The Riemannian Geometry Associated to Gradient Flows of Linear Convolutional Networks

ArXi:2507.06367v2 Announce Type: replace We study geometric properties of the gradient flow for learning deep linear convolutional networks. For linear fully connected networks, it has been shown recently that the corresponding gradient flow on parameter space can be written as a Riemannian gradient flow on function space (i.e., on the product of weight matrices) if the initialization satisfies a so-called balancedness condition.