Related papers: Scaling Neural Tangent Kernels via Sketching and R…
Artificial neural networks have revolutionized machine learning in recent years, but a complete theoretical framework for their learning process is still lacking. Substantial advances were achieved for wide networks, within two disparate…
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…
It is well understood that neural networks with carefully hand-picked weights provide powerful function approximation and that they can be successfully trained in over-parametrized regimes. Since over-parametrization ensures zero training…
We study training one-hidden-layer ReLU networks in the neural tangent kernel (NTK) regime, where the networks' biases are initialized to some constant rather than zero. We prove that under such initialization, the neural network will have…
Model Reprogramming (MR) is a resource-efficient framework that adapts large pre-trained models to new tasks with minimal additional parameters and data, offering a promising solution to the challenges of training large models for diverse…
As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK…
Leveraging the kernel trick in both the input and output spaces, surrogate kernel methods are a flexible and theoretically grounded solution to structured output prediction. If they provide state-of-the-art performance on complex data sets…
Neural networks are known for their ability to approximate smooth functions, yet they fail to generalize perfectly to unseen inputs when trained on discrete operations. Such operations lie at the heart of algorithmic tasks such as…
We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. The standard deviation is exponential in the ratio of network depth to width.…
Convolutional Neural Networks (CNNs) have shown promising results in efficiency and accuracy in image classification. However, their efficacy often relies on large, labeled datasets, posing challenges for applications with limited data…
We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to…
Convolutional Neural Networks (CNNs) are now a well-established tool for solving computational imaging problems. Modern CNN-based algorithms obtain state-of-the-art performance in diverse image restoration problems. Furthermore, it has been…
A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based…
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…
The Neural Tangent Kernel (NTK) offers a powerful tool to study the functional dynamics of neural networks. In the so-called lazy, or kernel regime, the NTK remains static during training and the network function is linear in the static…
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 study the eigenvalue distributions of the Conjugate Kernel and Neural Tangent Kernel associated to multi-layer feedforward neural networks. In an asymptotic regime where network width is increasing linearly in sample size, under random…
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…
Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the…
This paper investigates the Neural Tangent Kernel (NTK) to search vision transformers without training. In contrast with the previous observation that NTK-based metrics can effectively predict CNNs performance at initialization, we…