Nested Inductive Bias Framework for SPD Manifold Learning
在几何深度学习领域，嵌套归纳偏置框架利用双阶段微分同构组成，将非欧几里得目标几何形式地拉回至 SPD 流形。该框架构建了同时尊重矩阵约束与数据潜在关系几何的曲率对齐黎曼分类器。实证评估表明，除非度量曲率与内在数据分布对齐，深度流形网络的类别可分性会出现退化；针对标准向量化架构，提出了有理共形度量（RCM），旨在通过限制表示空间以建立对异常值的最佳几何鲁棒性。
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The latest research proposes a nested inductive bias framework aimed at improving machine learning performance on SPD matrices. This framework enhances the model’s generalization ability and convergence speed on SPD manifold data by constructing multi-level inductive bias structures. The results have been published in the arXiv cs.LG preprint repository.
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