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We study the problem of PAC learning one-hidden-layer ReLU networks with $k$ hidden units on $mathbb{R}^d$ under Gaussian marginals in the presence of additive label noise. For the case of positive coefficients, we give the first polynomial-time algorithm for this learning problem for $k$ up to $tilde{O}(sqrt{log d})$. Previously, no polynomial time algorithm was known, even for $k=3$. This answers an open question posed by~cite{Kliv17}. Importantly, our algorithm does not require any assumptions about the rank of the weight matrix and its complexity is independent of its condition number. On the negative side, for the more general task of PAC learning one-hidden-layer ReLU networks with arbitrary real coefficients, we prove a Statistical Query lower bound of $d^{Omega(k)}$. Thus, we provide a separation between the two classes in terms of efficient learnability. Our upper and lower bounds are general, extending to broader families of activation functions.
We study the complexity of training neural network models with one hidden nonlinear activation layer and an output weighted sum layer. We analyze Gradient Descent applied to learning a bounded target function on $n$ real-valued inputs. We give an agn
We study the fundamental problems of agnostically learning halfspaces and ReLUs under Gaussian marginals. In the former problem, given labeled examples $(mathbf{x}, y)$ from an unknown distribution on $mathbb{R}^d times { pm 1}$, whose marginal distr
Transfer learning has emerged as a powerful technique for improving the performance of machine learning models on new domains where labeled training data may be scarce. In this approach a model trained for a source task, where plenty of labeled train
In this work, we initiate a formal study of probably approximately correct (PAC) learning under evasion attacks, where the adversarys goal is to emph{misclassify} the adversarially perturbed sample point $widetilde{x}$, i.e., $h(widetilde{x}) eq c(wi
We present polynomial time and sample efficient algorithms for learning an unknown depth-2 feedforward neural network with general ReLU activations, under mild non-degeneracy assumptions. In particular, we consider learning an unknown network of the