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[R] Piecewise Strong Convexity of Neural Networks

Paper: https://arxiv.org/abs/1810.12805

Video summary: https://www.youtube.com/watch?v=z89BTMQGVn

Earlier related work: https://arxiv.org/abs/1607.04917 (piecewise convexity)

I am not the author. This paper will be presented at NeurIPS this month and exposes some convexity results about piece-wise linear nns under the least squares loss – namely piecewise strong-convexity & the non-existance of differentiable local maxima. The approach is a spectral analysis of the Hessian and weights of the nn. The result is a relatively attractive convergence estimate for sgd.

I guess this provides some more motivation for studying techniques like ADMM which have convergence properties for some classes of piece-wise functions and can exploit lipschitz cts gradients. Nice work!

submitted by /u/i-heart-turtles
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Toronto AI is a social and collaborative hub to unite AI innovators of Toronto and surrounding areas. We explore AI technologies in digital art and music, healthcare, marketing, fintech, vr, robotics and more. Toronto AI was founded by Dave MacDonald and Patrick O'Mara.