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Mean Field Analysis of Neural Networks: A Central Limit Theorem
Justin Sirignano, Konstantinos Spiliopoulos
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A)…
Importance sampling for slow-fast diffusions based on moderate deviations
Matthew R. Morse, Konstantinos Spiliopoulos
We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation…
Mean Field Analysis of Neural Networks: A Law of Large Numbers
Justin Sirignano, Konstantinos Spiliopoulos
Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in…