Learning with Logical Constraints but without Shortcut Satisfaction

Recent studies in neuro-symbolic learning have explored the integration of logical knowledge into deep learning via encoding logical constraints as an additional loss function. However, existing approaches tend to vacuously satisfy logical constraints through shortcuts, failing to fully exploit the knowledge. In this paper, we present a new framework for learning with logical constraints. Specifically, we address the shortcut satisfaction issue by introducing dual variables for logical connectives, encoding how the constraint is satisfied. We further propose a variational framework where the encoded logical constraint is expressed as a distributional loss that is compatible with the model's original training loss. The theoretical analysis shows that the proposed approach bears salient properties, and the experimental evaluations demonstrate its superior performance in both model generalizability and constraint satisfaction.

Full Bayesian Significance Testing for Neural Networks

Significance testing aims to determine whether a proposition about the population distribution is the truth or not given observations. However, traditional significance testing often needs to derive the distribution of the testing statistic, failing to deal with complex nonlinear relationships. In this paper, we propose to conduct Full Bayesian Significance Testing for neural networks, called \textit{n}FBST, to overcome the limitation in relationship characterization of traditional approaches. A Bayesian neural network is utilized to fit the nonlinear and multi-dimensional relationships with small errors and avoid hard theoretical derivation by computing the evidence value. Besides, \textit{n}FBST can test not only global significance but also local and instance-wise significance, which previous testing methods don't focus on. Moreover, \textit{n}FBST is a general framework that can be extended based on the measures selected, such as Grad-\textit{n}FBST, LRP-\textit{n}FBST, DeepLIFT-\textit{n}FBST, LIME-\textit{n}FBST. A range of experiments on both simulated and real data are conducted to show the advantages of our method.

EPCS: Endpoint-based Part-aware Curve Skeleton Extraction for Low-quality Point Clouds

The curve skeleton is an important shape descriptor that has been utilized in various applications in computer graphics, machine vision, and artificial intelligence. In this study, the endpoint-based part-aware curve skeleton (EPCS) extraction method for low-quality point clouds is proposed. The novel random center shift (RCS) method is first proposed for detecting the endpoints on point clouds. The endpoints are used as the initial seed points for dividing each part into layers, and then the skeletal points are obtained by computing the center points of the oriented bounding box (OBB) of the layers. Subsequently, the skeletal points are connected, thus forming the branches. Furthermore, the multi-vector momentum-driven (MVMD) method is also proposed for locating the junction points that connect the branches. Due to the shape differences between different parts on point clouds, the global topology of the skeleton is finally optimized by removing the redundant junction points, re-connecting some branches using the proposed MVMD method, and applying an interpolation method based on the splitting operator. Consequently, a complete and smooth curve skeleton is achieved. The proposed EPCS method is compared with several state-of-the-art methods, and the experimental results verify its robustness, effectiveness, and efficiency. Furthermore, the skeleton extraction and model segmentation results on the point clouds of broken Terracotta also highlight the utility of the proposed method.