
Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime
Deep neural networks can achieve remarkable generalization performances ...
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Benign Overfitting and Noisy Features
Modern machine learning often operates in the regime where the number of...
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On the Universality of the Double Descent Peak in Ridgeless Regression
We prove a nonasymptotic distributionindependent lower bound for the e...
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Surprises in HighDimensional Ridgeless Least Squares Interpolation
Interpolators  estimators that achieve zero training error  have att...
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Understanding overfitting peaks in generalization error: Analytical risk curves for l_2 and l_1 penalized interpolation
Traditionally in regression one minimizes the number of fitting paramete...
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A finite sample analysis of the double descent phenomenon for ridge function estimation
Recent extensive numerical experiments in high scale machine learning ha...
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Learning Sparse Neural Networks via SensitivityDriven Regularization
The everincreasing number of parameters in deep neural networks poses c...
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Triple descent and the two kinds of overfitting: Where why do they appear?
A recent line of research has highlighted the existence of a double descent phenomenon in deep learning, whereby increasing the number of training examples N causes the generalization error of neural networks to peak when N is of the same order as the number of parameters P. In earlier works, a similar phenomenon was shown to exist in simpler models such as linear regression, where the peak instead occurs when N is equal to the input dimension D. In both cases, the location of the peak coincides with the interpolation threshold. In this paper, we show that despite their apparent similarity, these two scenarios are inherently different. In fact, both peaks can coexist when neural networks are applied to noisy regression tasks. The relative size of the peaks is governed by the degree of nonlinearity of the activation function. Building on recent developments in the analysis of random feature models, we provide a theoretical ground for this samplewise triple descent. As shown previously, the nonlinear peak at N=P is a true divergence caused by the extreme sensitivity of the output function to both the noise corrupting the labels and the initialization of the random features (or the weights in neural networks). This peak survives in the absence of noise, but can be suppressed by regularization. In contrast, the linear peak at N=D is solely due to overfitting the noise in the labels, and forms earlier during training. We show that this peak is implicitly regularized by the nonlinearity, which is why it only becomes salient at high noise and is weakly affected by explicit regularization. Throughout the paper, we compare the analytical results obtained in the random feature model with the outcomes of numerical experiments involving realistic neural networks.
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