Research map / Optimization / Implicit bias and generalization
Efficient Representation of Low-Dimensional Manifolds using Deep Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Represent the Swiss Roll with a hand-constructed ReLU network that divides it into monotonic chains and piecewise-linear segments | Swiss Roll · Swiss Roll | mean relative embedding error: 0.98 | Helped |
| Represent the Swiss Roll with a hand-constructed ReLU network that divides it into monotonic chains and piecewise-linear segments | Swiss Roll · Swiss Roll | maximum relative embedding error: does not exceed 2.5 | Mixed |
| Choose separating hyperplanes whose normals are not nearly orthogonal to the next segment | Monotonic-chain embedding of nearby points · Monotonic chains with bounded total curvature | embedding error: ||E(p0+δ)|| ≤ e^{cT} ||δ|| | Helped |
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