Research map / Learning theory and algorithms / Sample complexity
A Law of Robustness beyond Isoperimetry
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Remove the isoperimetry assumption on the input distribution (arbitrary bounded-support distribution) and keep J-Lipschitz parametrization with p parameters | robust interpolation Lipschitzness lower bound · theoretical: bounded-support arbitrary distributions | Lipschitzness lower bound order | Helped |
| Remove both isoperimetry and J-Lipschitz parametrization assumptions; use Rademacher complexity and covering argument | robust interpolation Lipschitzness lower bound · theoretical: any function class on bounded support | Lipschitzness lower bound order | Helped |
| Overparametrized regime removed: sample size n exponentially large in d (n = exp(omega(d))) for any O(1)-Lipschitz learner | robust interpolation with any approximator · theoretical: bounded-support arbitrary distributions | Lipschitzness lower bound order | Hurt |
| Increase input dimension d by padding covariates (scattering data in higher dimension) | robust interpolation Lipschitzness lower bound · theoretical: bounded-support arbitrary distributions | Lipschitzness lower bound order n^{1/d} | Helped |
Closest papers by meaning
- A Universal Law of Robustness via Isoperimetry (NeurIPS 2021 · similarity 0.92)
- Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective (NeurIPS 2022 · similarity 0.88)
- Robust learning of halfspaces under log-concave marginals (NeurIPS 2025 · similarity 0.87)
- Some Fundamental Aspects about Lipschitz Continuity of Neural Networks (ICLR 2024 · similarity 0.87)
- 1-Lipschitz Layers Compared: Memory Speed and Certifiable Robustness (CVPR 2024 · similarity 0.86)
- Diffusion Models are Certifiably Robust Classifiers (NeurIPS 2024 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.