Related papers: Neural Tangent Kernels for Complex Genetic Risk Pr…

The genetic etiologies of common diseases are highly complex and heterogeneous. Classic statistical methods, such as linear regression, have successfully identified numerous genetic variants associated with complex diseases. Nonetheless,…

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…

We provide evidence that eigenanalysis of the empirical neural tangent kernel (eNTK) can surface feature directions in trained neural networks. Across three increasingly realistic settings -- a 1-layer MLP trained on modular addition, a…

Model Agnostic Meta-Learning (MAML) has emerged as a standard framework for meta-learning, where a meta-model is learned with the ability of fast adapting to new tasks. However, as a double-looped optimization problem, MAML needs to…

Infinite width limit has shed light on generalization and optimization aspects of deep learning by establishing connections between neural networks and kernel methods. Despite their importance, the utility of these kernel methods was…

We analyze the generalization properties of two-layer neural networks in the neural tangent kernel (NTK) regime, trained with gradient descent (GD). For early stopped GD we derive fast rates of convergence that are known to be minimax…

Multiple Kernel Learning is a conventional way to learn the kernel function in kernel-based methods. MKL algorithms enhance the performance of kernel methods. However, these methods have a lower complexity compared to deep learning models…

Deep neural networks (DNNs) have achieved remarkable empirical success, yet their training dynamics remain understood mainly from optimization rather than statistical principles. Here we develop a statistical framework for DNN training in…

Contrastive learning is a paradigm for learning representations from unlabelled data that has been highly successful for image and text data. Several recent works have examined contrastive losses to claim that contrastive models effectively…

Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be…

The paradigm of Next Token Prediction (NTP) has driven the unprecedented success of Large Language Models (LLMs), but is also the source of their most persistent weaknesses such as poor long-term planning, error accumulation, and…

Understanding the decision-making process of a machine/deep learning model is crucial, particularly in security-sensitive applications. In this study, we introduce a neural network framework that combines the global and exact…

Prompting and context-based fine-tuning methods, which we call Prefix Learning, have been proposed to enhance the performance of language models on various downstream tasks. They are empirically efficient and effective, matching the…

Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for…

Yang (2020a) recently showed that the Neural Tangent Kernel (NTK) at initialization has an infinite-width limit for a large class of architectures including modern staples such as ResNet and Transformers. However, their analysis does not…

Deep neural networks dominate modern machine learning, while alternative function approximators remain comparatively underexplored at scale. In this work, we revisit kernel methods as drop-in components for standard deep learning pipelines.…

This paper introduces a new and effective algorithm for learning kernels in a Multi-Task Learning (MTL) setting. Although, we consider a MTL scenario here, our approach can be easily applied to standard single task learning, as well. As…

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…

In this article a surprising result is demonstrated using the neural tangent kernel. This kernel is defined as the inner product of the vector of the gradient of an underlying model evaluated at training points. This kernel is used to…

Recent works have shown that on sufficiently over-parametrized neural nets, gradient descent with relatively large initialization optimizes a prediction function in the RKHS of the Neural Tangent Kernel (NTK). This analysis leads to global…