Research map / Learning theory and algorithms / Sample complexity
A closer look at the approximation capabilities of neural networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a continuous non-polynomial activation | One-hidden-layer networks · Continuous functions on compact X | hidden units sufficient: N ∈ O(ε^{-n}) | Helped |
| Use a single hidden layer with \binom{n+d}{d} units | Approximation of degree-at-most-d polynomials · Polynomial functions on compact X | uniform approximation: \binom{n+d}{d} | Helped |
| Restrict output-layer non-bias weights to |w| < δ | One-hidden-layer networks · Continuous functions on compact X | uniform approximation: |w| < δ | No clear effect |
| Require first-layer non-bias weights to have magnitude above λ | One-hidden-layer networks · Continuous functions on compact X | uniform approximation: |w|>λ | No clear effect |
| Fix first-layer non-bias weights to random draws from a suitable range | One-hidden-layer networks with trainable biases and output weights · Continuous functions on compact X | probability of uniform approximation: with probability 1 | Helped |
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