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Title:
Ricci Flow and Neural Network Gradient Descent
Speaker:
Abstract:
In this talk I will present a framework for studying metric flows induced by neural network gradient descent, which has recently been utilized to construct approximate Ricci-flat metrics. Adapting neural tangent kernel (NTK) theory to the case of metric flows, I will demonstrate that metric flows simplify in certain infinite width limits and have dynamics given by a non-local update equation governed by the NTK. For appropriately chosen architecture and loss function, this infinite neural network metric flow reduces to Perelman's formulation of Ricci flow.
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