Characterizing the astrophysical neutrino flux with the IceCube Neutrino Observatory traditionally relies on a binned forward-folding likelihood approach. Insufficient Monte Carlo (MC) statistics in each bin limits the granularity and dimensionality of the binning scheme. A neural network can be employed to optimize a summary statistic that serves as the input for data analysis, yielding the best possible outcomes. This end-to-end optimized summary statistic allows for the inclusion of more observables while maintaining adequate MC statistics per bin. This work will detail the application of end-to-end optimized summary statistics in analyzing and characterizing the galactic neutrino flux, achieving improved resolution in the likelihood contours for selected signal parameters and models.