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The Power of Depth for Feedforward Neural Networks
Ronen Eldan, Ohad Shamir
We show that there is a simple (approximately radial) function on , expressible by a small 3-layer feedforward neural networks, which cannot be approximated by any 2-laye…
Multi-scale exploration of convex functions and bandit convex optimization
Sébastien Bubeck, Ronen Eldan
We construct a new map from a convex function to a distribution on its domain, with the property that this distribution is a multi-scale exploration of the function. We use this ma…
Sampling from a log-concave distribution with Projected Langevin Monte Carlo
Sébastien Bubeck, Ronen Eldan, Joseph Lehec
We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (project…
Braess's paradox for the spectral gap in random graphs and delocalization of eigenvectors
Ronen Eldan, Miklós Rácz, Tselil Schramm
We study how the spectral gap of the normalized Laplacian of a random graph changes when an edge is added to or removed from the graph. There are known examples of graphs where, pe…