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We propose a method to substantially increase the flexibility and power oftemplate fitting-based photometric redshifts by transforming a large numbers ofgalaxy spectral templates into a corrresponding collection of "fuzzyarchetypes" using a suitable set of perturbative priors designed to account forempirical variation in dust attenuation and emission line strengths. To bypasswidely seperated degeneracies in parameter space (e.g., the redshift-reddeningdegeneracy), we train Self-Organizing Maps (SOMs) on a large "model catalogs"generated from appropriate Monte Carlo sampling of our fuzzy archetypes tocluster the predicted observables in a topologically smooth fashion. Subsequentsampling over the SOM then allows full reconstruction of the relevantprobability distribution functions (PDFs) using the associated set of inversemappings from the SOM to the underlying model parameters. This combinedapproach enables the multi-modal exploration of known variation among galaxyspectral energy distributions (SEDs) using large numbers of archetypes withminimal modeling assumptions. We demonstrate the power of this approach torecover full redshift PDFs using discrete Markov Chain Monte Carlo (MCMC)sampling methods combined with SOMs constructed from model catalogs based onLSST $ugrizY$ and Euclid $YJH$ mock photometry.

Deriving Photometric Redshifts using Fuzzy Archetypes and Self-Organizing Maps. I. Methodology