文中,作者加速训练的具体方法为:(1) 使用 shifted NTK (neural tangent kernel),(2) 证明了在每一个训练 iteration中,每一个 data point input 下,事实上只有很小一部分的 neuron 被激活了。(3) 通过 geometric search 来找到 activated neurons (4) 证明了新算法可以线性收敛地把 training loss 降为0。此...
This is in contrast to Neural Tangent Kernel which is unable to explain predictions of finite width networks. Our convex geometric characterization also provides intuitive explanations of hidden neurons as auto-encoders. In higher dimensions, we show that the training problem can be cast as a ...
We show that wide neural networks satisfy the PL⁎ condition, which explains the (S)GD convergence to a global minimum. Finally we propose a relaxation of the PL⁎ condition applicable to “almost” over-parameterized systems. Introduction A singular feature of modern machine learning is a ...
Known by practitioners that overparameterized neural networks are easy to learn, in the past few years there have been important theoretical developments in the analysis of overparameterized neural networks. In particular, it was shown that such systems behave like convex systems under various ...
1 The great success of deep neural networks (LeCun, Bengio, and Hinton 2015; Goodfellow, Bengio, and Courville 2016) has been reported in many applied fields, such as natural language processing, i...
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It is shown that over-parameterized neural networks can achieve minimax optimal rates of convergence (up to logarithmic factors) for learning functions from certain smooth function classes, if the weights are suitably constrained or regularized. Specifically, we consider the nonparametric regression of ...
Over-parameterizedOnline learningAdaptive gradientNeural networksNeural Processing Letters - In recent years, deep learning has dramatically improved state of the art in many practical applications. However, this utility is highly dependent on fine-tuning of......
We consider training over-parameterized two-layer neural networks with Rectified Linear Unit (ReLU) using gradient descent (GD) method. Inspired by a recent line of work, we study the evolutions of network prediction errors across GD iterations, which can be neatly described in a matrix form. ...
The practice of deep learning has shown that neural networks generalize remarkably well even with an extreme number of learned parameters. This appears to contradict traditional statistical wisdom, in which a trade-off between model complexity and fit to the data is essential. We aim to address ...