用高斯马尔可夫场建模组件间关系，提升多组件生成的结构一致性。
Multi-Component VAE with Gaussian Markov Random Field
- 将高斯马尔可夫场嵌入先验与后验分布，显式建模组件间依赖关系。
- 在合成数据集上达到当前最优性能，真实数据集上显著提升结构连贯性。
- 适合工业装配、多模态成像等需精确组件协同建模的应用场景。
具有复杂依赖关系的多组件数据集（如工业装配或多模态影像）对现有生成建模技术构成挑战。现有多组件变分自编码器通常采用简化的聚合策略，忽略关键细节，从而损害生成组件间的结构连贯性。为弥补这一不足，我们提出高斯马可夫随机场多组件变分自编码器（GMRF MCVAE），将高斯马尔可夫场嵌入先验与后验分布中，显式建模跨组件关系，实现更丰富的表征与复杂交互的忠实再现。实证表明，该模型在专门设计用于评估组件复杂关系的合成Copula数据集上达到当前最优性能，在PolyMNIST基准上表现竞争力，并在真实世界BIKED数据集上显著提升结构连贯性。结果表明，GMRF MCVAE特别适用于需要鲁棒且真实的多组件协同建模的实际应用。
原文摘要 · Abstract (English)
Multi-component datasets with intricate dependencies, like industrial assemblies or multi-modal imaging, challenge current generative modeling techniques. Existing Multi-component Variational AutoEncoders typically rely on simplified aggregation strategies, neglecting critical nuances and consequently compromising structural coherence across generated components. To explicitly address this gap, we introduce the Gaussian Markov Random Field Multi-Component Variational AutoEncoder , a novel generative framework embedding Gaussian Markov Random Fields into both prior and posterior distributions. This design choice explicitly models cross-component relationships, enabling richer representation and faithful reproduction of complex interactions. Empirically, our GMRF MCVAE achieves state-of-the-art performance on a synthetic Copula dataset specifically constructed to evaluate intricate component relationships, demonstrates competitive results on the PolyMNIST benchmark, and significantly enhances structural coherence on the real-world BIKED dataset. Our results indicate that the GMRF MCVAE is especially suited for practical applications demanding robust and realistic modeling of multi-component coherence
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