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The Positivity of the Neural Tangent Kernel
The Neural Tangent Kernel (NTK) has emerged as a fundamental concept in the study of wide Neural Networks.
Wide neural networks: From non-gaussian random fields at initialization to the NTK geometry of training
In particular, using a certain metric in the space of measures we find that, along training, the resulting measure is within $n^{-\frac{1}{2}}(\log n)^{1+}$ of the time dependent Gaussian process corresponding to the infinite width network (which is explicitly given by precomposing the initial Gaussian process with the linear flow corresponding to training in the infinite width limit).
Nonminimal solutions to the Ginzburg-Landau equations on surfaces
We prove the existence of novel, nonminimal and irreducible solutions to the (self-dual) Ginzburg-Landau equations on closed surfaces.
Differential Geometry Mathematical Physics Analysis of PDEs Mathematical Physics 35Q56, 53C07, 58E15
Automatic Graphic Logo Detection via Fast Region-based Convolutional Networks
Brand recognition is a very challenging topic with many useful applications in localization recognition, advertisement and marketing.
