发表机构
University of Southern California; AWS AI（南加州大学; AWS人工智能）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一种基于多重分形阶梯图和神经逆算子的生成图模型，在函数空间统一机制可解释性与摊销推理，实现零样本迁移和单观测网络推断，并提升脑状态追踪敏感性。
AI 中文摘要
生成图模型对于理解和模拟复杂网络至关重要。然而，现有方法各有互补的优势和局限性。机制模型具有可解释性，但依赖于特定实例的估计方法。另一方面，深度生成模型以牺牲可解释性为代价提供摊销推理，并且很大程度上局限于训练期间见过的图规模。科学应用促使需要一个保留两种范式优势的框架。我们通过在函数空间中制定生成模型和参数恢复来弥合这一差距。多重分形阶梯图扩展了标准阶梯图，采用递归构造，紧凑地参数化复杂网络。该公式允许使用神经逆算子恢复其参数，从而能够对未见过的图规模进行推理。我们仅基于合成的多重分形阶梯图实现训练我们的模型，并针对两种范式进行评估。与在经验网络上预训练的图基础模型相比，我们的方法在零样本图生成基准的四个指标中的三个上取得了最佳平均性能，表明该模型可迁移到现实世界的图。我们还将该方法应用于单观测网络，这是深度模型通常无法访问的领域，因为深度模型需要训练语料库，而我们的方法在此领域的表现与针对每个图进行优化的特定实例方法相当。在多受试者脑电图案例研究中，推断的参数比传统网络统计更敏感地追踪脑状态的可逆变化。综合这些结果表明，机制可解释性和摊销推理可以在生成图模型中有效统一，以增强我们对复杂网络的理解。
英文摘要
Generative graph models are central to understanding and simulating complex networks. However, existing approaches have complementary strengths and limitations. Mechanistic models offer interpretability but rely on instance-specific estimation methods. Deep generative models, on the other hand, offer amortized inference at the cost of interpretability and are largely limited to graph sizes seen during training. Scientific applications motivate a framework that retains the strengths of both paradigms. We bridge them by formulating both the generative model and parameter recovery in function space. A multifractal step graphon extends standard step graphons with a recursive construction that compactly parameterizes complex networks. This formulation admits a neural inverse operator to recover its parameters, enabling inference on unseen graph sizes. We evaluate our model, trained only on synthetic multifractal step graphon realizations, against both paradigms. Against a graph foundation model pretrained on empirical networks, our method achieves the best average performance on three of four metrics in a zero-shot graph-generation benchmark, indicating that the model transfers to real-world graphs. We also apply our method to single-observation networks, a regime largely inaccessible to deep models that require training corpora, where it performs comparably to an instance-specific method that optimizes on each graph. In a multi-subject EEG case study, the inferred parameters track a reversible change in brain state more sensitively than traditional network statistics. Together, these results indicate that mechanistic interpretability and amortized inference can be effectively unified in a generative graph model to enhance our understanding of complex networks.
