# A representation learning approach to probe for dynamical dark energy in matter power spectra

arXiv: https://arxiv.org/abs/2310.10717 · HTML: https://mlsanity.com/paper/2310.10717/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 88 references that are in the map.
- First posted on arXiv 16 Oct 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Review of Feature Selection Methods Based on Mutual Information](https://mlsanity.com/paper/1509.07577/) (2015)
- [Machines Learn to Infer Stellar Parameters Just by Looking at a Large Number of Spectra](https://mlsanity.com/paper/2009.12872/) (2020)
- [Discovering the building blocks of dark matter halo density profiles with neural networks](https://mlsanity.com/paper/2203.08827/) (2022)
- [CosmoPower-JAX: high-dimensional Bayesian inference with differentiable cosmological emulators](https://mlsanity.com/paper/2305.06347/) (2023)
- [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)
- [Cosmological model discrimination with Deep Learning](https://mlsanity.com/paper/1707.05167/) (2017)

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

- [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)

We present DE-VAE, a variational autoencoder (VAE) architecture to search for a compressed representation of dynamical dark energy (DE) models in observational studies of the cosmic large-scale structure. DE-VAE is trained on matter power spectra boosts generated at wavenumbers k∈(0.01-2.5)  h/rmMpc and at four redshift values z∈(0.1,0.48,0.78,1.5) for the most typical dynamical DE parametrization with two extra parameters describing an evolving DE equation of state. The boosts are compressed to a lower-dimensional representation, which is concatenated with standard cold dark matter (CDM) parameters and then mapped back to reconstructed boosts; both the compression and the reconstruction components are parametrized as neural networks. Remarkably, we find that a single latent parameter is sufficient to predict 95% (99%) of DE power spectra generated over a broad range of cosmological parameters within 1σ (2σ) of a Gaussian error which includes cosmic variance, shot noise and systematic effects for a Stage IV-like survey. This single parameter shows a high mutual information with the two DE parameters, and these three variables can be linked together with an explicit equation through symbolic regression. Considering a model with two latent variables only marginally improves the accuracy of the predictions, and adding a third latent variable has no significant impact on the model's performance. We discuss how the DE-VAE architecture can be extended from a proof of concept to a general framework to be employed in the search for a common lower-dimensional parametrization of a wide range of beyond-LambdaCDM models and for different cosmological datasets. Such a framework could then both inform the development of cosmological surveys by targeting optimal probes, and provide theoretical insight into the common phenomenological aspects of beyond-LambdaCDM models.