Related papers: Learning with Neural Tangent Kernels in Near Input…

Matrix completion problems arise in many applications including recommendation systems, computer vision, and genomics. Increasingly larger neural networks have been successful in many of these applications, but at considerable computational…

We develop a solvable model of neural scaling laws beyond the kernel limit. Theoretical analysis of this model shows how performance scales with model size, training time, and the total amount of available data. We identify three scaling…

Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further,…

In the era of large language models (LLMs), fine-tuning pretrained models has become ubiquitous. Yet the theoretical underpinning remains an open question. A central question is why only a few epochs of fine-tuning are typically sufficient…

Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…

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…

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these 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…

A convergence analysis is developed for the regularized Newton method for training neural networks (NNs) in the overparameterized limit. As the number of hidden units tends to infinity, the NN training dynamics converge in probability to…

Recently, there has been growing evidence that if the width and depth of a neural network are scaled toward the so-called rich feature learning limit (\mup and its depth extension), then some hyperparameters -- such as the learning rate --…

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…

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…

Sequential deep learning models such as RNN, causal CNN and attention mechanism do not readily consume continuous-time information. Discretizing the temporal data, as we show, causes inconsistency even for simple continuous-time processes.…

Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit…

Graph neural networks (GNNs) have achieved superior performance on node classification tasks in the last few years. Commonly, this is framed in a transductive semi-supervised learning setup wherein the entire graph, including the target…

We consider gradient-based optimisation of wide, shallow neural networks, where the output of each hidden node is scaled by a positive parameter. The scaling parameters are non-identical, differing from the classical Neural Tangent Kernel…

Neural networks in the lazy training regime converge to kernel machines. Can neural networks in the rich feature learning regime learn a kernel machine with a data-dependent kernel? We demonstrate that this can indeed happen due to a…

A theory of neural networks (NNs) built upon collective variables would provide scientists with the tools to better understand the learning process at every stage. In this work, we introduce two such variables, the entropy and the trace of…

Deep residual network architectures have been shown to achieve superior accuracy over classical feed-forward networks, yet their success is still not fully understood. Focusing on massively over-parameterized, fully connected residual…

A longstanding goal in the theory of deep learning is to characterize the conditions under which a given neural network architecture will be trainable, and if so, how well it might generalize to unseen data. In this work, we provide such a…