tensor code with the problem of describing bipartite rigid graphs or low-rank completable matrix patterns. Additionally, we relate dependencies among symmetric products of generic vectors to graph rigidity and symmetric matrix completion. With an eye toward applications to computer science, we study the dependency of these matroids on the characteristic by giving new combinatorial descriptions in several cases, including the first description of the correctable patterns in an (m, n, a=2, b=2) maximally recoverable tensor code.

In this paper, we give a complete characterization of rank $k-1$ positroids that are quotients of the uniform matroid $U_{k,n}$, completing a partial result by Bendetti-Chavez-Jim\'enez. Furthermore, we show that any pair of concordant positroids with adjacent ranks are related by a cyclic shift on their decorated permutations. We also use the concept of conecklaces to give a full characterization of concordant lattice path matroids (LPMs)., Comment: 32 pages, 10 figures; This research was carried out as part of the PACE program in the summer of 2023 at Peking University, Beijing; Comments very welcome

Quantum Bruhat graph is a weighted directed graph on a finite Weyl group first defined by Brenti-Fomin-Postnikov. It encodes quantum Monk's rule and can be utilized to study the $3$-point Gromov-Witten invariants of the flag variety. In this paper, we provide an explicit formula for the minimal weights between any pair of permutations on the quantum Bruhat graph, and consequently obtain an Ehresmann-like characterization for the tilted Bruhat order. Moreover, for any ordered pair of permutations $u$ and $v$, we define the tilted Richardson variety $T_{u,v}$, with a stratification that gives a geometric meaning to intervals in the tilted Bruhat order. We provide a few equivalent definitions to this new family of varieties that include Richardson varieties, and establish some fundamental geometric properties including their dimensions and closure relations., Comment: 28 pages

We present a new correspondence between acyclic orientations and coloring of a signed graph (symmetric graph). Goodall et al. introduced a bivariate chromatic polynomial $\chi_G(k,l)$ that counts the number of signed colorings using colors $0,\pm1,\dots,\pm k$ along with $l-1$ symmetric colors $0_1,\dots,0_{l-1}$. We show that the evaluation of the bivariate chromatic polynomial $|\chi_G(-1,2)|$ is equal to the number of acyclic orientations of the signed graph modulo the equivalence relation generated by swapping sources and sinks. We present three proofs of this fact, a proof using toric hyperplane arrangements, a proof using deletion-contraction, and a direct proof., Comment: 17 pages, 7 figures

We introduce balanced shifted tableaux, as an analogue of balanced tableaux of Edelman and Greene, from the perspective of root systems of type B and C. We show that they are equinumerous to standard Young tableaux of the corresponding shifted shape by presenting an explicit bijection., Comment: 20 pages

High Definition (HD) maps are maps with precise definitions of road lanes with rich semantics of the traffic rules. They are critical for several key stages in an autonomous driving system, including motion forecasting and planning. However, there are only a small amount of real-world road topologies and geometries, which significantly limits our ability to test out the self-driving stack to generalize onto new unseen scenarios. To address this issue, we introduce a new challenging task to generate HD maps. In this work, we explore several autoregressive models using different data representations, including sequence, plain graph, and hierarchical graph. We propose HDMapGen, a hierarchical graph generation model capable of producing high-quality and diverse HD maps through a coarse-to-fine approach. Experiments on the Argoverse dataset and an in-house dataset show that HDMapGen significantly outperforms baseline methods. Additionally, we demonstrate that HDMapGen achieves high scalability and efficiency.

Predicting the future behavior of moving agents is essential for real world applications. It is challenging as the intent of the agent and the corresponding behavior is unknown and intrinsically multimodal. Our key insight is that for prediction within a moderate time horizon, the future modes can be effectively captured by a set of target states. This leads to our target-driven trajectory prediction (TNT) framework. TNT has three stages which are trained end-to-end. It first predicts an agent's potential target states $T$ steps into the future, by encoding its interactions with the environment and the other agents. TNT then generates trajectory state sequences conditioned on targets. A final stage estimates trajectory likelihoods and a final compact set of trajectory predictions is selected. This is in contrast to previous work which models agent intents as latent variables, and relies on test-time sampling to generate diverse trajectories. We benchmark TNT on trajectory prediction of vehicles and pedestrians, where we outperform state-of-the-art on Argoverse Forecasting, INTERACTION, Stanford Drone and an in-house Pedestrian-at-Intersection dataset.

Behavior prediction in dynamic, multi-agent systems is an important problem in the context of self-driving cars, due to the complex representations and interactions of road components, including moving agents (e.g. pedestrians and vehicles) and road context information (e.g. lanes, traffic lights). This paper introduces VectorNet, a hierarchical graph neural network that first exploits the spatial locality of individual road components represented by vectors and then models the high-order interactions among all components. In contrast to most recent approaches, which render trajectories of moving agents and road context information as bird-eye images and encode them with convolutional neural networks (ConvNets), our approach operates on a vector representation. By operating on the vectorized high definition (HD) maps and agent trajectories, we avoid lossy rendering and computationally intensive ConvNet encoding steps. To further boost VectorNet's capability in learning context features, we propose a novel auxiliary task to recover the randomly masked out map entities and agent trajectories based on their context. We evaluate VectorNet on our in-house behavior prediction benchmark and the recently released Argoverse forecasting dataset. Our method achieves on par or better performance than the competitive rendering approach on both benchmarks while saving over 70% of the model parameters with an order of magnitude reduction in FLOPs. It also outperforms the state of the art on the Argoverse dataset., Comment: CVPR 2020

Detecting pedestrians and predicting future trajectories for them are critical tasks for numerous applications, such as autonomous driving. Previous methods either treat the detection and prediction as separate tasks or simply add a trajectory regression head on top of a detector. In this work, we present a novel end-to-end two-stage network: Spatio-Temporal-Interactive Network (STINet). In addition to 3D geometry modeling of pedestrians, we model the temporal information for each of the pedestrians. To do so, our method predicts both current and past locations in the first stage, so that each pedestrian can be linked across frames and the comprehensive spatio-temporal information can be captured in the second stage. Also, we model the interaction among objects with an interaction graph, to gather the information among the neighboring objects. Comprehensive experiments on the Lyft Dataset and the recently released large-scale Waymo Open Dataset for both object detection and future trajectory prediction validate the effectiveness of the proposed method. For the Waymo Open Dataset, we achieve a bird-eyes-view (BEV) detection AP of 80.73 and trajectory prediction average displacement error (ADE) of 33.67cm for pedestrians, which establish the state-of-the-art for both tasks.

The task of referring relationships is to localize subject and object entities in an image satisfying a relationship query, which is given in the form of \texttt{}. This requires simultaneous localization of the subject and object entities in a specified relationship. We introduce a simple yet effective proposal-based method for referring relationships. Different from the existing methods such as SSAS, our method can generate a high-resolution result while reducing its complexity and ambiguity. Our method is composed of two modules: a category-based proposal generation module to select the proposals related to the entities and a predicate analysis module to score the compatibility of pairs of selected proposals. We show state-of-the-art performance on the referring relationship task on two public datasets: Visual Relationship Detection and Visual Genome., Comment: CVPR 2020 Workshop on Multimodal Learning

The sandpile group of a connected graph $G$, defined to be the torsion part of the cokernel of the graph Laplacian, is a subtle graph invariant with combinatorial, algebraic, and geometric descriptions. Extending and improving previous works on the sandpile group of hypercubes, we study the sandpile groups of the Cayley graphs of $\mathbb{F}_2^r$, focusing on their poorly understood Sylow-$2$ component. We find the number of Sylow-$2$ cyclic factors for "generic" Cayley graphs and deduce a bound for the non-generic ones. Moreover, we provide a sharp upper bound for their largest Sylow-$2$ cyclic factors. In the case of hypercubes, we give exact formulae for the largest $n-1$ Sylow-$2$ cyclic factors. Some key ingredients of our work include the natural ring structure on these sandpile groups from representation theory, and calculation of the $2$-adic valuations of binomial sums via the combinatorics of carries., Comment: v2: 19 pages, 1 figure, 1 table; proved Conjecture 6.1 in older version (now Theorem 2.9), change of authorship. v3: 20 pages, 1 figure, 1 table; minor revision from v2

Recent work on 3D object detection advocates point cloud voxelization in birds-eye view, where objects preserve their physical dimensions and are naturally separable. When represented in this view, however, point clouds are sparse and have highly variable point density, which may cause detectors difficulties in detecting distant or small objects (pedestrians, traffic signs, etc.). On the other hand, perspective view provides dense observations, which could allow more favorable feature encoding for such cases. In this paper, we aim to synergize the birds-eye view and the perspective view and propose a novel end-to-end multi-view fusion (MVF) algorithm, which can effectively learn to utilize the complementary information from both. Specifically, we introduce dynamic voxelization, which has four merits compared to existing voxelization methods, i) removing the need of pre-allocating a tensor with fixed size; ii) overcoming the information loss due to stochastic point/voxel dropout; iii) yielding deterministic voxel embeddings and more stable detection outcomes; iv) establishing the bi-directional relationship between points and voxels, which potentially lays a natural foundation for cross-view feature fusion. By employing dynamic voxelization, the proposed feature fusion architecture enables each point to learn to fuse context information from different views. MVF operates on points and can be naturally extended to other approaches using LiDAR point clouds. We evaluate our MVF model extensively on the newly released Waymo Open Dataset and on the KITTI dataset and demonstrate that it significantly improves detection accuracy over the comparable single-view PointPillars baseline., Comment: CoRL2019

The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces $\mathbb{P}^1 \times \mathbb{P}^1$, we investigate which sets of points have a virtual resolution that is a Koszul complex on a regular sequence. This paper provides conditions on sets of points; some of which guarantee the points have this property, and some of which guarantee the points do not have this property., Comment: Minor revisions

The labeling cost of large number of bounding boxes is one of the main challenges for training modern object detectors. To reduce the dependence on expensive bounding box annotations, we propose a new semi-supervised object detection formulation, in which a few seed box level annotations and a large scale of image level annotations are used to train the detector. We adopt a training-mining framework, which is widely used in weakly supervised object detection tasks. However, the mining process inherently introduces various kinds of labelling noises: false negatives, false positives and inaccurate boundaries, which can be harmful for training the standard object detectors (e.g. Faster RCNN). We propose a novel NOise Tolerant Ensemble RCNN (NOTE-RCNN) object detector to handle such noisy labels. Comparing to standard Faster RCNN, it contains three highlights: an ensemble of two classification heads and a distillation head to avoid overfitting on noisy labels and improve the mining precision, masking the negative sample loss in box predictor to avoid the harm of false negative labels, and training box regression head only on seed annotations to eliminate the harm from inaccurate boundaries of mined bounding boxes. We evaluate the methods on ILSVRC 2013 and MSCOCO 2017 dataset; we observe that the detection accuracy consistently improves as we iterate between mining and training steps, and state-of-the-art performance is achieved., Comment: 8 pages

We address the problem of language-based temporal localization in untrimmed videos. Compared to temporal localization with fixed categories, this problem is more challenging as the language-based queries not only have no pre-defined activity list but also may contain complex descriptions. Previous methods address the problem by considering features from video sliding windows and language queries and learning a subspace to encode their correlation, which ignore rich semantic cues about activities in videos and queries. We propose to mine activity concepts from both video and language modalities by applying the actionness score enhanced Activity Concepts based Localizer (ACL). Specifically, the novel ACL encodes the semantic concepts from verb-obj pairs in language queries and leverages activity classifiers' prediction scores to encode visual concepts. Besides, ACL also has the capability to regress sliding windows as localization results. Experiments show that ACL significantly outperforms state-of-the-arts under the widely used metric, with more than 5% increase on both Charades-STA and TACoS datasets., Comment: WACV 2019

Temporal action proposal generation is an important task, akin to object proposals, temporal action proposals are intended to capture "clips" or temporal intervals in videos that are likely to contain an action. Previous methods can be divided to two groups: sliding window ranking and actionness score grouping. Sliding windows uniformly cover all segments in videos, but the temporal boundaries are imprecise; grouping based method may have more precise boundaries but it may omit some proposals when the quality of actionness score is low. Based on the complementary characteristics of these two methods, we propose a novel Complementary Temporal Action Proposal (CTAP) generator. Specifically, we apply a Proposal-level Actionness Trustworthiness Estimator (PATE) on the sliding windows proposals to generate the probabilities indicating whether the actions can be correctly detected by actionness scores, the windows with high scores are collected. The collected sliding windows and actionness proposals are then processed by a temporal convolutional neural network for proposal ranking and boundary adjustment. CTAP outperforms state-of-the-art methods on average recall (AR) by a large margin on THUMOS-14 and ActivityNet 1.3 datasets. We further apply CTAP as a proposal generation method in an existing action detector, and show consistent significant improvements., Comment: ECCV 2018 main conference paper (camera ready version). Code is available in http://www.github.com/jiyanggao/CTAP

Video-based person reID is an important task, which has received much attention in recent years due to the increasing demand in surveillance and camera networks. A typical video-based person reID system consists of three parts: an image-level feature extractor (e.g. CNN), a temporal modeling method to aggregate temporal features and a loss function. Although many methods on temporal modeling have been proposed, it is hard to directly compare these methods, because the choice of feature extractor and loss function also have a large impact on the final performance. We comprehensively study and compare four different temporal modeling methods (temporal pooling, temporal attention, RNN and 3D convnets) for video-based person reID. We also propose a new attention generation network which adopts temporal convolution to extract temporal information among frames. The evaluation is done on the MARS dataset, and our methods outperform state-of-the-art methods by a large margin. Our source codes are released at https://github.com/jiyanggao/Video-Person-ReID., Comment: codes available at https://github.com/jiyanggao/Video-Person-ReID

Video Question Answering (QA) is an important task in understanding video temporal structure. We observe that there are three unique attributes of video QA compared with image QA: (1) it deals with long sequences of images containing richer information not only in quantity but also in variety; (2) motion and appearance information are usually correlated with each other and able to provide useful attention cues to the other; (3) different questions require different number of frames to infer the answer. Based these observations, we propose a motion-appearance comemory network for video QA. Our networks are built on concepts from Dynamic Memory Network (DMN) and introduces new mechanisms for video QA. Specifically, there are three salient aspects: (1) a co-memory attention mechanism that utilizes cues from both motion and appearance to generate attention; (2) a temporal conv-deconv network to generate multi-level contextual facts; (3) a dynamic fact ensemble method to construct temporal representation dynamically for different questions. We evaluate our method on TGIF-QA dataset, and the results outperform state-of-the-art significantly on all four tasks of TGIF-QA., Comment: CVPR 2018

Given a natural language query, a phrase grounding system aims to localize mentioned objects in an image. In weakly supervised scenario, mapping between image regions (i.e., proposals) and language is not available in the training set. Previous methods address this deficiency by training a grounding system via learning to reconstruct language information contained in input queries from predicted proposals. However, the optimization is solely guided by the reconstruction loss from the language modality, and ignores rich visual information contained in proposals and useful cues from external knowledge. In this paper, we explore the consistency contained in both visual and language modalities, and leverage complementary external knowledge to facilitate weakly supervised grounding. We propose a novel Knowledge Aided Consistency Network (KAC Net) which is optimized by reconstructing input query and proposal's information. To leverage complementary knowledge contained in the visual features, we introduce a Knowledge Based Pooling (KBP) gate to focus on query-related proposals. Experiments show that KAC Net provides a significant improvement on two popular datasets., Comment: CVPR 2018 conference paper

Fine-grained image labels are desirable for many computer vision applications, such as visual search or mobile AI assistant. These applications rely on image classification models that can produce hundreds of thousands (e.g. 100K) of diversified fine-grained image labels on input images. However, training a network at this vocabulary scale is challenging, and suffers from intolerable large model size and slow training speed, which leads to unsatisfying classification performance. A straightforward solution would be training separate expert networks (specialists), with each specialist focusing on learning one specific vertical (e.g. cars, birds...). However, deploying dozens of expert networks in a practical system would significantly increase system complexity and inference latency, and consumes large amounts of computational resources. To address these challenges, we propose a Knowledge Concentration method, which effectively transfers the knowledge from dozens of specialists (multiple teacher networks) into one single model (one student network) to classify 100K object categories. There are three salient aspects in our method: (1) a multi-teacher single-student knowledge distillation framework; (2) a self-paced learning mechanism to allow the student to learn from different teachers at various paces; (3) structurally connected layers to expand the student network capacity with limited extra parameters. We validate our method on OpenImage and a newly collected dataset, Entity-Foto-Tree (EFT), with 100K categories, and show that the proposed model performs significantly better than the baseline generalist model.

In this work, we address the problem of spatio-temporal action detection in temporally untrimmed videos. It is an important and challenging task as finding accurate human actions in both temporal and spatial space is important for analyzing large-scale video data. To tackle this problem, we propose a cascade proposal and location anticipation (CPLA) model for frame-level action detection. There are several salient points of our model: (1) a cascade region proposal network (casRPN) is adopted for action proposal generation and shows better localization accuracy compared with single region proposal network (RPN); (2) action spatio-temporal consistencies are exploited via a location anticipation network (LAN) and thus frame-level action detection is not conducted independently. Frame-level detections are then linked by solving an linking score maximization problem, and temporally trimmed into spatio-temporal action tubes. We demonstrate the effectiveness of our model on the challenging UCF101 and LIRIS-HARL datasets, both achieving state-of-the-art performance., Comment: Accepted at BMVC 2017 (oral)

Action anticipation aims to detect an action before it happens. Many real world applications in robotics and surveillance are related to this predictive capability. Current methods address this problem by first anticipating visual representations of future frames and then categorizing the anticipated representations to actions. However, anticipation is based on a single past frame's representation, which ignores the history trend. Besides, it can only anticipate a fixed future time. We propose a Reinforced Encoder-Decoder (RED) network for action anticipation. RED takes multiple history representations as input and learns to anticipate a sequence of future representations. One salient aspect of RED is that a reinforcement module is adopted to provide sequence-level supervision; the reward function is designed to encourage the system to make correct predictions as early as possible. We test RED on TVSeries, THUMOS-14 and TV-Human-Interaction datasets for action anticipation and achieve state-of-the-art performance on all datasets.

This paper focuses on temporal localization of actions in untrimmed videos. Existing methods typically train classifiers for a pre-defined list of actions and apply them in a sliding window fashion. However, activities in the wild consist of a wide combination of actors, actions and objects; it is difficult to design a proper activity list that meets users' needs. We propose to localize activities by natural language queries. Temporal Activity Localization via Language (TALL) is challenging as it requires: (1) suitable design of text and video representations to allow cross-modal matching of actions and language queries; (2) ability to locate actions accurately given features from sliding windows of limited granularity. We propose a novel Cross-modal Temporal Regression Localizer (CTRL) to jointly model text query and video clips, output alignment scores and action boundary regression results for candidate clips. For evaluation, we adopt TaCoS dataset, and build a new dataset for this task on top of Charades by adding sentence temporal annotations, called Charades-STA. We also build complex sentence queries in Charades-STA for test. Experimental results show that CTRL outperforms previous methods significantly on both datasets., Comment: ICCV 2017 camera ready (with supplemental material)

Temporal action detection in long videos is an important problem. State-of-the-art methods address this problem by applying action classifiers on sliding windows. Although sliding windows may contain an identifiable portion of the actions, they may not necessarily cover the entire action instance, which would lead to inferior performance. We adapt a two-stage temporal action detection pipeline with Cascaded Boundary Regression (CBR) model. Class-agnostic proposals and specific actions are detected respectively in the first and the second stage. CBR uses temporal coordinate regression to refine the temporal boundaries of the sliding windows. The salient aspect of the refinement process is that, inside each stage, the temporal boundaries are adjusted in a cascaded way by feeding the refined windows back to the system for further boundary refinement. We test CBR on THUMOS-14 and TVSeries, and achieve state-of-the-art performance on both datasets. The performance gain is especially remarkable under high IoU thresholds, e.g. map@tIoU=0.5 on THUMOS-14 is improved from 19.0% to 31.0%.

Temporal Action Proposal (TAP) generation is an important problem, as fast and accurate extraction of semantically important (e.g. human actions) segments from untrimmed videos is an important step for large-scale video analysis. We propose a novel Temporal Unit Regression Network (TURN) model. There are two salient aspects of TURN: (1) TURN jointly predicts action proposals and refines the temporal boundaries by temporal coordinate regression; (2) Fast computation is enabled by unit feature reuse: a long untrimmed video is decomposed into video units, which are reused as basic building blocks of temporal proposals. TURN outperforms the state-of-the-art methods under average recall (AR) by a large margin on THUMOS-14 and ActivityNet datasets, and runs at over 880 frames per second (FPS) on a TITAN X GPU. We further apply TURN as a proposal generation stage for existing temporal action localization pipelines, it outperforms state-of-the-art performance on THUMOS-14 and ActivityNet., Comment: ICCV 2017 camera ready

Action classification in still images has been a popular research topic in computer vision. Labelling large scale datasets for action classification requires tremendous manual work, which is hard to scale up. Besides, the action categories in such datasets are pre-defined and vocabularies are fixed. However humans may describe the same action with different phrases, which leads to the difficulty of vocabulary expansion for traditional fully-supervised methods. We observe that large amounts of images with sentence descriptions are readily available on the Internet. The sentence descriptions can be regarded as weak labels for the images, which contain rich information and could be used to learn flexible expressions of action categories. We propose a method to learn an Action Concept Tree (ACT) and an Action Semantic Alignment (ASA) model for classification from image-description data via a two-stage learning process. A new dataset for the task of learning actions from descriptions is built. Experimental results show that our method outperforms several baseline methods significantly., Comment: 16 pages, 5 figures

Action classification in still images is an important task in computer vision. It is challenging as the appearances of ac- tions may vary depending on their context (e.g. associated objects). Manually labeling of context information would be time consuming and difficult to scale up. To address this challenge, we propose a method to automatically discover and cluster action concepts, and learn their classifiers from weakly supervised image-sentence corpora. It obtains candidate action concepts by extracting verb-object pairs from sentences and verifies their visualness with the associated images. Candidate action concepts are then clustered by using a multi-modal representation with image embeddings from deep convolutional networks and text embeddings from word2vec. More than one hundred human action concept classifiers are learned from the Flickr 30k dataset with no additional human effort and promising classification results are obtained. We further apply the AdaBoost algorithm to automatically select and combine relevant action concepts given an action query. Promising results have been shown on the PASCAL VOC 2012 action classification benchmark, which has zero overlap with Flickr30k., Comment: 8 pages, accepted by ICMR 2016