arXiv：cs.LG（机器学习，全量分类）· Achleshwar Luthra, Lucas Bryant, Tracy Zhu, Tomer Galanti·· 5 小时前AI 评分35
哪些任务能在自监督学习中幸存？——语义可恢复性的谱刻画
Which Tasks Survive Self-Supervised Learning?
AI 导读
研究提出"语义可恢复性"概念，定义为任务后验分数被表示函数空间捕获的程度，用于回答同实例自监督学习（SSL）究竟保留哪些下游任务信息。对中心化白化表示，可恢复性精确决定方向性 CDNV、控制少样本最近质心分类，并给出闭式谱刻画：任务后验落在所选谱子空间内即被保留。在合成与真实数据集、多种 SSL 方法上验证了可恢复性、方向几何、谱结构与少样本迁移之间的关系。
正文
Abstract: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.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2609.38393 [cs.LG] |
| (or arXiv:2609.38393v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.38393 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Achleshwar Luthra [view email]
[v1]
Tue, 29 Sep 2026 18:51:03 UTC (408 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org