发表机构
Adam Mickiewicz University in Poznań; IDEAS NCBR（波兹南亚当·密茨凯维奇大学; IDEAS NCBR）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出尺度分辨统计量，发现图像编码器特征响应随扰动增大呈平台-上升-峰值-衰减的“凸起”轮廓，该轮廓依赖训练数据与目标，标志学习塑造的表示几何。
AI 中文摘要
理解学习表示如何响应有限输入变化，对于刻画其敏感性、不变性和鲁棒性具有重要意义。然而，现有的几何分析主要局限于局部，仅描述无穷小扰动。我们引入了一种尺度分辨统计量，该统计量在扰动幅度增大时，将编码器测得的特征位移与其局部线性预测进行比较。在多种图像编码器中，我们发现了一个特征性的平台-上升-峰值-衰减轮廓，我们称之为“凸起”。该凸起在初始化时不存在，在标准训练早期出现，并且在随机标签或随机噪声输入下不会形成。其形状也随训练分布和鲁棒性目标而变化。这些结果确立了偏离局部几何作为编码器表示如何被学习塑造的一个标志。
英文摘要
Understanding how learned representations respond to finite input changes is important for characterizing their sensitivity, invariances, and robustness. Yet existing geometric analyses are predominantly local and describe only infinitesimal perturbations. We introduce a scale-resolved statistic that compares an encoder's measured feature displacement with its local linear prediction as the perturbation magnitude increases. Across diverse image encoders, we discover a characteristic plateau-rise-peak-decay profile, which we call the bump. The bump is absent at initialization, emerges early during standard training, and does not form under randomized labels or random-noise inputs. Its shape also varies with the training distribution and robustness objective. These results establish departures from local geometry as a signature of how encoder representations are shaped by learning.
CommentsExtended abstract, NeurIPS 2026 Workshop on Symmetry and Geometry in Neural Representations (NeurReps). 14 pages, 5 figures
