# On the Architectural Complexity of Neural Networks

arXiv: https://arxiv.org/abs/2605.04325 · HTML: https://mlsanity.com/paper/2605.04325/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 48 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 1 of 1)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)

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

- [Higher Structures in Deep Learning](https://mlsanity.com/paper/2609.00472/) (2026)

## Abstract (arXiv)

We introduce a unified theoretical framework for the rigorous analysis and systematic construction of deep neural networks (DNNs). This framework addresses a gap in existing theory by explicitly modeling the structure of tensor operations -- lower level information that is often abstracted. Our framework enables two novel objectives: (1) analysis of the evolution of architectural complexity over deep learning history, and (2) automatic construction of novel architectures based on new types of tensor operations. Our study of DNNs introduced over the past 40 years reveals a connection between groundbreaking architectures and increases in different types of architectural complexity. Moreover, we identify several large classes of higher complexity architectures that have not yet been explored. We then collect a dataset of 3,000+ higher complexity architectures, which we publicly release at: https://github.com/combinatoriallabs/ArchitecturalComplexity.