MaDeL：用于生成建模的流形分解特征损失
MaDeL: Manifold-Decomposed Feature Losses for Generative Modeling
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中文总结 AI 辅助
针对生成模型各向同性损失混淆流形内外位移的问题，提出流形分解特征损失MaDeL，通过互补表示区分内在变异与流形外偏差，在多个基准上提升支持恢复并减少蛋白质骨架空间冲突。
中文摘要 AI 辅助
生成模型通常使用各向同性的目标函数进行训练，例如均方误差。然而，对于集中在低维流形附近的数据，此类损失将沿流形的位移（可能代表有效的变异）与远离流形的位移（会产生无效样本）混为一谈。这种不匹配在稀疏且高度受限的领域中尤其成问题，在这些领域中，环境空间回归可能鼓励流形外的插值。我们提出一个问题：生成目标能否直接根据数据区分流形平行变异与流形正交偏差，而无需显式估计流形。我们引入了一种流形分解特征损失（MaDeL），它从损坏的观测中学习互补的表示：一个表示被训练用于恢复干净样本，而另一个表示被训练用于恢复损坏。我们表明，在特征瓶颈下，它们的雅可比矩阵与切空间和法空间对齐，对于线性流形是精确的，对于光滑流形是局部的。这些表示共同定义了一个各向异性的目标函数，分别度量内在变异和流形外偏差。在合成、地球与气候科学以及扭转角基准测试中，MaDeL在单步采样下改善了支持恢复和平均角度$W_1$；在蛋白质骨架上，它在一步和几步采样预算下减少了空间冲突。
英文摘要
Generative models are often trained with isotropic objectives such as mean-squared error. For data concentrated near a low-dimensional manifold, however, such losses conflate displacement along the manifold, which may represent valid variation, with displacement away from it, which produces invalid samples. This mismatch is especially problematic in sparse, highly constrained domains, where ambient-space regression can encourage off-manifold interpolation. We ask whether a generative objective can distinguish manifold-parallel variation from manifold-orthogonal deviation directly from data, without explicitly estimating the manifold. We introduce a manifold-decomposed feature loss (MaDeL) that learns complementary representations from corrupted observations: one is trained to recover the clean sample, while the other is trained to recover the corruption. We show that, under a feature bottleneck, their Jacobians align with the tangent and normal spaces, exactly for linear manifolds and locally for smooth manifolds. Together, these representations define an anisotropic objective that separately measures intrinsic variation and off-manifold deviation. Across synthetic, Earth and climate science, and torsion-angle benchmarks, MaDeL improves support recovery and average angular $W_1$ under single-step sampling; on protein backbones, it reduces steric clashes across one- and few-step sampling budgets.
发表机构
- KAIST（韩国科学技术院）
- GIST（光州科学技术院）
机构由 AI 辅助整理，请以论文原文为准。
