Derives ODEs and explicit solutions for geodesics between full-rank matrices in deep linear network geometry and shows that certain horizontal straight lines in the invariant balanced manifold remain geodesics under Riemannian submersion.
AppendixA.Informal Note on Equation 2.11 The geodesic in Equation 2.11 also appears in another geometry [4] when the endpoints are positive definite diagonal matrices
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Geodesics in the Deep Linear Network
Derives ODEs and explicit solutions for geodesics between full-rank matrices in deep linear network geometry and shows that certain horizontal straight lines in the invariant balanced manifold remain geodesics under Riemannian submersion.