# LambdaCDM and early dark energy in latent space: a data-driven parametrization of the CMB temperature power spectrum

arXiv: https://arxiv.org/abs/2502.09810 · HTML: https://mlsanity.com/paper/2502.09810/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 94 references that are in the map.
- First posted on arXiv 13 Feb 2025.

## Builds on (most cited first, 6 of 6)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Review of Feature Selection Methods Based on Mutual Information](https://mlsanity.com/paper/1509.07577/) (2015)
- [Discovering the building blocks of dark matter halo density profiles with neural networks](https://mlsanity.com/paper/2203.08827/) (2022)
- [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)
- [A representation learning approach to probe for dynamical dark energy in matter power spectra](https://mlsanity.com/paper/2310.10717/) (2023)

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

- [Interpreting "Interpretability" and Explaining "Explainability" in Machine Learning in Physics](https://mlsanity.com/paper/2606.26228/) (2026)

## Abstract (arXiv)

Finding the best parametrization for cosmological models in the absence of first-principle theories is an open question. We propose a data-driven parametrization of cosmological models given by the disentangled 'latent' representation of a variational autoencoder (VAE) trained to compress cosmic microwave background (CMB) temperature power spectra. We consider a broad range of LambdaCDM and beyond-LambdaCDM cosmologies with an additional early dark energy (EDE) component. We show that these spectra can be compressed into 5 (LambdaCDM) or 8 (EDE) independent latent parameters, as expected when using temperature power spectra alone, and which reconstruct spectra at an accuracy well within the Planck errors. These latent parameters have a physical interpretation in terms of well-known features of the CMB temperature spectrum: these include the position, height and even-odd modulation of the acoustic peaks, as well as the gravitational lensing effect. The VAE also discovers one latent parameter which entirely isolates the EDE effects from those related to LambdaCDM parameters, thus revealing a previously unknown degree of freedom in the CMB temperature power spectrum. We further showcase how to place constraints on the latent parameters using Planck data as typically done for cosmological parameters, obtaining latent values consistent with previous LambdaCDM and EDE cosmological constraints. Our work demonstrates the potential of a data-driven reformulation of current beyond-LambdaCDM phenomenological models into the independent degrees of freedom to which the data observables are sensitive.