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Algorithmic Aspects of Learning General ReLU Neural Networks.

General Note: Source: Dissertations Abstracts International, Volume: 85-11, Section: B.

Abstracts/Etc: 요약Non-linear activation functions enable deep neural networks to represent arbitrary relations. Rectified Linear Unit (ReLU) is one of the most commonly used activation function in modern neural network systems. Despite its empirical success, most of the theoretical principles governing ReLU-activated neural networks, including tractable learning algorithms, training dynamics and convergence rate remain unknown. To bridge this gap, we first present a convergence analysis of gradient descent for the problem of agnostically learning a single ReLU neuron with potentially non-zero bias under Gaussian distributions. Following our previous results, we generalize our analysis from a single neuron to neural networks by presenting polynomial-time and sample-efficient algorithms for learning an unknown depth-2 feedforward ReLU-activated neural network with non-zero bias, under mild non-degeneracy assumptions. Using these ideas we establish identifiability of the neural network parameters, as well as polynomial-time learnability of 2-layer ReLU-activated neural networks in the smoothed analysis framework under minimal assumptions.

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