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We prove that a randomly initialized neural network of *any architecture* has its Tangent Kernel (NTK) converge to a deterministic limit, as the network widths tend to infinity. We demonstrate how to calculate this limit. In prior literature, the heuristic study of neural network gradients often assumes every weight matrix used in forward propagation is independent from its transpose used in backpropagation (Schoenholz et al. 2017). This is known as the *gradient independence assumption (GIA)*. We identify a commonly satisfied condition, which we call *Simple GIA Check*, such that the NTK limit calculation based on GIA is correct. Conversely, when Simple GIA Check fails, we show GIA can result in wrong answers. Our material here presents the NTK results of Yang (2019a) in a friendly manner and showcases the *tensor programs* technique for understanding wide neural networks. We provide reference implementations of infinite-width NTKs of recurrent neural network, transformer, and batch normalization at https://github.com/thegregyang/NTK4A.
We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by identifying a connection between neural tangent kernel (NTK) and MMD statistic. This connection enables us to develop a computationally efficient and memory-efficient appro
We analyze the convergence of the averaged stochastic gradient descent for overparameterized two-layer neural networks for regression problems. It was recently found that a neural tangent kernel (NTK) plays an important role in showing the global con
We study the SIMP method with a density field generated by a fully-connected neural network, taking the coordinates as inputs. In the large width limit, we show that the use of DNNs leads to a filtering effect similar to traditional filtering techniq
The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key DNN archi
A recent line of work has analyzed the theoretical properties of deep neural networks via the Neural Tangent Kernel (NTK). In particular, the smallest eigenvalue of the NTK has been related to the memorization capacity, the global convergence of grad