Research map / Learning theory and algorithms / Sample complexity
Why Deep Neural Networks for Function Approximation?
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase depth to Θ(log(1/ε)) instead of restricting it to o(log(1/ε)) | ReLU/BSU networks approximating sufficiently smooth univariate functions · Univariate function approximation on [0,1] | network size for ε-approximation: Ω(poly(1/ε)) neurons -> polylog(1/ε) neurons | Helped |
| Use a deep architecture with Θ(log(1/ε)) layers | ReLU/BSU networks approximating differentiable strongly convex functions · Strongly convex function approximation | minimum network size | Helped |
| Use depth growing with polynomial degree rather than a three-layer network | Networks approximating univariate polynomials · Univariate polynomial approximation | network size growth with degree: exponentially with respect to p -> p log p | Helped |
| Use a deep network rather than a three-layer network | Networks approximating multivariate polynomials · Multivariate polynomial approximation | network size growth with degree at fixed input dimension: O(exp(p)) -> O(poly(p)) | Helped |
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