# Reducing Deep Network Complexity via Sparse Hierarchical Fourier Interaction Networks

arXiv: https://arxiv.org/abs/1801.01451 · HTML: https://mlsanity.com/paper/1801.01451/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2017.

## Built on by (most cited first, 2 of 2)

- [Can we integrate spatial verification methods into neural-network loss functions for atmospheric science?](https://mlsanity.com/paper/2203.11141/) (2022)
- [From Pixels and Words to Waves: A Unified Framework for Spectral Dictionary vLLMs](https://mlsanity.com/paper/2506.18943/) (2025)

## Abstract (arXiv)

This paper presents a Sparse Hierarchical Fourier Interaction Networks, an architectural building block that unifies three complementary principles of frequency domain modeling: A hierarchical patch wise Fourier transform that affords simultaneous access to local detail and global context; A learnable, differentiable top K masking mechanism which retains only the most informative spectral coefficients, thereby exploiting the natural compressibility of visual and linguistic signals.