# Can Implicit Bias Explain Generalization? Stochastic Convex Optimization as a Case Study

@article{Dauber2020CanIB, title={Can Implicit Bias Explain Generalization? Stochastic Convex Optimization as a Case Study}, author={Assaf Dauber and Meir Feder and Tomer Koren and Roi Livni}, journal={ArXiv}, year={2020}, volume={abs/2003.06152} }

The notion of implicit bias, or implicit regularization, has been suggested as a means to explain the surprising generalization ability of modern-days overparameterized learning algorithms. This notion refers to the tendency of the optimization algorithm towards a certain structured solution that often generalizes well. Recently, several papers have studied implicit regularization and were able to identify this phenomenon in various scenarios. We revisit this paradigm in arguably the simplest…

## 16 Citations

Implicit Regularization in Deep Learning May Not Be Explainable by Norms

- Computer ScienceNeurIPS
- 2020

The results suggest that, rather than perceiving the implicit regularization via norms, a potentially more useful interpretation is minimization of rank, and it is demonstrated empirically that this interpretation extends to a certain class of non-linear neural networks, and hypothesize that it may be key to explaining generalization in deep learning.

Implicit Regularization in ReLU Networks with the Square Loss

- Computer ScienceCOLT
- 2021

It is proved that even for a single ReLU neuron, it is impossible to characterize the implicit regularization with the square loss by any explicit function of the model parameters, and a more general framework than the one considered so far may be needed to understand implicit regularizations for nonlinear predictors.

SGD Generalizes Better Than GD (And Regularization Doesn't Help)

- Computer ScienceCOLT
- 2021

It is shown that with the same number of steps GD may overfit and emit a solution with Ω(1) generalization error, and how regularizing the empirical risk minimized by GD essentially does not change the above result.

Is SGD a Bayesian sampler? Well, almost

- Computer ScienceJ. Mach. Learn. Res.
- 2021

Estimating the probability that an overparameterised DNN, trained with stochastic gradient descent or one of its variants, converges on a function consistent with a training set, implies that strong inductive bias in the parameter-function map, rather than a special property of SGD, is the primary explanation for why DNNs generalise so well in the overparametersised regime.

A Limitation of the PAC-Bayes Framework

- Computer ScienceNeurIPS
- 2020

An easy learning task that is not amenable to a PAC-Bayes analysis is demonstrated, and it is shown that for any algorithm that learns 1-dimensional linear classifiers there exists a (realizable) distribution for which the PAC- Bayes bound is arbitrarily large.

On Convergence and Generalization of Dropout Training

- Computer ScienceNeurIPS
- 2020

It is shown that dropout training with logistic loss achieves $\epsilon$-suboptimality in testerror in test error in $O(1/\ep silon)$ iterations.

Stochastic Training is Not Necessary for Generalization

- Computer ScienceArXiv
- 2021

It is demonstrated that non-stochastic full-batch training can achieve strong performance on CIFAR-10 that is on-par with SGD, using modern architectures in settings with and without data augmentation.

SGD: The Role of Implicit Regularization, Batch-size and Multiple-epochs

- Computer ScienceNeurIPS
- 2021

This paper considers the problem of SCO and explores the role of implicit regularization, batch size and multiple epochs for SGD, and extends the results to the general learning setting by showing a problem which is learnable for any data distribution, and SGD is strictly better than RERM for any regularization function.

Benign Underfitting of SGD in Stochastic Convex Optimization

- Computer Science
- 2022

It turns out that SGD is not algorithmically stable in any sense, and its generalization ability cannot be explained by uniform convergence or any other currently known generalization bound technique for that matter (other than that of its classical analysis).

Benign Underfitting of Stochastic Gradient Descent

- Computer ScienceArXiv
- 2022

It turns out that SGD is not algorithmically stable in any sense, and its generalization ability cannot be explained by uniform convergence or any other currently known generalization bound technique for that matter (other than that of its classical analysis).

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