Extracting latent representations from X-ray spectra. Classification, regression, and accretion signatures of Chandra sources

TL;DR

The paper tackles extracting compact, physically meaningful representations from Chandra X-ray spectra to enable classification and property estimation. It introduces a transformer-based autoencoder that compresses spectra into an $8$-dimensional latent space and evaluates reconstruction quality, unsupervised clustering into eight classes, regression of physical quantities, and symbolic regression for interpretability. Key findings include spectral reconstruction MAE $<0.06$, clustering accuracy around 40% across eight classes and about 69% for AGN vs stellar-mass compact objects, and latent features that correlate with hardness ratios and $N_H$ via nonlinear relations uncovered by symbolic regression. The approach demonstrates a scalable, interpretable deep learning framework for X-ray spectral studies with potential for multimodal extensions and anomaly detection in future large-field missions.

Abstract

The study of X-ray spectra is crucial to understanding the physical nature of astrophysical sources. Machine learning methods can extract compact and informative representations of data from large datasets. The Chandra Source Catalog (CSC) provides a rich archive of X-ray spectral data, which remains largely underexplored in this context. This work aims to develop a compact and physically meaningful representation of Chandra X-ray spectra using deep learning. To verify that the learned representation captures relevant information, we evaluate it through classification, regression, and interpretability analyses. We use a transformer-based autoencoder to compress X-ray spectra. The input spectra, drawn from the CSC, include only high-significance detections. Astrophysical source types and physical summary statistics are compiled from external catalogs. We evaluate the learned representation in terms of spectral reconstruction accuracy, clustering performance on 8 known astrophysical source classes, and correlation with physical quantities such as hardness ratios and hydrogen column density ($N_H$). The autoencoder accurately reconstructs spectra with 8 latent variables. Clustering in the latent space yields a balanced classification accuracy of $\sim$40% across the 8 source classes, increasing to $\sim$69% when restricted to AGNs and stellar-mass compact objects exclusively. Moreover, latent features correlate with non-linear combinations of spectral fluxes, suggesting that the compressed representation encodes physically relevant information. The proposed autoencoder-based pipeline is a powerful tool for the representation and interpretation of X-ray spectra, providing a compact latent space that supports both classification and the estimation of physical properties. This work demonstrates the potential of deep learning for spectral studies and uncovering new patterns in X-ray data.

Figures (15)

• Figure 1: An example of resampling with $N = 400$ points.
• Figure 2: Our pipeline. The blue rectangles indicate the inputs, the green rectangles indicate the clustering outputs, and the orange rectangle indicates the physical interpretation of the results.
• Figure 3: The autoencoder takes in input the resampled normalized spectrum $\hat{f}$, encodes it into a compressed representation $z$ and reconstructs it as $\check f$.
• Figure 4: The training (left panel) and validation (right panel) losses of the autoencoder, measured using MAE. The dark blue line is the mean loss across different hyperparameter configurations in the grid search (see \ref{['sec:autoencoder']}), and the light blue region indicates the mean $\pm 1\sigma$.
• Figure 5: Examples of autoencoder reconstructions (red) compared to the input resampled normalized spectra (blue). Left: the autoencoder reconstructs the fluxes for lower energy values better (source: 2CXO J034639.3+240611, Obs. ID: 17250, type: LM-STAR). Centre: the autoencoder reconstructs the fluxes for higher energy values better (source: 2CXO J111438.8+324133, Obs. ID: 3137, type: AGN). Right: the autoencoder reconstruction capabilities are comparable for the fluxes at all energies (source: 2CXO J100433.8+411234, Obs. ID: 14498, type: AGN).