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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

Sequential training from task to task is becoming one of the major objects in deep learning applications such as continual learning and transfer learning. Nevertheless, it remains unclear under what conditions the trained model's…

Machine Learning · Statistics 2022-03-21 Ryo Karakida , Shotaro Akaho

It has become standard to solve NLP tasks by fine-tuning pre-trained language models (LMs), especially in low-data settings. There is minimal theoretical understanding of empirical success, e.g., why fine-tuning a model with $10^8$ or more…

Machine Learning · Computer Science 2023-06-07 Sadhika Malladi , Alexander Wettig , Dingli Yu , Danqi Chen , Sanjeev Arora

Knowledge embedded in the weights of the artificial neural network can be used to improve the network structure, such as in network compression. However, the knowledge is set up by hand, which may not be very accurate, and relevant…

Neural and Evolutionary Computing · Computer Science 2021-10-13 Mengqiao Han , Xiabi Liu , Zhaoyang Hai , Xin Duan

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether…

Machine Learning · Computer Science 2023-05-03 Adityanarayanan Radhakrishnan , Mikhail Belkin , Caroline Uhler

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show…

Machine Learning · Computer Science 2024-11-01 Andrea Bonfanti , Giuseppe Bruno , Cristina Cipriani

In suitably initialized wide networks, small learning rates transform deep neural networks (DNNs) into neural tangent kernel (NTK) machines, whose training dynamics is well-approximated by a linear weight expansion of the network at…

Machine Learning · Computer Science 2020-10-29 Stanislav Fort , Gintare Karolina Dziugaite , Mansheej Paul , Sepideh Kharaghani , Daniel M. Roy , Surya Ganguli

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

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…

Machine Learning · Computer Science 2020-07-14 Lechao Xiao , Jeffrey Pennington , Samuel S. Schoenholz

Can deep learning solve multiple tasks simultaneously, even when they are unrelated and very different? We investigate how the representations of the underlying tasks affect the ability of a single neural network to learn them jointly. We…

Machine Learning · Computer Science 2021-03-30 Atish Agarwala , Abhimanyu Das , Brendan Juba , Rina Panigrahy , Vatsal Sharan , Xin Wang , Qiuyi Zhang

Deep neural networks (NN) have achieved great success in many applications. However, why do deep neural networks obtain good generalization at an over-parameterization regime is still unclear. To better understand deep NN, we establish the…

Machine Learning · Statistics 2021-12-02 Yueming Lyu , Ivor Tsang

This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and…

Machine Learning · Computer Science 2020-02-18 Ziwei Ji , Matus Telgarsky , Ruicheng Xian

Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods. At the same time, there is a vast amount of existing functions that programmatically solve different…

Machine Learning · Computer Science 2019-01-15 Alon Jacovi , Guy Hadash , Einat Kermany , Boaz Carmeli , Ofer Lavi , George Kour , Jonathan Berant

This work studies the neural tangent kernel (NTK) of the deep equilibrium (DEQ) model, a practical ``infinite-depth'' architecture which directly computes the infinite-depth limit of a weight-tied network via root-finding. Even though the…

Machine Learning · Computer Science 2023-10-24 Zhili Feng , J. Zico Kolter

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

Although the neural network (NN) technique plays an important role in machine learning, understanding the mechanism of NN models and the transparency of deep learning still require more basic research. In this study, we propose a novel…

Machine Learning · Computer Science 2023-11-10 Shuyue Guan , Murray Loew

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…

Machine Learning · Computer Science 2022-09-12 Insu Han , Amir Zandieh , Jaehoon Lee , Roman Novak , Lechao Xiao , Amin Karbasi

We introduce a method to train Binarized Neural Networks (BNNs) - neural networks with binary weights and activations at run-time. At training-time the binary weights and activations are used for computing the parameters gradients. During…

Machine Learning · Computer Science 2016-03-18 Matthieu Courbariaux , Itay Hubara , Daniel Soudry , Ran El-Yaniv , Yoshua Bengio

Deep learning has received considerable empirical successes in recent years. However, while many ad hoc tricks have been discovered by practitioners, until recently, there has been a lack of theoretical understanding for tricks invented in…

Machine Learning · Computer Science 2020-12-29 Cong Fang , Hanze Dong , Tong Zhang

Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) \citep{jacot2018neural}. Under the squared loss, the infinite-width NN trained…

Machine Learning · Statistics 2022-07-08 Yilan Chen , Wei Huang , Lam M. Nguyen , Tsui-Wei Weng