AI RESEARCH
Geodesics in the Deep Linear Network
arXiv CS.LG
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ArXi:2510.07324v2 Announce Type: replace-cross 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 find horizontal straight lines in the invariant balanced manifold that remain geodesics under Riemannian submersion.