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Achieve the Minimum Width of Neural Networks for Universal Approximation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use leaky-ReLU networks at width max(d_x,d_y) when at least one dimension exceeds one | L^p universal approximation on compact domains · L^p(K, R^dy) | minimum width for UAP: w_min = max(d_x, d_y,2) -> w_min^* = max(d_x,d_y) | Helped |
| Add ABS to leaky-ReLU | L^p universal approximation on compact domains · L^p(K, R^dy), d_x=d_y=1 | minimum width for UAP: max(d_x, d_y,2) -> max(d_x, d_y) | Helped |
| Use ReLU+FLOOR | C universal approximation on compact domains · C(K, R^dy) | minimum width for UAP: w_min = max(d_x, 2, d_y) | Mixed |
| Use UOE+FLOOR instead of ReLU+FLOOR | C universal approximation on compact domains · C(K, R^dy) | minimum width for UAP: max(d_x, 2, d_y) -> max(d_x, d_y) | Helped |
| Use UOE for one-dimensional continuous functions | C universal approximation · C([0,1], R^dy) | minimum width for UAP: width d_y | Helped |
| Restrict network width below max(d_x,d_y) | Networks with any finite set of activations · L^p(K, R^dy) and C(K, R^dy) | universal approximation: w < max(d_x,d_y) | Hurt |
| Use width-one leaky-ReLU alone in the one-dimensional input and output case | L^p universal approximation · L^p(K, R), d_x=1 | universal approximation: w_min = max(d_x, d_y,2) | Hurt |
| Use continuous monotone activations at width d_x | C universal approximation · C(K, R^dy) | minimum width for UAP: at least width d_x+1 | Hurt |
Closest papers by meaning
- Minimum width for universal approximation using ReLU networks on compact domain (ICLR 2024 · similarity 0.94)
- ReLU Network with Width $d+\mathcal{O}(1)$ Can Achieve Optimal Approximation Rate (ICML 2024 · similarity 0.92)
- Minimum Width for Deep, Narrow MLP: A Diffeomorphism Approach (NeurIPS 2025 · similarity 0.91)
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- Characterizing ResNet's Universal Approximation Capability (ICML 2024 · similarity 0.88)
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