The Quest of Finding the Antidote to Sparse Double Descent

In energy-efficient schemes, finding the optimal size of deep learning models is very important and has a broad impact. Meanwhile, recent studies have reported an unexpected phenomenon, the sparse double descent: as the model's sparsity increases, the performance first worsens, then improves, and finally deteriorates. Such a non-monotonic behavior raises serious questions about the optimal model's size to maintain high performance: the model needs to be sufficiently over-parametrized, but having too many parameters wastes training resources. In this paper, we aim to find the best trade-off efficiently. More precisely, we tackle the occurrence of the sparse double descent and present some solutions to avoid it. Firstly, we show that a simple $\ell_2$ regularization method can help to mitigate this phenomenon but sacrifices the performance/sparsity compromise. To overcome this problem, we then introduce a learning scheme in which distilling knowledge regularizes the student model. Supported by experimental results achieved using typical image classification setups, we show that this approach leads to the avoidance of such a phenomenon

Reconciling modern machine learning practice and the bias-variance trade-off

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine learning practice. The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns. However, in the modern practice, very rich models such as neural networks are trained to exactly fit (i.e., interpolate) the data. Classically, such models would be considered over-fit, and yet they often obtain high accuracy on test data. This apparent contradiction has raised questions about the mathematical foundations of machine learning and their relevance to practitioners. In this paper, we reconcile the classical understanding and the modern practice within a unified performance curve. This "double descent" curve subsumes the textbook U-shaped bias-variance trade-off curve by showing how increasing model capacity beyond the point of interpolation results in improved performance. We provide evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets, and we posit a mechanism for its emergence. This connection between the performance and the structure of machine learning models delineates the limits of classical analyses, and has implications for both the theory and practice of machine learning

Dropout Drops Double Descent

In this paper, we find and analyze that we can easily drop the double descent by only adding one dropout layer before the fully-connected linear layer. The surprising double-descent phenomenon has drawn public attention in recent years, making the prediction error rise and drop as we increase either sample or model size. The current paper shows that it is possible to alleviate these phenomena by using optimal dropout in the linear regression model and the nonlinear random feature regression, both theoretically and empirically. % ${y}=X{\beta}^0+{\epsilon}$ with $X\in\mathbb{R}^{n\times p}$. We obtain the optimal dropout hyperparameter by estimating the ground truth ${\beta}^0$ with generalized ridge typed estimator $\hat{{\beta}}=(X^TX+\alpha\cdot\mathrm{diag}(X^TX))^{-1}X^T{y}$. Moreover, we empirically show that optimal dropout can achieve a monotonic test error curve in nonlinear neural networks using Fashion-MNIST and CIFAR-10. Our results suggest considering dropout for risk curve scaling when meeting the peak phenomenon. In addition, we figure out why previous deep learning models do not encounter double-descent scenarios -- because we already apply a usual regularization approach like the dropout in our models. To our best knowledge, this paper is the first to analyze the relationship between dropout and double descent

Can we avoid Double Descent in Deep Neural Networks?

Finding the optimal size of deep learning models is very actual and of broad impact, especially in energy-saving schemes. Very recently, an unexpected phenomenon, the ``double descent'', has caught the attention of the deep learning community. As the model's size grows, the performance gets first worse, and then goes back to improving. It raises serious questions about the optimal model's size to maintain high generalization: the model needs to be sufficiently over-parametrized, but adding too many parameters wastes training resources. Is it possible to find, in an efficient way, the best trade-off? Our work shows that the double descent phenomenon is potentially avoidable with proper conditioning of the learning problem, but a final answer is yet to be found. We empirically observe that there is hope to dodge the double descent in complex scenarios with proper regularization, as a simple $\ell_2$ regularization is already positively contributing to such a perspective

Label Noise in Adversarial Training: A Novel Perspective to Study Robust Overfitting

We show that label noise exists in adversarial training. Such label noise is due to the mismatch between the true label distribution of adversarial examples and the label inherited from clean examples - the true label distribution is distorted by the adversarial perturbation, but is neglected by the common practice that inherits labels from clean examples. Recognizing label noise sheds insights on the prevalence of robust overfitting in adversarial training, and explains its intriguing dependence on perturbation radius and data quality. Also, our label noise perspective aligns well with our observations of the epoch-wise double descent in adversarial training. Guided by our analyses, we proposed a method to automatically calibrate the label to address the label noise and robust overfitting. Our method achieves consistent performance improvements across various models and datasets without introducing new hyper-parameters or additional tuning.Comment: Neurips 2022 (Oral); A previous version of this paper (v1) used the title `Double Descent in Adversarial Training: An Implicit Label Noise Perspective