GEPC: 组等变后验一致性用于扩散模型中的分布外检测
GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models
AI总结：
GEPC通过测量分数在有限群下的变换一致性，实现扩散模型中分布外检测的后验一致性，提供轻量级且可解释的检测方法。
摘要：
扩散模型学习了一个时间索引的分数场s_θ(x_t,t)，通常继承了从分布内（ID）数据和卷积主干中近似的等变性（翻转、旋转、圆周位移）。大多数基于扩散的分布外（OOD）检测器利用分数幅度或局部几何（能量、曲率、协方差谱）并 largely 忽略等变性。我们引入了组等变后验一致性（GEPC），一种无需训练的探针，测量学习的分数在有限群G下变换的一致性，即使分数幅度保持不变，也能检测到等变性破坏。在总体层面，我们提出了理想的GEPC残差，它在G上平均等变残差函数，并在温和假设下推导出ID上界和OOD下界。GEPC只需分数评估，产生可解释的等变性破坏地图。在分布外图像基准数据集上，我们显示GEPC在与最近的扩散基线相比时实现了竞争或改进的AUROC，同时保持计算轻量。在高分辨率合成雷达图像中，其中OOD对应于杂波中的目标或异常，GEPC产生了强的目标-背景分离和可解释的等变性破坏地图。代码可在https://github.com/RouzAY/gepc-diffusion/上获得。
英文摘要：
Diffusion models learn a time-indexed score field $\mathbf{s}_θ(\mathbf{x}_t,t)$ that often inherits approximate equivariances (flips, rotations, circular shifts) from in-distribution (ID) data and convolutional backbones. Most diffusion-based out-of-distribution (OOD) detectors exploit score magnitude or local geometry (energies, curvature, covariance spectra) and largely ignore equivariances. We introduce Group-Equivariant Posterior Consistency (GEPC), a training-free probe that measures how consistently the learned score transforms under a finite group $\mathcal{G}$, detecting equivariance breaking even when score magnitude remains unchanged. At the population level, we propose the ideal GEPC residual, which averages an equivariance-residual functional over $\mathcal{G}$, and we derive ID upper bounds and OOD lower bounds under mild assumptions. GEPC requires only score evaluations and produces interpretable equivariance-breaking maps. On OOD image benchmark datasets, we show that GEPC achieves competitive or improved AUROC compared to recent diffusion-based baselines while remaining computationally lightweight. On high-resolution synthetic aperture radar imagery where OOD corresponds to targets or anomalies in clutter, GEPC yields strong target-background separation and visually interpretable equivariance-breaking maps. Code is available at https://github.com/RouzAY/gepc-diffusion/.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
