# Understanding Deep Learning via Notions of Rank

arXiv: https://arxiv.org/abs/2408.02111 · HTML: https://mlsanity.com/paper/2408.02111/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2024.

## Built on by (most cited first, 1 of 1)

- [Neural Networks Generalize on Low Complexity Data](https://mlsanity.com/paper/2409.12446/) (2024)

## Abstract (arXiv)

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.