  To understand the fundamental parameters of galaxy evolution, we investigated
the minimum set of parameters that explain the observed galaxy spectra in the
local Universe. We identified four latent variables that efficiently represent
the diversity of high-dimensional galaxy spectral energy distributions (SEDs)
observed by the Sloan Digital Sky Survey. Additionally, we constructed
meaningful latent representation using conditional variational autoencoders
trained with different permutations of galaxy physical properties, which helped
us quantify the information that these traditionally used properties have on
the reconstruction of galaxy spectra. The four parameters suggest a view that
complex SED population models with a very large number of parameters will be
difficult to constrain even with spectroscopic galaxy data. Through an
Explainable AI (XAI) method, we found that the region below 5000\textup{\AA}
and prominent emission lines ([O II], [O III], and H$\alpha$) are particularly
informative for predicting the latent variables. Our findings suggest that
these latent variables provide a more efficient and fundamental representation
of galaxy spectra than conventionally considered galaxy physical properties.
