What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?

Authors: Lorenzo Loconte, Antonio Mari, Gennaro Gala, Robert Peharz, Cassio de Campos, Erik Quaeghebeur, Gennaro Vessio, Antonio Vergari

Project URL: https://arxiv.org/abs/2409.07953v1

Paper: https://arxiv.org/pdf/2409.07953v1

Abstract: This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportunities that can benefit both communities. Our work generalizes popular tensor factorizations within the circuit language, and unifies various circuit learning algorithms under a single, generalized hierarchical factorization framework. Specifically, we introduce a modular 'Lego block' approach to build tensorized circuit architectures. This, in turn, allows us to systematically construct and explore various circuit and tensor factorization models while maintaining tractability. This connection not only clarifies similarities and differences in existing models, but also enables the development of a comprehensive pipeline for building and optimizing new circuit/tensor factorization architectures. We show the effectiveness of our framework through extensive empirical evaluations, and highlight new research opportunities for tensor factorizations in probabilistic modeling.

@misc{loconte2024relationshiptensorfactorizationscircuits, title={What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?}, author={Lorenzo Loconte and Antonio Mari and Gennaro Gala and Robert Peharz and Cassio de Campos and Erik Quaeghebeur and Gennaro Vessio and Antonio Vergari}, year={2024}, eprint={2409.07953}, archivePrefix={arXiv}, primaryClass={cs.LG}, url={https://arxiv.org/abs/2409.07953}, }