用逻辑博弈约束生成对抗网络，让模型生成更符合规则的图数据。
Logical GANs: Adversarial Learning through Ehrenfeucht Fraisse Games
- 将判别器设为有限深度逻辑观察者，生成器需通过其检验
- 真实训练中关键属性满足率提升至98%，连通性达标率98%
- 适合需要可解释性与规则约束的图生成场景
GANs承诺不可区分性，逻辑提供解释。我们设定预算：判别器只能观测最多逻辑深度k，生成器必须对这种受限观察者显得正确。LOGAN（逻辑生成对抗网络）将判别器视为深度-k的埃伦费斯特-弗赖西（EF）对手，寻找小而明显的缺陷（奇数环、非平面交叉、有向桥），生成器则扮演建造者角色，产出能与目标理论T在k轮匹配的样本。我们提供最小工具包——一个EF探测模拟器和MSO风格图检查器，并开展四项实验，包括使用PyTorch的真实神经GAN训练。除验证外，我们用一种逻辑损失评分，结合预算内EF抗扰性与低成本证书项，实现深度控制的实用课程。框架验证显示，模拟实验中属性满足率达92%–98%（实验3）；真实神经GAN训练中，复杂属性改善5%–14%，连通性满足率达98%（与模拟一致）（实验4）。LOGAN是一条紧凑、可复现的逻辑约束生成路径，具备可解释失败分析、实证有效性及可控调节旋钮。
原文摘要 · Abstract (English)
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.
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