pop-cosmos: Disentangling galaxy properties from observables using data-driven approaches

The physical processes that shape a galaxy's spectrum are strongly degenerate in observations, obscuring which processes act independently. Leveraging the pop-cosmos generative galaxy population model, we investigate how many independent degrees of freedom the rest-frame optical SED contains. We use a $\beta$-variational autoencoder (VAE) to compress a 16-parameter stellar population synthesis (SPS) description into a disentangled latent representation interpreted through mutual information (MI). We find that five independent dimensions suffice, corresponding to stellar mass, recent star formation, dust, and two -- not the three or four assumed by standard nebular models -- degrees of freedom in the ionization state of the gas. Stellar metallicity and stellar age are not among these primary drivers; their spectral effects are distributed across the others rather than independently encoded. By tying each dimension to specific spectral features, this decomposition breaks the star-formation--dust--metallicity degeneracies that limit broadband photometry, and recovers the physical conditions of the gas more cleanly than the line-ratio diagnostics in standard use.