Research map / Architectures and efficiency / RNNs and normalization
Empirical Bounds on Linear Regions of Deep Rectifier 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 an activation-based empirical upper bound instead of the Configuration UB | Linear-region bound for trained ReLU networks · MNIST networks, widths 1;21;10 | gap closed (%): 73.1 | Helped |
| Use an activation-based empirical upper bound instead of the Configuration UB | Linear-region bound for trained ReLU networks · MNIST networks, widths 21;1;10 | gap closed (%): 98.3 | Helped |
| Use an activation-based empirical upper bound instead of the Configuration UB | Linear-region bound for trained ReLU networks · MNIST networks, widths 8;14;10 | gap closed (%): 0 | No clear effect |
| Use universal-hash parity constraints with the MIPBound algorithm to estimate activation-pattern counts | Trained ReLU networks with many linear regions · MNIST | computation time | Helped |
| Increase XOR constraint size | MIPBound approximate linear-region count · MNIST networks | approximation accuracy | Helped |
| Use XOR-2 constraints rather than larger XOR constraints | MIPBound approximate linear-region count · MNIST networks | computation time | Helped |
| Use XOR-2 lower bounds for relative expressiveness comparisons | MIPBound approximate linear-region count · MNIST networks | relative expressiveness comparison | No clear effect |
| Combine empirical upper and probabilistic lower bounds | Approximate linear-region count · MNIST networks without particularly narrow layers | correlation with accuracy | Helped |
Closest papers by meaning
- Bounding and Counting Linear Regions of Deep Neural Networks (ICML 2018 · similarity 0.92)
- The Computational Complexity of Counting Linear Regions in ReLU Neural Networks (NeurIPS 2025 · similarity 0.89)
- Comparing Linear Regions in ReLU-Type Networks: Theory and Monte Carlo Methods (NeurIPS 2026 · similarity 0.89)
- Compelling ReLU Networks to Exhibit Exponentially Many Linear Regions at Initialization and During Training (ICML 2025 · similarity 0.86)
- Depth-Bounds for Neural Networks via the Braid Arrangement (NeurIPS 2025 · similarity 0.85)
- On the Local Complexity of Linear Regions in Deep ReLU Networks (ICML 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.