{"paper":{"title":"Convergence and Sample Complexity of SGD in GANs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Christos Tzamos, Sihan Liu, Vasilis Kontonis","submitted_at":"2020-12-01T18:50:38Z","abstract_excerpt":"We provide theoretical convergence guarantees on training Generative Adversarial Networks (GANs) via SGD. We consider learning a target distribution modeled by a 1-layer Generator network with a non-linear activation function $\\phi(\\cdot)$ parametrized by a $d \\times d$ weight matrix $\\mathbf W_*$, i.e., $f_*(\\mathbf x) = \\phi(\\mathbf W_* \\mathbf x)$.\n  Our main result is that by training the Generator together with a Discriminator according to the Stochastic Gradient Descent-Ascent iteration proposed by Goodfellow et al. yields a Generator distribution that approaches the target distribution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.00732","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.00732/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}