Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANs

Authors: Sitan Chen, Jerry Li, Yuanzhi Li, Raghu Meka

ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental To complement these theoretical results, we also perform some empirical validations of our findings (see Section 4). Our theorem is constructive; that is, given a local PRG, we give an explicit generator which satisfies the theorem. We instantiate this construction with Goldreich s PRG with the Tri-Sum-And (TSA) predicate (Goldreich, 2011), which is an explicit function which is believed to satisfy the local PRG property. We then demonstrate that a neural network discriminator trained via standard methods empirically cannot distinguish between the output of this generator and the uniform distribution. While of course we cannot guarantee that we achieve the truly optimal discriminator using these methods, this still demonstrates that our construction leads to a function which does appear to be hard to distinguish in practice. Section 4: EXPERIMENTAL RESULTS
Researcher Affiliation Collaboration Sitan Chen UC Berkeley Jerry Li Microsoft Research Yuanzhi Li CMU Raghu Meka UCLA
Pseudocode No The paper does not contain any pseudocode or algorithm blocks.
Open Source Code No The paper states: 'Our theorem is constructive; that is, given a local PRG, we give an explicit generator which satisfies the theorem.' However, it does not explicitly state that the code for this construction or their experiments is open-sourced or provide a link.
Open Datasets Yes The target distribution D is the uniform distribution U200 over { 1}200. As we prove in Lemma A.13, Ud is sufficiently diverse that W1(G(Um), Ud) Ω(1).
Dataset Splits No The paper does not provide specific training, validation, or test dataset splits. It only mentions 'batch-size 128'.
Hardware Specification No The paper does not specify any hardware used for the experiments (e.g., CPU, GPU models, memory, or cloud instances).
Software Dependencies No The paper mentions 'Adam optimizer' and 'DCGAN training objective', but does not provide specific version numbers for any software libraries or dependencies.
Experiment Setup Yes We trained four different discriminators given respectively by 1, 2, 3, 4 hidden-layer Re LU networks, where each hidden layer is fully connected with dimensions 200 200, to discriminate the output of the generator G(Um) from the target distribution Ud. We used the Adam optimizer with step size 0.001 over the DCGAN training objective, with batch-size 128.