Related papers: The Recurrent Neural Tangent Kernel

Temporal point process (TPP) is an important tool for modeling and predicting irregularly timed events across various domains. Recently, the recurrent neural network (RNN)-based TPPs have shown practical advantages over traditional…

Sequential training from task to task is becoming one of the major objects in deep learning applications such as continual learning and transfer learning. Nevertheless, it remains unclear under what conditions the trained model's…

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show…

Adversarial training (AT) is a canonical method for enhancing the robustness of deep neural networks (DNNs). However, recent studies empirically demonstrated that it suffers from robust overfitting, i.e., a long time AT can be detrimental…

A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but highly correlated when they are in close proximity in receptive…

We perform a careful, thorough, and large scale empirical study of the correspondence between wide neural networks and kernel methods. By doing so, we resolve a variety of open questions related to the study of infinitely wide neural…

In wireless communications, estimation of channels in OFDM systems spans frequency and time, which relies on sparse collections of pilot data, posing an ill-posed inverse problem. Moreover, deep learning estimators require large amounts of…

An interesting observation in artificial neural networks is their favorable generalization error despite typically being extremely overparameterized. It is well known that the classical statistical learning methods often result in vacuous…

Recurrent Neural Networks (RNNs) are very successful at solving challenging problems with sequential data. However, this observed efficiency is not yet entirely explained by theory. It is known that a certain class of multiplicative RNNs…

The Neural Tangent Kernel (NTK) framework explains optimization in over-parameterized neural networks via approximately linearized dynamics, yielding exponential convergence guarantees. However, existing results are often overly pessimistic…

Recurrent Neural Networks (RNNs) represent the de facto standard machine learning tool for sequence modelling, owing to their expressive power and memory. However, when dealing with large dimensional data, the corresponding exponential…

The overparameterization of variational quantum circuits, as a model of Quantum Neural Networks (QNN), not only improves their trainability but also serves as a method for evaluating the property of a given ansatz by investigating their…

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…

The development of methods to guide the design of neural networks is an important open challenge for deep learning theory. As a paradigm for principled neural architecture design, we propose the translation of high-performing kernels, which…

The Neural Tangent Kernel (NTK) has emerged as a fundamental concept in the study of wide Neural Networks. In particular, it is known that the positivity of the NTK is directly related to the memorization capacity of sufficiently wide…

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…

The Neural Tangent Kernel (NTK) characterizes how a model's state evolves over Gradient Descent. Computing the full NTK matrix is often infeasible, especially for recurrent architectures. Here, we introduce a matrix-free perspective, using…

This paper aims to discuss the impact of random initialization of neural networks in the neural tangent kernel (NTK) theory, which is ignored by most recent works in the NTK theory. It is well known that as the network's width tends to…

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various…

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…