# Fourier Basis Density Model

arXiv: https://arxiv.org/abs/2402.15345 · HTML: https://mlsanity.com/paper/2402.15345/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 11 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [An Introduction to Neural Data Compression](https://mlsanity.com/paper/2202.06533/) (2022)

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

- [Fourier Head: Helping Large Language Models Learn Complex Probability Distributions](https://mlsanity.com/paper/2410.22269/) (2024)
- [Understanding Rate-Distortion Performance in Distributed Transformer Inference](https://mlsanity.com/paper/2601.22002/) (2026)

## Abstract (arXiv)

We introduce a lightweight, flexible and end-to-end trainable probability density model parameterized by a constrained Fourier basis. We assess its performance at approximating a range of multi-modal 1D densities, which are generally difficult to fit. In comparison to the deep factorized model introduced in [1], our model achieves a lower cross entropy at a similar computational budget. In addition, we also evaluate our method on a toy compression task, demonstrating its utility in learned compression.