Research map / Learning theory and algorithms / Sample complexity
Bounds on the Approximation Power of Feedforward Neural Networks
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 |
|---|---|---|---|
| Use the state-transition-based bound on breakpoints instead of the previous general-network bound | General feedforward networks · General networks | maximum linear pieces along a segment: (t\cdot \omega \cdot d_f)^{d_f} -> ((t-1)\omega_f+1)^{d_f}; multiplicative factor d_f^{d_f} | Helped |
| Include dimension in the strongly convex function lower bound | Feedforward neural networks approximating strongly convex functions · Strongly convex functions on [0,1]^n | hidden units required: \frac{1}{2}\log_2 (\frac{\mu}{16\varepsilon}) -> \frac{1}{2}\log_2 (\frac{\mu \cdot n}{16\varepsilon}) | Helped |
| Add a linear factor in depth to the lower bound for positive definite Hessian functions | Sigma_2 networks approximating functions with positive definite Hessian · Positive definite Hessian, Sigma_2 activations | hidden units required: q_1\varepsilon^{\frac{-1}{2d_f}} -> d_f q_2 \varepsilon^{\frac{-1}{2d_f}} | Helped |
| Use the Hessian-eigenvalue bound rather than the Laplacian-based bound | Network approximation lower-bound analysis · g_1(x_1,x_2)=20x_1^2-2x_2^2+x_1^2x_2^2 | lower bound on required linear pieces: zero -> \frac{0.737}{\sqrt{\varepsilon}} | Mixed |
| Use the Hessian-eigenvalue bound rather than the Laplacian-based bound | Network approximation lower-bound analysis · g_2(x_1,x_2)=10x_1^2+10x_2^2+x_1^2x_2^2 | lower bound on required linear pieces: \frac{0.82}{\sqrt{\varepsilon}} -> \frac{1.37}{\sqrt{\varepsilon}} | Mixed |
Closest papers by meaning
- Generalization Bounds for Rank-sparse Neural Networks (NeurIPS 2025 · similarity 0.87)
- Exact Upper and Lower Bounds for the Output Distribution of Neural Networks with Random Inputs (ICML 2025 · similarity 0.86)
- ReLU Network with Width $d+\mathcal{O}(1)$ Can Achieve Optimal Approximation Rate (ICML 2024 · similarity 0.85)
- Characterizing ResNet's Universal Approximation Capability (ICML 2024 · similarity 0.85)
- Sharper Guarantees for Learning Neural Network Classifiers with Gradient Methods (ICLR 2025 · similarity 0.85)
- Generalizability of Neural Networks Minimizing Empirical Risk Based on Expressive Power (ICLR 2025 · similarity 0.85)
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.