无监督学习 (Unsupervised learning),三维形状补全(3D shape completion),深度先验 (Deep Prior),神经网络正切核 (Neural Tangent Kernel, NTK) 这些元素碰撞在一起会擦起什么样的火花呢? 来自香港大学和微软亚洲研究院的专家学者最近在Arxiv上挂出文章,提出了一个新方法,使用了深度神经网络进行无监督学习,从扫描的...
We provide a precise high-dimensional asymptotic analysis of generalization under kernel regression with the Neural Tangent Kernel, which characterizes the behavior of wide neural networks optimized with gradient descent. Our results reveal that the test error has non-monotonic behavior deep in the over...
个人简介 Generalization ability of wide neural networks on R We perform a study on the generalization ability of the wide two-layer ReLU neural network on R. We first establish some spectral properties of the neural tangent kernel (NTK): a)Kd, the NTK defined onRd, is positive definite; b...
The neural tangent kernel (NTK) was created in the context of using the limit idea to study the theory of neural network. NTKs are defined from neural network models in the infinite-width limit trained by gradient descent. Such over-parameterized models achieved good test accuracy in experiments...
RG Flow of the Neural Tangent Kernel Effective Theory of the NTK at Initialization Kernel Learning Representation Learning 0.2 The Theoretical Minimum 从high-level 给出文章方法的overview,揭示为什么 a first-principles 理论可能可以解释Deep Learning (DL) 简单的假设神经网络是一个参数方程: f(x;θ) ,...
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 DNN architecture remains to be kernelized, namely, th...
Many approaches have been takento characterize this phenomenon more rigorously, including landscape analysis, the neural tangentkernel approach, and mean-f i eld analysis. All such viewpoints aim to give an idea of the structureand size of the NN required to ensure global convergence.Ourapproachin...
For regression problems, we establish using the neural tangent kernel perspective that GD achieves global linear convergence of the objective function when the hidden dimension of KANs is sufficiently large. We further extend these results to SGD, demonstrating a similar global convergence in expectation...
Neural tangent kernel beyond the infinite-width limit: effects of depth and initialization. Preprint at https://arxiv.org/abs/2202.00553 (2022). Vyas, N., Bansal, Y. & Preetum, N. Limitations of the NTK for understanding generalization in deep learning. Preprint at https://arxiv.org/abs...
从表达式子看,有一点和Neural Tangent Kernel (NTK)不同的是,有一个1/N的系数。而在NTK理论中,系数是½(1/N)½。 假设我们使用,squared loss,那么考虑stochastic gradient descent,参数更新公式为 这里作者假设每次梯度下降只经一个数据,而且这个数据只出现一次。