相关论文: MLPs at the EOC: Concentration of the NTK

We study the properties of the Neural Tangent Kernel (NTK) $\overset{\scriptscriptstyle\infty}{K} : \mathbb{R}^{m_0} \times \mathbb{R}^{m_0} \to \mathbb{R}^{m_l \times m_l}$ corresponding to infinitely wide $l$-layer Multilayer Perceptrons…

Neural Tangent Kernel (NTK) is widely used to analyze overparametrized neural networks due to the famous result by Jacot et al. (2018): in the infinite-width limit, the NTK is deterministic and constant during training. However, this result…

Recent work by Jacot et al. (2018) has shown that training a neural network using gradient descent in parameter space is related to kernel gradient descent in function space with respect to the Neural Tangent Kernel (NTK). Lee et al. (2019)…

The Neural Tangent Kernel (NTK), defined as $\Theta_\theta^f(x_1, x_2) = \left[\partial f(\theta, x_1)\big/\partial \theta\right] \left[\partial f(\theta, x_2)\big/\partial \theta\right]^T$ where $\left[\partial f(\theta,…

The tremendous recent progress in analyzing the training dynamics of overparameterized neural networks has primarily focused on wide networks and therefore does not sufficiently address the role of depth in deep learning. In this work, we…

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…

In this work, we study the Neural Tangent Kernel (NTK) of Matrix Product States (MPS) and the convergence of its NTK in the infinite bond dimensional limit. We prove that the NTK of MPS asymptotically converges to a constant matrix during…

The Neural Tangent Kernel (NTK) has emerged as a powerful tool to provide memorization, optimization and generalization guarantees in deep neural networks. A line of work has studied the NTK spectrum for two-layer and deep networks with at…

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…

The evolution of a deep neural network trained by the gradient descent can be described by its neural tangent kernel (NTK) as introduced in [20], where it was proven that in the infinite width limit the NTK converges to an explicit limiting…

In training a neural network with gradient descent (GD), each iteration induces a linear operator that governs first-order updates to a model's internal state variables. We define this operator as the Global Empirical Neural Tangent Kernel…

We investigate the mathematical foundations of neural networks in the infinite-width regime through the Neural Tangent Kernel (NTK). We propose the NTK-Eigenvalue-Controlled Residual Network (NTK-ECRN), an architecture integrating Fourier…

Neural Tangent Kernel (NTK) theory is widely used to study the dynamics of infinitely-wide deep neural networks (DNNs) under gradient descent. But do the results for infinitely-wide networks give us hints about the behavior of real…

Modern deep networks are heavily overparameterized yet often generalize well, suggesting a form of low intrinsic complexity not reflected by parameter counts. We study this complexity at initialization through the effective rank of the…

Empirical neural tangent kernels (eNTKs) can provide a good understanding of a given network's representation: they are often far less expensive to compute and applicable more broadly than infinite width NTKs. For networks with O output…

This paper demonstrates that in classification problems, fully connected neural networks (FCNs) and residual neural networks (ResNets) cannot be approximated by kernel logistic regression based on the Neural Tangent Kernel (NTK) under…

Recent theoretical works based on the neural tangent kernel (NTK) have shed light on the optimization and generalization of over-parameterized networks, and partially bridge the gap between their practical success and classical learning…

In wide neural networks, the Neural Tangent Kernel (NTK) remains approximately constant during training, providing a powerful theoretical tool for studying training dynamics, generalization, and connections to kernel methods. However, this…

This work studies the neural tangent kernel (NTK) of the deep equilibrium (DEQ) model, a practical ``infinite-depth'' architecture which directly computes the infinite-depth limit of a weight-tied network via root-finding. Even though the…

Recent research has been focused on two different approaches to studying neural networks training in the limit of infinite width (1) a mean-field (MF) and (2) a constant neural tangent kernel (NTK) approximations. These two approaches have…