Recent breakthroughs and rapid integration of generative models (GMs) have sparked interest in the problem of model attribution and their fingerprints. For instance, service providers need reliable methods of authenticating their models to protect their IP, while users and law enforcement seek to verify the source of generated content for accountability and trust. In addition, a growing threat of model collapse is arising, as more model-generated data are being fed back into sources (e.g., YouTube) that are often harvested for training ("regurgitative training"), heightening the need to differentiate synthetic from human data. Yet, a gap still exists in understanding generative models' fingerprints, we believe, stemming from the lack of a formal framework that can define, represent, and analyze the fingerprints in a principled way. To address this gap, we take a geometric approach and propose a new definition of artifact and fingerprint of GMs using Riemannian geometry, which allows us to leverage the rich theory of differential geometry. Our new definition generalizes previous work (Song et al., 2024) to non-Euclidean manifolds by learning Riemannian metrics from data and replacing the Euclidean distances and nearest-neighbor search with geodesic distances and kNN-based Riemannian center of mass. We apply our theory to a new gradient-based algorithm for computing the fingerprints in practice. Results show that it is more effective in distinguishing a large array of GMs, spanning across 4 different datasets in 2 different resolutions (64 by 64, 256 by 256), 27 model architectures, and 2 modalities (Vision, Vision-Language). Using our proposed definition significantly improves the performance on model attribution, as well as a generalization to unseen datasets, model types, and modalities, suggesting its practical efficacy.

翻译：近期生成模型的突破性进展及其快速普及，引发了关于模型归属识别及其指纹特征的研究兴趣。例如，服务提供商需要可靠的方法来认证其模型以保护知识产权，而用户和执法机构则希望验证生成内容的来源以确保可问责性与可信度。此外，随着更多模型生成数据被反馈至常被用于训练的数据源（如YouTube，形成“反刍式训练”），模型崩溃的威胁日益加剧，这强化了区分合成数据与人类数据的需求。然而，我们认为，当前对生成模型指纹的理解仍存在空白，这源于缺乏一个能够以原则性方式定义、表示和分析指纹的形式化框架。为填补这一空白，我们采用几何方法，利用黎曼几何提出了生成模型伪影与指纹的新定义，从而得以借助微分几何的丰富理论。我们的新定义通过从数据中学习黎曼度量，并以测地距离和基于kNN的黎曼质心替代欧氏距离与最近邻搜索，将先前工作（Song等人，2024）推广至非欧几里得流形。我们将该理论应用于一种新的基于梯度的算法，以实际计算指纹。实验结果表明，该方法在区分广泛类型的生成模型上更为有效，涵盖2种分辨率（64×64、256×256）下的4个不同数据集、27种模型架构以及2种模态（视觉、视觉-语言）。使用我们提出的定义显著提升了模型归属识别的性能，并能泛化至未见过的数据集、模型类型和模态，体现了其实用效能。