Quantitative 2-Wasserstein bounds are established between finite-width deep neural networks and their infinite-width Gaussian limits using a Lindeberg principle for successive Gaussian replacement of weights.
Hanin, Random neural networks in the infinite width limit as gaussian processes (2021) arXiv:2107.01562 [math.PR]
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α=0 architecture in NNFT minimizes finite-width variance, removes IR corrections, and sets a fundamental SNR bound for correlation functions in scalar field theory.
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Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle
Quantitative 2-Wasserstein bounds are established between finite-width deep neural networks and their infinite-width Gaussian limits using a Lindeberg principle for successive Gaussian replacement of weights.
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Optimal Architecture and Fundamental Bounds in Neural Network Field Theory
α=0 architecture in NNFT minimizes finite-width variance, removes IR corrections, and sets a fundamental SNR bound for correlation functions in scalar field theory.