Two classes of minimal generic fundamental invariants for tensors

Motivated by the problems raised by B\"{u}rgisser and Ikenmeyer, we discuss two classes of minimal generic fundamental invariants for tensors of order 3. The first one is defined on $\otimes^3 \mathbb{C}^m$, where $m=n^2-1$. We study its construction by obstruction design introduced by B\"{u}rgisser and Ikenmeyer, which partially answers one problem raised by them. The second one is defined on $\mathbb{C}^{\ell m}\otimes \mathbb{C}^{mn}\otimes \mathbb{C}^{n\ell}$. We study its evaluation on the matrix multiplication tensor $\langle\ell,m,n\rangle$ and unit tensor $\langle n^2 \rangle$ when $\ell=m=n$. The evaluation on the unit tensor leads to the definition of Latin cube and 3-dimensional Alon-Tarsi problem. We generalize some results on Latin square to Latin cube, which enrich the understanding of 3-dimensional Alon-Tarsi problem. It is also natural to generalize the constructions to tensors of other orders. We illustrate the distinction between even and odd dimensional generalizations by concrete examples. Finally, some open problems in related fields are raised.Comment: Some typos were changed.New publication information has been update

GoGNN: Graph of Graphs Neural Network for Predicting Structured Entity Interactions

Entity interaction prediction is essential in many important applications such as chemistry, biology, material science, and medical science. The problem becomes quite challenging when each entity is represented by a complex structure, namely structured entity, because two types of graphs are involved: local graphs for structured entities and a global graph to capture the interactions between structured entities. We observe that existing works on structured entity interaction prediction cannot properly exploit the unique graph of graphs model. In this paper, we propose a Graph of Graphs Neural Network, namely GoGNN, which extracts the features in both structured entity graphs and the entity interaction graph in a hierarchical way. We also propose the dual-attention mechanism that enables the model to preserve the neighbor importance in both levels of graphs. Extensive experiments on real-world datasets show that GoGNN outperforms the state-of-the-art methods on two representative structured entity interaction prediction tasks: chemical-chemical interaction prediction and drug-drug interaction prediction. Our code is available at Github.Comment: Accepted by IJCAI 202

A Universal Semantic-Geometric Representation for Robotic Manipulation

Robots rely heavily on sensors, especially RGB and depth cameras, to perceive and interact with the world. RGB cameras record 2D images with rich semantic information while missing precise spatial information. On the other side, depth cameras offer critical 3D geometry data but capture limited semantics. Therefore, integrating both modalities is crucial for learning representations for robotic perception and control. However, current research predominantly focuses on only one of these modalities, neglecting the benefits of incorporating both. To this end, we present Semantic-Geometric Representation (SGR), a universal perception module for robotics that leverages the rich semantic information of large-scale pre-trained 2D models and inherits the merits of 3D spatial reasoning. Our experiments demonstrate that SGR empowers the agent to successfully complete a diverse range of simulated and real-world robotic manipulation tasks, outperforming state-of-the-art methods significantly in both single-task and multi-task settings. Furthermore, SGR possesses the unique capability to generalize to novel semantic attributes, setting it apart from the other methods

VidPlat: A Tool for Fast Crowdsourcing of Quality-of-Experience Measurements

For video or web services, it is crucial to measure user-perceived quality of experience (QoE) at scale under various video quality or page loading delays. However, fast QoE measurements remain challenging as they must elicit subjective assessment from human users. Previous work either (1) automates QoE measurements by letting crowdsourcing raters watch and rate QoE test videos or (2) dynamically prunes redundant QoE tests based on previously collected QoE measurements. Unfortunately, it is hard to combine both ideas because traditional crowdsourcing requires QoE test videos to be pre-determined before a crowdsourcing campaign begins. Thus, if researchers want to dynamically prune redundant test videos based on other test videos' QoE, they are forced to launch multiple crowdsourcing campaigns, causing extra overheads to re-calibrate or train raters every time. This paper presents VidPlat, the first open-source tool for fast and automated QoE measurements, by allowing dynamic pruning of QoE test videos within a single crowdsourcing task. VidPlat creates an indirect shim layer between researchers and the crowdsourcing platforms. It allows researchers to define a logic that dynamically determines which new test videos need more QoE ratings based on the latest QoE measurements, and it then redirects crowdsourcing raters to watch QoE test videos dynamically selected by this logic. Other than having fewer crowdsourcing campaigns, VidPlat also reduces the total number of QoE ratings by dynamically deciding when enough ratings are gathered for each test video. It is an open-source platform that future researchers can reuse and customize. We have used VidPlat in three projects (web loading, on-demand video, and online gaming). We show that VidPlat can reduce crowdsourcing cost by 31.8% - 46.0% and latency by 50.9% - 68.8%