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Context. Spectral signatures are crucial in the era of large X-ray surveys, as effective methods for source identification and classification are needed due to the scale of the data they yield. Automatic machine learning methods have proven useful for such tasks, but so far they have not been applied to large spectral datasets, such as the Chandra Source Catalog. Aims. Our aim was 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 evaluated it through classification, regression, and interpretability analyses, and we measured the mutual information between spectral and time-domain properties of these sources to aid in future identification of transient events. Methods. We used a transformer-based autoencoder to compress X-ray spectra into representations in an eight-dimensional latent space. Astrophysical source types and physical summary statistics were compiled from external catalogs. We evaluated the learned representation in terms of spectral reconstruction accuracy, clustering performance regarding eight known astrophysical source classes, and correlation with physical quantities such as hardness ratios and hydrogen column densities (N<SUB>H</SUB>). Results. Upon reconstruction, clustering in the latent space yielded a balanced classification accuracy of ~40% across the eight source classes, increasing to ~69% when restricted to Active Galactic Nuclei and stellar-mass compact objects exclusively. Moreover, latent features correlate with spectral and temporal properties, suggesting that the compressed representation captures physically relevant information. Conclusions. Features learned directly from X-ray spectra capture relevant physical information as effectively as human-extracted features that require additional computations. They can be used for both classification and regression in large surveys, and they also share mutual information with time-domain properties. The methodology presented in this paper can be adapted to existing and upcoming X-ray catalogs.