AI RESEARCH
Metric-Aware PCA as a Linear Instance of Geometric Deep Learning
arXiv CS.LG
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ArXi:2605.27456v1 Announce Type: new Geometric deep learning organises neural architectures around the symmetries of their data domain, with the choice of symmetry group serving as a geometric prior that determines what representations can be learned. Metric-Aware Principal Component Analysis (MAPCA) parameterises principal component analysis by a positive-definite metric matrix, with a canonical subfamily interpolating between standard PCA and output whitening and a diagonal-metric point recovering Invariant.