Long Sha

Tong Yang, Yifei Wang, Long Sha et al.

Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion and link prediction. However, existing KG embedding methods fell short to provide a systematic solution for the global consistency of knowledge representation. We developed a mathematical language for KG based on an observation of their inherent algebraic structure, which we termed as Knowledgebra. By analyzing five distinct algebraic properties, we proved that the semigroup is the most reasonable algebraic structure for the relation embedding of a general knowledge graph. We implemented an instantiation model, SemE, using simple matrix semigroups, which exhibits state-of-the-art performance on standard datasets. Moreover, we proposed a regularization-based method to integrate chain-like logic rules derived from human knowledge into embedding training, which further demonstrates the power of the developed language. As far as we know, by applying abstract algebra in statistical learning, this work develops the first formal language for general knowledge graphs, and also sheds light on the problem of neural-symbolic integration from an algebraic perspective.

Zilong Guo, Yi Luo, Long Sha et al.

End-to-end autonomous driving has drawn tremendous attention recently. Many works focus on using modular deep neural networks to construct the end-to-end archi-tecture. However, whether using powerful large language models (LLM), especially multi-modality Vision Language Models (VLM) could benefit the end-to-end driving tasks remain a question. In our work, we demonstrate that combining end-to-end architectural design and knowledgeable VLMs yield impressive performance on the driving tasks. It is worth noting that our method only uses a single camera and is the best camera-only solution across the leaderboard, demonstrating the effectiveness of vision-based driving approach and the potential for end-to-end driving tasks.

Zhixuan Yu, Haozheng Yu, Long Sha et al.

This paper presents a new end-to-end semi-supervised framework to learn a dense keypoint detector using unlabeled multiview images. A key challenge lies in finding the exact correspondences between the dense keypoints in multiple views since the inverse of the keypoint mapping can be neither analytically derived nor differentiated. This limits applying existing multiview supervision approaches used to learn sparse keypoints that rely on the exact correspondences. To address this challenge, we derive a new probabilistic epipolar constraint that encodes the two desired properties. (1) Soft correspondence: we define a matchability, which measures a likelihood of a point matching to the other image's corresponding point, thus relaxing the requirement of the exact correspondences. (2) Geometric consistency: every point in the continuous correspondence fields must satisfy the multiview consistency collectively. We formulate a probabilistic epipolar constraint using a weighted average of epipolar errors through the matchability thereby generalizing the point-to-point geometric error to the field-to-field geometric error. This generalization facilitates learning a geometrically coherent dense keypoint detection model by utilizing a large number of unlabeled multiview images. Additionally, to prevent degenerative cases, we employ a distillation-based regularization by using a pretrained model. Finally, we design a new neural network architecture, made of twin networks, that effectively minimizes the probabilistic epipolar errors of all possible correspondences between two view images by building affinity matrices. Our method shows superior performance compared to existing methods, including non-differentiable bootstrapping in terms of keypoint accuracy, multiview consistency, and 3D reconstruction accuracy.

Tong Yang, Long Sha, Pengyu Hong

While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this work, we propose a universal principle which reduces the random error accumulation by exploiting statistic information hidden in mini-batch gradients. This is achieved by regularizing the learning-rate according to mini-batch variances. Due to the complementarity of our perspective, this regularization could provide a further improvement for stochastic implementation of generic 1st order approaches. With empirical results, we demonstrated the variance regularization could speed up the convergence as well as stabilize the stochastic optimization.

Tong Yang, Long Sha, Justin Li et al.

In this work, we developed a deep learning model-based approach to forecast the spreading trend of SARS-CoV-2 in the United States. We implemented the designed model using the United States to confirm cases and state demographic data and achieved promising trend prediction results. The model incorporates demographic information and epidemic time-series data through a Gated Recurrent Unit structure. The identification of dominating demographic factors is delivered in the end.

Tong Yang, Long Sha, Pengyu Hong

We demonstrated the existence of a group algebraic structure hidden in relational knowledge embedding problems, which suggests that a group-based embedding framework is essential for designing embedding models. Our theoretical analysis explores merely the intrinsic property of the embedding problem itself hence is model-independent. Motivated by the theoretical analysis, we have proposed a group theory-based knowledge graph embedding framework, in which relations are embedded as group elements, and entities are represented by vectors in group action spaces. We provide a generic recipe to construct embedding models associated with two instantiating examples: SO3E and SU2E, both of which apply a continuous non-Abelian group as the relation embedding. Empirical experiments using these two exampling models have shown state-of-the-art results on benchmark datasets.

Jennifer Hobbs, Matthew Holbrook, Nathan Frank et al.

Central to all machine learning algorithms is data representation. For multi-agent systems, selecting a representation which adequately captures the interactions among agents is challenging due to the latent group structure which tends to vary depending on context. However, in multi-agent systems with strong group structure, we can simultaneously learn this structure and map a set of agents to a consistently ordered representation for further learning. In this paper, we present a dynamic alignment method which provides a robust ordering of structured multi-agent data enabling representation learning to occur in a fraction of the time of previous methods. We demonstrate the value of this approach using a large amount of soccer tracking data from a professional league.

Eric Zhan, Stephan Zheng, Yisong Yue et al.

We study the problem of training sequential generative models for capturing coordinated multi-agent trajectory behavior, such as offensive basketball gameplay. When modeling such settings, it is often beneficial to design hierarchical models that can capture long-term coordination using intermediate variables. Furthermore, these intermediate variables should capture interesting high-level behavioral semantics in an interpretable and manipulatable way. We present a hierarchical framework that can effectively learn such sequential generative models. Our approach is inspired by recent work on leveraging programmatically produced weak labels, which we extend to the spatiotemporal regime. In addition to synthetic settings, we show how to instantiate our framework to effectively model complex interactions between basketball players and generate realistic multi-agent trajectories of basketball gameplay over long time periods. We validate our approach using both quantitative and qualitative evaluations, including a user study comparison conducted with professional sports analysts.

Long Sha, Patrick Lucey, Stephan Zheng et al.

We propose a novel method for effective retrieval of multi-agent spatiotemporal tracking data. Retrieval of spatiotemporal tracking data offers several unique challenges compared to conventional text-based retrieval settings. Most notably, the data is fine-grained meaning that the specific location of agents is important in describing behavior. Additionally, the data often contains tracks of multiple agents (e.g., multiple players in a sports game), which generally leads to a permutational alignment problem when performing relevance estimation. Due to the frequent position swap of agents, it is difficult to maintain the correspondence of agents, and such issues make the pairwise comparison problematic for multi-agent spatiotemporal data. To address this issue, we propose a tree-based method to estimate the relevance between multi-agent spatiotemporal tracks. It uses a hierarchical structure to perform multi-agent data alignment and partitioning in a coarse-to-fine fashion. We validate our approach via user studies with domain experts. Our results show that our method boosts performance in retrieving similar sports plays -- especially in interactive situations where the user selects a subset of trajectories compared to current state-of-the-art methods.