# Breaking the Geometric Bottleneck: Contrastive Expansion in Asymmetric Cross-Modal Distillation

arXiv: https://arxiv.org/abs/2603.06698 · HTML: https://mlsanity.com/paper/2603.06698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 5 of its 7 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)

## Abstract (arXiv)

Knowledge distillation between asymmetric architectures often induces severe geometric constraints on the learned representation space. We investigate dimensional collapse when distilling global Vision Transformers into capacity-constrained, local-receptive-field CNNs (0.5M-8.0M parameters). Using strictly centered SVD and Shannon Entropy Effective Rank, we confirm capacity-agnostic collapse under cosine distillation: a CLIP ViT-B/32 Teacher exhibits Effective Rank 88.68 on CIFAR-10, while all cosine-distilled students collapse to ~17 regardless of parameter count. An auxiliary InfoNCE objective expands this to ~41 dimensions. Critically, we ask whether this expansion is functionally useful. Multi-seed linear-probe evaluation shows InfoNCE expansion degrades downstream accuracy by 15-18 points relative to the collapsed baseline, despite more than doubling Effective Rank. A class-structure decomposition traces this to signal dilution: InfoNCE's class-blind uniformity pressure weakens class-discriminative structure in the original dimensions while adding only weakly relevant structure elsewhere. We then test a label-aware alternative, Supervised Contrastive distillation. On CIFAR-100, where we swept student capacity directly, its Effective Rank is invariant to capacity; on CIFAR-10, at a single tested width, it settles to a lower rank while matching baseline accuracy. Sweeping temperature instead of capacity, rank and downstream accuracy increase together monotonically. These results show Effective Rank alone is not a reliable proxy for representation quality: whether expansion helps or harms downstream performance depends on whether the driving objective is label-aware, not the magnitude of expansion itself.