Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNN) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as its relationship to current developments in neural-symbolic computing.Comment: Updated version, draft of accepted IJCAI2020 Survey Pape

DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization

Neural network-based Combinatorial Optimization (CO) methods have shown promising results in solving various NP-complete (NPC) problems without relying on hand-crafted domain knowledge. This paper broadens the current scope of neural solvers for NPC problems by introducing a new graph-based diffusion framework, namely DIFUSCO. Our framework casts NPC problems as discrete {0, 1}-vector optimization problems and leverages graph-based denoising diffusion models to generate high-quality solutions. We investigate two types of diffusion models with Gaussian and Bernoulli noise, respectively, and devise an effective inference schedule to enhance the solution quality. We evaluate our methods on two well-studied NPC combinatorial optimization problems: Traveling Salesman Problem (TSP) and Maximal Independent Set (MIS). Experimental results show that DIFUSCO strongly outperforms the previous state-of-the-art neural solvers, improving the performance gap between ground-truth and neural solvers from 1.76% to 0.46% on TSP-500, from 2.46% to 1.17% on TSP-1000, and from 3.19% to 2.58% on TSP10000. For the MIS problem, DIFUSCO outperforms the previous state-of-the-art neural solver on the challenging SATLIB benchmark. Our code is available at "https://github.com/Edward-Sun/DIFUSCO"

Navigational Guidance – A Deep Learning Approach

The useful navigation guidance is favorable to considerably reducing navigation time. The navigation problems involved with multiple destinations are formulated as the Directed Steiner Tree (DST) problems over directed graphs. In this paper, we propose a deep learning (to be exact, graph neural networks) based approach to tackle the DST problem in a supervised manner. Experiments are conducted to evaluate the proposed approach, and the results suggest that our approach can effectively solve the DST problems. In particular, the accuracy of the network model can reach 95.04% or even higher

Improving 6D Pose Estimation of Objects in Clutter via Physics-aware Monte Carlo Tree Search

This work proposes a process for efficiently searching over combinations of individual object 6D pose hypotheses in cluttered scenes, especially in cases involving occlusions and objects resting on each other. The initial set of candidate object poses is generated from state-of-the-art object detection and global point cloud registration techniques. The best-scored pose per object by using these techniques may not be accurate due to overlaps and occlusions. Nevertheless, experimental indications provided in this work show that object poses with lower ranks may be closer to the real poses than ones with high ranks according to registration techniques. This motivates a global optimization process for improving these poses by taking into account scene-level physical interactions between objects. It also implies that the Cartesian product of candidate poses for interacting objects must be searched so as to identify the best scene-level hypothesis. To perform the search efficiently, the candidate poses for each object are clustered so as to reduce their number but still keep a sufficient diversity. Then, searching over the combinations of candidate object poses is performed through a Monte Carlo Tree Search (MCTS) process that uses the similarity between the observed depth image of the scene and a rendering of the scene given the hypothesized pose as a score that guides the search procedure. MCTS handles in a principled way the tradeoff between fine-tuning the most promising poses and exploring new ones, by using the Upper Confidence Bound (UCB) technique. Experimental results indicate that this process is able to quickly identify in cluttered scenes physically-consistent object poses that are significantly closer to ground truth compared to poses found by point cloud registration methods.Comment: 8 pages, 4 figure