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On the Universal Approximability and Complexity Bounds of Quantized ReLU Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Restrict ReLU network weights to two distinct values | ReLU networks approximating functions in F_{d,n} · Functions in F_{d,n} | approximation error: arbitrary accuracy | Helped |
| Use quantized rather than unquantized ReLU weights | ReLU networks approximating functions in F_{d,n} · Same approximation error ε | number of weights overhead: \mathcal{O}(\log^5(1/\epsilon)) times | Hurt |
| Make network structure depend on the target function | Quantized ReLU approximation of F_{1,1} · Sobolev class F_{1,1} | number of weights: function-independent: \mathcal{O}\left(\lambda \log^{\frac{1}{\lambda-1}+1}\left(1/\epsilon\right)\left(1/\epsilon\right | Helped |
| Use linear quantization instead of nonlinear quantization | Function-dependent quantized ReLU approximation of F_{1,1} · Sobolev class F_{1,1} | number of weights: nonlinear: \mathcal{O}\left(\lambda\left(\log\log\left(1/\epsilon\right)\right)^{\frac{1}{\lambda-1}+1}+(1/\epsilon)\rig | Mixed |
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