# Discovering the building blocks of dark matter halo density profiles with neural networks

arXiv: https://arxiv.org/abs/2203.08827 · HTML: https://mlsanity.com/paper/2203.08827/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 61 references that are in the map.
- First posted on arXiv 16 Mar 2022.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Measuring Disentanglement: A Review of Metrics](https://mlsanity.com/paper/2012.09276/) (2020)
- [Machines Learn to Infer Stellar Parameters Just by Looking at a Large Number of Spectra](https://mlsanity.com/paper/2009.12872/) (2020)
- [Deep learning insights into cosmological structure formation](https://mlsanity.com/paper/2011.10577/) (2020)

## Built on by (most cited first, 5 of 5)

- [A robust estimator of mutual information for deep learning interpretability](https://mlsanity.com/paper/2211.00024/) (2022)
- [Explaining dark matter halo density profiles with neural networks](https://mlsanity.com/paper/2305.03077/) (2023)
- [Interpreting "Interpretability" and Explaining "Explainability" in Machine Learning in Physics](https://mlsanity.com/paper/2606.26228/) (2026)
- [A representation learning approach to probe for dynamical dark energy in matter power spectra](https://mlsanity.com/paper/2310.10717/) (2023)
- [LambdaCDM and early dark energy in latent space: a data-driven parametrization of the CMB temperature power spectrum](https://mlsanity.com/paper/2502.09810/) (2025)

## Abstract (arXiv)

The density profiles of dark matter halos are typically modeled using empirical formulae fitted to the density profiles of relaxed halo populations. We present a neural network model that is trained to learn the mapping from the raw density field containing each halo to the dark matter density profile. We show that the model recovers the widely-used Navarro-Frenk-White (NFW) profile out to the virial radius, and can additionally describe the variability in the outer profile of the halos. The neural network architecture consists of a supervised encoder-decoder framework, which first compresses the density inputs into a low-dimensional latent representation, and then outputs ρ(r) for any desired value of radius r. The latent representation contains all the information used by the model to predict the density profiles. This allows us to interpret the latent representation by quantifying the mutual information between the representation and the halos' ground-truth density profiles. A two-dimensional representation is sufficient to accurately model the density profiles up to the virial radius; however, a three-dimensional representation is required to describe the outer profiles beyond the virial radius. The additional dimension in the representation contains information about the infalling material in the outer profiles of dark matter halos, thus discovering the splashback boundary of halos without prior knowledge of the halos' dynamical history.