Research map / Optimization / Implicit bias and generalization
Frequency Bias in Neural Networks for Input of Non-Uniform Density
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train on a non-uniform rather than uniform input density | NTK-modeled networks learning a harmonic target · S^1, piecewise-constant density | iterations to convergence: O(κ²/p*) | Mixed |
| Increase the target harmonic frequency | Two-layer NTK · S^1, non-uniform density | iterations to convergence: O(κ²/p*) | Hurt |
| Increase local training-data density | Two-layer network · S^1, density ratio 1:2:4 | regional convergence time: 1:1.96:3.89 | Helped |
| Use a deep rather than shallow fully connected network | NTK-modeled networks · Uniform data, low and middle frequencies | iterations to convergence | Helped |
| Increase harmonic frequency | Deep FC network · S^1, uniform density | iterations to convergence: O(κ^2) | Hurt |
| Increase harmonic frequency | Deep FC network · S^2, uniform density | iterations to convergence: O(κ^3) | Hurt |
| Train with non-uniform instead of uniform density | Deep FC NTK · Non-uniform density on the hypersphere | iterations to convergence: O(κ^d/p*) | Hurt |
| Use two-layer instead of deep FC networks | NTK-modeled networks · Uniform data, low and middle frequencies | iterations to convergence | Hurt |
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