发表机构
Texas A&M University（得克萨斯A&M大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出语义可恢复性概念，从理论上阐明同实例自监督学习保留哪些下游任务信息，并揭示其与方向几何、谱结构及少样本迁移的定量关系。
AI 中文摘要
同实例自监督学习（SSL）通过强制同一底层实例的两个视图之间的一致性来学习表示。然而，仅凭这一原则并不能确定从学习到的表示中哪些下游任务仍然可以恢复。我们通过“语义可恢复性”来研究这个问题，将其定义为表示函数空间所捕获的任务后验分数的量。我们表明，对于中心化和白化的表示，可恢复性精确地决定了方向性类间距离归一化方差（CDNV），控制了少样本最近质心分类，并支配了任务相关语义方向的强度。总体线性探针和质心轴一致，多个恢复良好的任务趋近于因子化的质心几何结构。然后，我们分析了一个典型的两视图SSL目标，并表明其总体最优解跨越了相关联的两视图算子的主要跨视图稳定模式。这产生了语义可恢复性的闭式谱特征：下游任务被保留的程度取决于其后验位于所选谱子空间内。我们在多个SSL方法上对合成和真实数据集验证了这些预测，测试了可恢复性、方向几何、谱结构和少样本迁移之间的预测关系。总之，这些结果提供了关于同实例SSL中哪些信息得以保留以及保留的信息如何出现在下游几何和迁移中的任务级解释。
英文摘要
Same-instance self-supervised learning (SSL) learns representations by enforcing consistency across two views of the same underlying instance. This principle alone, however, does not determine which downstream tasks remain recoverable from the learned representation. We study this question through \emph{semantic recoverability}, defined as the amount of a task's posterior score captured by the represented function space. We show that, for centered and whitened representations, recoverability exactly determines directional class-distance-normalized variance (CDNV), controls few-shot nearest-centroid classification, and governs the strength of task-relevant semantic directions. The population linear probe and centroid axis coincide, and multiple well-recovered tasks approach a factorial centroid geometry. We then analyze a canonical two-view SSL objective and show that its population optimum spans the leading cross-view-stable modes of the associated two-view operator. This yields a closed-form spectral characterization of semantic recoverability: a downstream task is preserved to the extent that its posterior lies in the selected spectral subspace. We validate these predictions on synthetic and real datasets across several SSL methods, testing the predicted relationships among recoverability, directional geometry, spectral structure, and few-shot transfer. Together, these results give a task-level account of what information survives same-instance SSL and how the retained information appears in downstream geometry and transfer.
