Research map / Adversarial robustness and security / Certified and empirical robustness
Adversarial Examples Exist in Two-Layer ReLU Networks for Low Dimensional Linear Subspaces
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 |
|---|---|---|---|
| Train by standard gradient methods on data confined to a low-dimensional linear subspace | Two-layer ReLU · Low-dimensional linear subspace | orthogonal input-gradient norm: ≥ \sqrt{\frac{k \ell}{2 m d}} | Hurt |
| Train by standard gradient methods on data confined to a low-dimensional linear subspace | Two-layer ReLU · Low-dimensional linear subspace | orthogonal adversarial perturbation norm: ≤ 8\sqrt{2}N(x_0)\cdot \frac{m}{k_{y_0}}\cdot \sqrt{\frac{d}{\ell}} | Hurt |
| Decrease the first-layer initialization scale (ablation) | Two-layer ReLU · Low-dimensional linear subspace | orthogonal input-gradient norm: \beta \sqrt{\frac{2 k \ell}{ m}} | Helped |
| Set initialization scale to \beta = \frac{1}{d\sqrt{2}} (ablation) | Two-layer ReLU · Low-dimensional linear subspace | orthogonal input-gradient norm: \frac{1}{\sqrt{d}} | Helped |
| Add L2 regularization during training (ablation) | Two-layer ReLU · Low-dimensional linear subspace | orthogonal input-gradient norm: (1- \eta \lambda)^T \sqrt{\frac{2 k \ell}{ m d}} | Helped |
| Reduce first-layer initialization scale (ablation) | Three-layer network · Random points on 28-dimensional sphere in 784 dimensions; MNIST projected to 32 dimensions | off-subspace PGD perturbation norm | Helped |
| Reduce first-layer initialization scale (ablation) | Three-layer network · Random points on 28-dimensional sphere in 784 dimensions; MNIST projected to 32 dimensions | on-subspace PGD perturbation norm | No clear effect |
| Add L2 regularization (ablation) | Two-layer ReLU · 7-point one-dimensional dataset | off-subspace distance to decision boundary | Helped |
Closest papers by meaning
- Most ReLU Networks Suffer from $\ell^2$ Adversarial Perturbations (NeurIPS 2020 · similarity 0.90)
- Wide Two-Layer Networks can Learn from Adversarial Perturbations (NeurIPS 2024 · similarity 0.89)
- Adversarial Training Can Provably Improve Robustness: Theoretical Analysis of Feature Learning Process Under Structured Data (ICLR 2025 · similarity 0.89)
- Stability and Generalization of Adversarial Training for Shallow Neural Networks with Smooth Activation (NeurIPS 2024 · similarity 0.88)
- Kernel Learning with Adversarial Features: Numerical Efficiency and Adaptive Regularization (NeurIPS 2025 · similarity 0.88)
- A Sublinear Adversarial Training Algorithm (ICLR 2024 · similarity 0.88)
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.