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The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely wide neural nets trained under least squares loss by gradient descent. However, despite its importance, the super-quadratic runtime of kernel methods limits the use of…

Machine Learning · Computer Science 2021-07-28 Amir Zandieh

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…

Machine Learning · Computer Science 2020-04-21 Jascha Sohl-Dickstein , Roman Novak , Samuel S. Schoenholz , Jaehoon Lee

The Neural Tangent Kernel (NTK) is the wide-network limit of a kernel defined using neural networks at initialization, whose embedding is the gradient of the output of the network with respect to its parameters. We study the "after kernel",…

Machine Learning · Computer Science 2021-12-14 Philip M. Long

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…

Machine Learning · Statistics 2024-10-10 Guhan Chen , Yicheng Li , Qian Lin

In low-latency or mobile applications, lower computation complexity, lower memory footprint and better energy efficiency are desired. Many prior works address this need by removing redundant parameters. Parameter quantization replaces…

Machine Learning · Computer Science 2021-11-16 Cheng-Chou Lan

Deep neural networks (DNNs) are quantized for efficient inference on resource-constrained platforms. However, training deep learning models with low-precision weights and activations involves a demanding optimization task, which calls for…

Machine Learning · Computer Science 2021-05-25 Ziang Long , Penghang Yin , Jack Xin

Representing signals using coordinate networks dominates the area of inverse problems recently, and is widely applied in various scientific computing tasks. Still, there exists an issue of spectral bias in coordinate networks, limiting the…

Computer Vision and Pattern Recognition · Computer Science 2024-07-26 Zhicheng Cai , Hao Zhu , Qiu Shen , Xinran Wang , Xun Cao

The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key…

Machine Learning · Computer Science 2021-06-16 Sina Alemohammad , Zichao Wang , Randall Balestriero , Richard Baraniuk

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a…

Machine Learning · Computer Science 2024-04-29 Rustem Takhanov

It has been recently observed in much of the literature that neural networks exhibit a bottleneck rank property: for larger depths, the activation and weights of neural networks trained with gradient-based methods tend to be of…

Machine Learning · Computer Science 2025-11-26 Antoine Ledent , Rodrigo Alves , Yunwen Lei

Recent theoretical works based on the neural tangent kernel (NTK) have shed light on the optimization and generalization of over-parameterized networks, and partially bridge the gap between their practical success and classical learning…

Machine Learning · Computer Science 2020-08-10 Kyung-Su Kim , Aurélie C. Lozano , Eunho Yang

The training dynamics and generalization properties of neural networks (NN) can be precisely characterized in function space via the neural tangent kernel (NTK). Structural changes to the NTK during training reflect feature learning and…

Machine Learning · Statistics 2022-02-11 Haozhe Shan , Blake Bordelon

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…

Machine Learning · Statistics 2023-09-18 Mike Nguyen , Nicole Mücke

Small generalization errors of over-parameterized neural networks (NNs) can be partially explained by the frequency biasing phenomenon, where gradient-based algorithms minimize the low-frequency misfit before reducing the high-frequency…

Machine Learning · Computer Science 2022-09-27 Annan Yu , Yunan Yang , Alex Townsend

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…

Machine Learning · Computer Science 2022-10-11 Nir Ailon , Supratim Shit

Despite their immense promise in performing a variety of learning tasks, a theoretical understanding of the limitations of Deep Neural Networks (DNNs) has so far eluded practitioners. This is partly due to the inability to determine the…

Machine Learning · Computer Science 2024-01-25 Saad Qadeer , Andrew Engel , Amanda Howard , Adam Tsou , Max Vargas , Panos Stinis , Tony Chiang

Expressiveness and generalization of deep models was recently addressed via the connection between neural networks (NNs) and kernel learning, where first-order dynamics of NN during a gradient-descent (GD) optimization were related to…

Machine Learning · Computer Science 2020-04-21 Dmitry Kopitkov , Vadim Indelman

While deep learning has achieved remarkable success across a wide range of applications, its theoretical understanding of representation learning remains limited. Deep neural kernels provide a principled framework to interpret…

Machine Learning · Computer Science 2025-11-11 Yong-Ming Tian , Shuang Liang , Shao-Qun Zhang , Feng-Lei Fan

The role of quantization within implicit/coordinate neural networks is still not fully understood. We note that using a canonical fixed quantization scheme during training produces poor performance at low-rates due to the network weight…

Computer Vision and Pattern Recognition · Computer Science 2024-10-14 Cameron Gordon , Shin-Fang Chng , Lachlan MacDonald , Simon Lucey

Quantizing the weights of a neural network has two steps: (1) Finding a good low bit-complexity representation for weights (which we call the quantization grid) and (2) Rounding the original weights to values in the quantization grid. In…

Machine Learning · Computer Science 2025-01-14 Jerry Chee , Arturs Backurs , Rainie Heck , Li Zhang , Janardhan Kulkarni , Thomas Rothvoss , Sivakanth Gopi