INTRINSIC DIMENSION DYNAMICS IN ACTIVE LEARNING: A GEOMETRIC DIAGNOSTIC OF ACQUISITION BEHAVIOR

Active learning reduces annotation cost by selectively querying data, yet existing evaluations rely almost exclusively on predictive performance, offering limited insight into how different acquisition strategies shape the labeled set. We study the behavior of active learning strategies through the lens of data geometry, using intrinsic dimensionality (ID) as a representation-level diagnostic. We analyze local and global intrinsic dimension statistics of samples selected by uncertainty-based (uncertainty, margin, DBAL), coverage-based (CoreSet, ProbCover), and random strategies across learning episodes, and we further conduct controlled ID-based acquisition schedules as a diagnostic stress test. To isolate acquisition effects from representation learning, we conduct the analysis in a fixed self-supervised. Across the settings we evaluate, uncertainty-based strategies tend to select samples from higher estimated intrinsic-dimensional regions, while coverage-based strategies tend to yield labeled sets with lower and more stable estimated global intrinsic dimension. Consistent with these trends, the ID-based schedules show that prioritizing low-ID samples early is substantially more effective than acquiring high-ID samples early. Overall, ID serves as a simple geometric diagnostic that complements accuracy-based evaluation.