Geodesics in the Deep Linear Network

Published 18 Sep 2025 in math.DG, cs.LG, and math.DS | (2510.07324v1)

Abstract: We derive a general system of ODEs and associated explicit solutions in a special case for geodesics between full rank matrices in the deep linear network geometry. In the process, we characterize all horizontal straight lines in the invariant balanced manifold that remain geodesics under Riemannian submersion.

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Authors (1)

Alan Chen

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