{"ID":2850135,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22824","arxiv_id":"2510.22824","title":"Logical GANs: Adversarial Learning through Ehrenfeucht Fraisse Games","abstract":"GANs promise indistinguishability, logic explains it. We put the two on a budget: a discriminator that can only ``see'' up to a logical depth $k$, and a generator that must look correct to that bounded observer. \\textbf{LOGAN} (LOGical GANs) casts the discriminator as a depth-$k$ Ehrenfeucht--Fraïssé (EF) \\emph{Opponent} that searches for small, legible faults (odd cycles, nonplanar crossings, directed bridges), while the generator plays \\emph{Builder}, producing samples that admit a $k$-round matching to a target theory $T$. We ship a minimal toolkit -- an EF-probe simulator and MSO-style graph checkers -- and four experiments including real neural GAN training with PyTorch. Beyond verification, we score samples with a \\emph{logical loss} that mixes budgeted EF round-resilience with cheap certificate terms, enabling a practical curriculum on depth. Framework validation demonstrates $92\\%$--$98\\%$ property satisfaction via simulation (Exp.~3), while real neural GAN training achieves $5\\%$--$14\\%$ improvements on challenging properties and $98\\%$ satisfaction on connectivity (matching simulation) through adversarial learning (Exp.~4). LOGAN is a compact, reproducible path toward logic-bounded generation with interpretable failures, proven effectiveness (both simulated and real training), and dials for control.","short_abstract":"GANs promise indistinguishability, logic explains it. We put the two on a budget: a discriminator that can only ``see'' up to a logical depth $k$, and a generator that must look correct to that bounded observer. \\textbf{LOGAN} (LOGical GANs) casts the discriminator as a depth-$k$ Ehrenfeucht--Fraïssé (EF) \\emph{Opponen...","url_abs":"https://arxiv.org/abs/2510.22824","url_pdf":"https://arxiv.org/pdf/2510.22824v1","authors":"[\"Mirco A. Mannucci\"]","published":"2025-10-26T20:34:00Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.LO\",\"math.LO\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}