Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Review

Advocates for Neuro-Symbolic Artificial Intelligence (NeSy) assert that combining deep learning with symbolic reasoning will lead to stronger AI than either paradigm on its own. As successful as deep learning has been, it is generally accepted that even our best deep learning systems are not very good at abstract reasoning. And since reasoning is inextricably linked to language, it makes intuitive sense that Natural Language Processing (NLP), would be a particularly well-suited candidate for NeSy. We conduct a structured review of studies implementing NeSy for NLP, with the aim of answering the question of whether NeSy is indeed meeting its promises: reasoning, out-of-distribution generalization, interpretability, learning and reasoning from small data, and transferability to new domains. We examine the impact of knowledge representation, such as rules and semantic networks, language structure and relational structure, and whether implicit or explicit reasoning contributes to higher promise scores. We find that systems where logic is compiled into the neural network lead to the most NeSy goals being satisfied, while other factors such as knowledge representation, or type of neural architecture do not exhibit a clear correlation with goals being met. We find many discrepancies in how reasoning is defined, specifically in relation to human level reasoning, which impact decisions about model architectures and drive conclusions which are not always consistent across studies. Hence we advocate for a more methodical approach to the application of theories of human reasoning as well as the development of appropriate benchmarks, which we hope can lead to a better understanding of progress in the field. We make our data and code available on github for further analysis.Comment: Surve