C{\AE}NL: Collapse-Based Active Neural Learning with Objective-Aligned Representation Control

Abstract

Active learning changes the representations used to acquire subsequent labels. We study this interaction through Collapse-Based Active Neural Learning (C{\AE}NL), which separates acquisition, Dynamic Collapse Regularization (DCR), and its coefficient policy. DCR penalizes a normalized within-class to between-class scatter residual above a frozen reference, with a separate class-separation safeguard. Fixed, scheduled, deterministic-feedback, and learned-feedback policies apply this objective. The analysis establishes scatter invariances, conditional local descent, and coefficient bounds, and shows why clean geometry alone cannot guarantee input robustness. Six-seed classification comparisons are complemented by a 104-run study with separate control selection and ten-seed evaluations on each of two backbones. At 60% annotations on ImageNet-100, entropy acquisition with DCR and MACC-Lite reaches 73.420 +/- 0.512% accuracy on ResNet-50 and 73.086 +/- 0.397% on ResNet-18 (mean +/- seed SD), exceeding entropy alone by 1.742 and 1.834 percentage points. Both gains survive Holm correction under paired-t and exact sign-flip tests, with unchanged feedback settings across backbones. Independently tuned constants attain slightly higher mean accuracy; the paired comparisons establish neither adaptive superiority nor equivalence. Separate six-seed spectral studies yield a small fixed-regularization C4 loss reduction, worse CIFAR-10 diffusion FID, and inconclusive AudioCaps captioning effects. Earlier classification studies find near-zero AutoAttack accuracy at L-infinity radius 8/255 and no added benefit from learned control. The results support the evaluated combined classification treatment and identify the task dependence of geometry-informed regularization.