Related papers: Neural Tangent Kernel Maximum Mean Discrepancy

There are currently two parameterizations used to derive fixed kernels corresponding to infinite width neural networks, the NTK (Neural Tangent Kernel) parameterization and the naive standard parameterization. However, the extrapolation of…

An adaptive bandwidth selection procedure for the mixture kernel in the maximum mean discrepancy (MMD) for fitting generative moment matching networks (GMMNs) is introduced, and its ability to improve the learning of copula random number…

We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize…

A major factor in the success of deep neural networks is the use of sophisticated architectures rather than the classical multilayer perceptron (MLP). Residual networks (ResNets) stand out among these powerful modern architectures. Previous…

Recently, neural tangent kernel (NTK) has been used to explain the dynamics of learning parameters of neural networks, at the large width limit. Quantitative analyses of NTK give rise to network widths that are often impractical and incur…

Large language models (LLMs) such as ChatGPT have exhibited remarkable performance in generating human-like texts. However, machine-generated texts (MGTs) may carry critical risks, such as plagiarism issues, misleading information, or…

Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…

Little is known about the training dynamics of equivariant neural networks, in particular how it compares to data augmented training of their non-equivariant counterparts. Recently, neural tangent kernels (NTKs) have emerged as a powerful…

The memory physics induced unknown offset of the channel is a critical and difficult issue to be tackled for many non-volatile memories (NVMs). In this paper, we first propose novel neural network (NN) detectors by using the multilayer…

Modern deep neural networks (DNNs) are extremely powerful; however, this comes at the price of increased depth and having more parameters per layer, making their training and inference more computationally challenging. In an attempt to…

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…

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean…

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy…

The Neural Tangent Kernel (NTK) framework has provided deep insights into the training dynamics of neural networks under gradient flow. However, it relies on the assumption that the network is differentiable with respect to its parameters,…

We explore the equivalence between neural networks and kernel methods by deriving the first exact representation of any finite-size parametric classification model trained with gradient descent as a kernel machine. We compare our exact…

Maximum mean discrepancy (MMD) has been widely adopted in domain adaptation to measure the discrepancy between the source and target domain distributions. Many existing domain adaptation approaches are based on the joint MMD, which is…

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…

The ``Neural Tangent Kernel'' (NTK) (Jacot et al 2018), and its empirical variants have been proposed as a proxy to capture certain behaviors of real neural networks. In this work, we study NTKs through the lens of scaling laws, and…

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…