Papers › Theoretically Principled Trade-off between Robustness and Accuracy
Theoretically Principled Trade-off between Robustness and Accuracy
Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P. Xing, Laurent El Ghaoui, Michael. I. Jordan
We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although this problem has been widely studied empirically, much remains unknown concerning the theory underlying this trade-off. In this work, we decompose the prediction error for adversarial examples (robust error) as the sum of the natural (classification) error and boundary error, and provide a differentiable upper bound using the theory of classification-calibrated loss, which is shown to be the tightest possible upper bound uniform over all probability distributions and measurable predictors. Inspired by our theoretical analysis, we also design a new defense method, TRADES, to trade adversarial robustness off against accuracy. Our proposed algorithm performs well experimentally in real-world datasets. The methodology is the foundation of our entry to the NeurIPS 2018 Adversarial Vision Challenge in which we won the 1st place out of ~2,000 submissions, surpassing the runner-up approach by 11.41% in terms of mean ℓ₂ perturbation distance.
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Code
Syntology Ran 12 of 15 code samples harvested from 5 repositories linked to this paper; 3 have no recorded run. Of those that ran: 4 ran · our draft was wrong; 1 ran · fixture could not drive it; 7 ran with no contract checked.
By repository: community (archive-listed): 13 samples from 5 repositories, 11 ran; 2 identical to code first harvested elsewhere. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
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Code Syntology ran Syntology
15 samples harvested; 12 ran; 0 honoured the contract we drafted; 3 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 4 of the 15 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
Harvested from 5 repositories linked to this paper, official or community; each sample names its own and says which. Some samples are identical code Syntology first harvested from another repository; for those, this paper's copy is not located and its licence is not recorded. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Adversarial Attack | CIFAR-10 | TRADES [zhang2019b] | Attack: PGD20 | 45.900 | #3 of 6 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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