Research map / Architectures and efficiency / RNNs and normalization
Size-Noise Tradeoffs in Generative Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use iterated tent maps to make the generator output space-filling | ReLU generator mapping lower-dimensional uniform noise to higher-dimensional uniform noise · Uniform [0,1] to uniform [0,1]^d | Wasserstein distance: W(f # μ, ν) ≤ √d ⌊(N - dL)/L⌋^(-⌊L/(d-1)⌋) | Helped |
| Parallelize tent-map constructions across input dimensions | ReLU generator mapping uniform noise from n dimensions to d dimensions · Uniform [0,1]^n to uniform [0,1]^d | Wasserstein distance: W(f # μ, ν) ≤ √d ⌊(N - dL)/(nL)⌋^(-⌊L/⌈(d-n)/n⌉⌋) | Helped |
| Increase network node count and depth in the tent-map construction | ReLU generator mapping lower-dimensional uniform noise to higher-dimensional uniform noise · Uniform [0,1]^n to uniform [0,1]^d | Wasserstein distance: Error exponentially decays with the number of layers, and polynomially decays with the number of nodes in the network. | Helped |
| Approximate the normal CDF with a ReLU network | Generative network with univariate normal noise · Standard normal to uniform [0,1] | Wasserstein distance: ε | Helped |
| Approximate the inverse normal CDF using function approximation and binary search | Generative network with univariate uniform noise · Uniform [0,1] to standard normal | Wasserstein distance: ε | Helped |
| Use a normalized sum of additional uniform inputs | Linear generator mapping uniform noise to a univariate output · Uniform noise to standard normal | Wasserstein distance: O(1/√n) | Helped |
| Use higher-dimensional input noise rather than a single uniform input | Generator mapping noise to a univariate normal target · Uniform noise to standard normal | Wasserstein distance: O(1/√n) | Helped |
| Approximate the Box-Muller transform with a ReLU network | Generator using two-dimensional uniform noise · Uniform [0,1]^2 to two independent standard normals | Approximation error: ε | Helped |
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