Research map / Architectures and efficiency / RNNs and normalization
Better depth-width trade-offs for neural networks through the lens of dynamical systems
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 refined period-specific oscillation analysis | Functions with odd prime period p · Continuous functions with odd prime period p | oscillation growth rate: ρ_p > ρ' | Helped |
| Use period-specific bounds under L1 approximation rather than classification error | Shallow ReLU networks approximating repeated compositions · Repeated compositions f^t | L1 approximation error: c(x,y) > 0 | Helped |
| Match the function's Lipschitz constant to its oscillation growth rate | Shallow ReLU networks approximating repeated compositions · Repeated compositions f^t with L = ρ | L1 approximation error: (y-x)^2/32 | Helped |
| Increase network depth | Neural network on the easy regression task · Synthetic regression, f^8(x) | regression performance | Helped |
| Apply the shallow-network separation to the hard regression task | Neural network on f^40(x) · Synthetic regression, f^40(x) | L1 approximation error | Mixed |
| Use the earlier oscillation-growth bound | Functions with odd prime period p · Functions with odd prime period p | oscillation growth rate: ρ > ρ' | Hurt |
Closest papers by meaning
- Depth-Width Trade-offs for ReLU Networks via Sharkovsky's Theorem (ICLR 2020 · similarity 0.94)
- Minimum Width for Deep, Narrow MLP: A Diffeomorphism Approach (NeurIPS 2025 · similarity 0.88)
- Feature Learning Dynamics in Infinite-Depth Neural Networks (NeurIPS 2026 · similarity 0.87)
- Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon (NeurIPS 2025 · similarity 0.86)
- ReLU Network with Width $d+\mathcal{O}(1)$ Can Achieve Optimal Approximation Rate (ICML 2024 · similarity 0.86)
- Depth-Bounds for Neural Networks via the Braid Arrangement (NeurIPS 2025 · 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.