Research map / Learning theory and algorithms / Kernels and regression theory
Tuning Frequency Bias in Neural Network Training with Nonuniform Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace squared L² loss with squared H^s loss, increasing s above 2 | 2-layer ReLU NN · S¹ trigonometric polynomial | frequency loss | Helped |
| Use squared H^s loss with s > 2 rather than the L²-based loss | 2-layer ReLU NN · S¹ trigonometric polynomial | frequency learning order | Mixed |
| Use quadrature-weighted L² loss instead of the standard mean-squared loss | 2-layer ReLU NN · S¹ trigonometric polynomial | frequency biasing | Helped |
| Use squared H^s loss with s = 2.5 instead of s = 0 | 2-layer ReLU NN · S² spherical harmonics | frequency learning order | Helped |
| Set the Sobolev exponent to s = -1 rather than s = 0 (ablation) | 2-layer ReLU NN · S² spherical harmonics | low-frequency biasing | Helped |
| Use squared H^s loss with s < 0 | autoencoder · MNIST denoising with high-frequency noise | denoising quality | Helped |
| Use squared H^s loss with s > 0 | autoencoder · MNIST denoising with low-frequency noise | deblurring quality | Helped |
| Set the Sobolev exponent to s = -1 (ablation) | 2-layer ReLU NN · S¹ trigonometric polynomial | frequency learning order | Hurt |
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