aiqbench analysis
This research proposes using tensor factorization and rank-based metrics to formally explain the generalization capabilities of deep learning models across audio, images, and text. By linking neural network architectures to concepts of entanglement from quantum physics, the study offers new theoretical tools for designing better regularization schemes and data preprocessing algorithms. While it touches on quantum terminology, the core contribution remains a fundamental advancement in machine learning theory rather than a report on quantum hardware or applications.
Understanding Deep Learning via Notions of Rank
arXiv:2408.02111v4 Announce Type: replace-cross Abstract: Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of generalization and expressiveness. In particular, we establish that gradient-based training can induce an implicit regularization towards low rank for several neural network architectures, and demonstrate empirically that this phenomenon may facilitate an explanation of generalization over natural data (e.g., audio, images, and text). Then, we characterize the ability of graph neural networks to model interactions via a notion of rank, which is commonly used for quantifying entanglement in quantum physics. A central tool underlying these results is a connection between neural networks and tensor factorizations. Practical implications of our theory for designing explicit regularization schemes and data preprocessing algorithms are presented.
Abstract:Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of generalization and expressiveness. In particular, we establish that gradient-based training can induce an implicit regularization towards low rank for several neural network architectures, and demonstrate empirically that this phenomenon may facilitate an explanation of generalization over natural data (e.g., audio, images, and text). Then, we characterize the ability of graph neural networks to model interactions via a notion of rank, which is commonly used for quantifying entanglement in quantum physics. A central tool underlying these results is a connection between neural networks and tensor factorizations. Practical implications of our theory for designing explicit regularization schemes and data preprocessing algorithms are presented.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Neural and Evolutionary Computing (cs.NE); Machine Learning (stat.ML)
arXiv:2408.02111 [cs.LG]
(or arXiv:2408.02111v4 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2408.02111 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 242 words
