# Deep double descent: where bigger models and more data hurt

@article{Nakkiran2019DeepDD, title={Deep double descent: where bigger models and more data hurt}, author={Preetum Nakkiran and Gal Kaplun and Yamini Bansal and Tristan Yang and Boaz Barak and Ilya Sutskever}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2019}, volume={2021} }

We show that a variety of modern deep learning tasks exhibit a ‘double-descent’ phenomenon where, as we increase model size, performance first gets worse and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We unify the above phenomena by defining a new complexity measure we call the effective model complexity and conjecture a generalized double descent with respect to this measure…

## 502 Citations

### Early Stopping in Deep Networks: Double Descent and How to Eliminate it

- Computer ScienceICLR
- 2021

Inspired by this theory, two standard convolutional networks are studied empirically and it is shown that eliminating epoch-wise double descent through adjusting stepsizes of different layers improves the early stopping performance significantly.

### When and how epochwise double descent happens

- Computer ScienceArXiv
- 2021

This work develops an analytically tractable model of epochwise double descent that allows us to characterise theoretically when this effect is likely to occur and shows experimentally that deep neural networks behave similarly to the theoretical model.

### Mitigating Deep Double Descent by Concatenating Inputs

- Computer ScienceCIKM
- 2021

This work proposes a construction which augments the existing dataset by artificially increasing the number of samples, and empirically mitigates the double descent curve in this setting.

### Multi-scale Feature Learning Dynamics: Insights for Double Descent

- Computer ScienceICML
- 2022

This work investigates the origins of the less studied epoch-wise double descent in which the test error undergoes two non-monotonous transitions, or de-scents as the training time increases, and derives closed-form analytical expressions describing the generalization error in terms of low-dimensional scalar macroscopic variables.

### Understanding the double descent phenomenon

- Computer Science
- 2022

This lecture explains the concept of double descent introduced by [4], and its mechanisms, and introduces inductive biases that appear to have a key role in double descent by selecting, among the multiple interpolating solutions, a smooth empirical risk minimizer.

### Comprehensive Understanding of Double Descent

- Computer Science
- 2020

We focus on the phenomenon of double descent in deep learning wherein when we increase model size or the number of epochs, performance on the test set initially improves (as expected), then worsens…

### Sparse Double Descent: Where Network Pruning Aggravates Overfitting

- Computer ScienceICML
- 2022

A novel learning distance interpretation that the curve of ℓ 2 learning distance of sparse models (from initialized parameters to final parameters) may correlate with the sparse double descent curve well and reflect generalization better than minima flatness is proposed.

### VC Theoretical Explanation of Double Descent

- Computer ScienceArXiv
- 2022

This paper presents a VC-theoretical analysis of double descent and shows that it can be fully explained by classical VC-generalization bounds and illustrates an application of analytic VC-bounds for modeling double descent for classiﬁcation problems, using empirical results for several learning methods.

### Rethinking Parameter Counting in Deep Models: Effective Dimensionality Revisited

- Computer ScienceArXiv
- 2020

Effective dimensionality is related to posterior contraction in Bayesian deep learning, model selection, width-depth tradeoffs, double descent, and functional diversity in loss surfaces, leading to a richer understanding of the interplay between parameters and functions in deep models.

### Double Descent Optimization Pattern and Aliasing: Caveats of Noisy Labels

- Computer ScienceArXiv
- 2021

It is shown that noisy labels must be present both in the training and generalization sets to observe a double descent pattern, and the learning rate has an influence on double descent, and how different optimizers and optimizer parameters influence the apparition of double descent is studied.

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