# Regularized Training and Tight Certification for Randomized Smoothed Classifier with Provable Robustness

Source: [Regularized Training and Tight Certification for Randomized Smoothed Classifier with Provable Robustness](<https://www.sota2.com/research/paper/68fa671b1e209131cea1441b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T22:06:19.934Z

Authors: Huijie Feng, Chunpeng Wu, Guoyang Chen, Weifeng Zhang, Yang Ning

Published: 2020-02-17T20:54:34.000Z

## Abstract

Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\\ell\_2$ norm bounded adversarial perturbations. However, how to train a good base classifier that is accurate and robust when smoothed has not been fully investigated. In this work, we derive a new regularized risk, in which the regularizer can adaptively encourage the accuracy and robustness of the smoothed counterpart when training the base classifier. It is computationally efficient and can be implemented in parallel with other empirical defense methods. We discuss how to implement it under both standard (non-adversarial) and adversarial training scheme. At the same time, we also design a new certification algorithm, which can leverage the regularization effect to provide tighter robustness lower bound that holds with high probability. Our extensive experimentation demonstrates the effectiveness of the proposed training and certification approaches on CIFAR-10 and ImageNet datasets.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Certified Robustness on CIFAR-10 (L2 Accuracy Profile)](<https://www.sota2.com/research/sota/certified-robustness-on-cifar-10-l2-accuracy-profile.md>): Certified Robustness; CIFAR-10; Certified Accuracy (L2, r=0.0): 65.2.

- [Certified Robustness on ImageNet (L2 Perturbation Bounds)](<https://www.sota2.com/research/sota/certified-robustness-on-imagenet-l2-perturbation-bounds.md>): Certified Robustness; ImageNet; Inference Time (s): 122.7.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2002.07246>)

[PDF](<https://arxiv.org/pdf/2002.07246.pdf>)