From Low-Rank Features to Encoding Mismatch: Rethinking Feature Distillation in Vision Transformers

Feature-map knowledge distillation (KD) is highly effective for convolutional networks but often fails for Vision Transformers (ViTs). To understand this failure and guide method design, we conduct a two-view representation analysis of ViTs. First, a layer-wise Singular Value Decomposition (SVD) of full feature matrices shows that final-layer representations are globally low-rank: for CaiT-S24, only $121/61/34/14$ dimensions suffice to capture $99\%/95\%/90\%/80\%$ of the energy. In principle, this suggests that a compact student plus a simple linear projector should be enough for feature alignment, contradicting the weak empirical performance of standard feature KD. To resolve this paradox, we introduce a token-level Spectral Energy Pattern (SEP) analysis that measures how each token uses channel capacity. SEP reveals that, despite the global low-rank structure, individual tokens distribute energy over most channels, forming a high-bandwidth encoding pattern. This results in an encoding mismatch between wide teachers and narrow students. Motivated by this insight, we propose two minimal, mismatch-driven strategies: (1) post-hoc feature lifting with a lightweight projector retained during inference, or (2) native width alignment that widens only the student's last block to the teacher's width. On ImageNet-1K, these strategies reactivate simple feature-map distillation in ViTs, raising DeiT-Tiny accuracy from $74.86\%$ to $77.53\%$ and $78.23\%$ when distilling from CaiT-S24, while also improving standalone students trained without any teacher. Our analysis thus explains why ViT feature distillation fails and shows how exploiting low-rank structure yields effective, interpretable remedies and concrete design guidance for compact ViTs.

Distillation Dynamics: Towards Understanding Feature-Based Distillation in Vision Transformers

While feature-based knowledge distillation has proven highly effective for compressing CNNs, these techniques unexpectedly fail when applied to Vision Transformers (ViTs), often performing worse than simple logit-based distillation. We provide the first comprehensive analysis of this phenomenon through a novel analytical framework termed as "distillation dynamics", combining frequency spectrum analysis, information entropy metrics, and activation magnitude tracking. Our investigation reveals that ViTs exhibit a distinctive U-shaped information processing pattern: initial compression followed by expansion. We identify the root cause of negative transfer in feature distillation: a fundamental representational paradigm mismatch between teacher and student models. Through frequency-domain analysis, we show that teacher models employ distributed, high-dimensional encoding strategies in later layers that smaller student models cannot replicate due to limited channel capacity. This mismatch causes late-layer feature alignment to actively harm student performance. Our findings reveal that successful knowledge transfer in ViTs requires moving beyond naive feature mimicry to methods that respect these fundamental representational constraints, providing essential theoretical guidance for designing effective ViTs compression strategies. All source code and experimental logs are provided at https://github.com/thy960112/Distillation-Dynamics.

SpectralKD: Understanding and Optimizing Vision Transformer Distillation through Spectral Analysis

Knowledge distillation effectively reduces model complexity while improving performance, yet the underlying knowledge transfer mechanisms remain poorly understood. We propose novel spectral analysis methods and guidelines to optimize distillation, making the knowledge transfer process more interpretable. Our analysis reveals that CaiT models concentrate information in their first and last few layers, informing optimal layer selection for feature map distillation. Surprisingly, we discover that Swin Transformer and CaiT exhibit similar spectral encoding patterns despite their architectural differences, enhancing our understanding of transformer architectures and leading to improved feature map alignment strategies. Based on these insights, we introduce a simple yet effective spectral alignment method named SpectralKD. Experimental results demonstrate that following our guidelines enables SpectralKD to achieve state-of-the-art performance (DeiT-Tiny: $+5.2\%$, Swin-Tiny: $+1.4\%$ in ImageNet-1k Top-1 accuracy). Furthermore, through spectral analysis of student models trained with and without distillation, we show that distilled models mirror spectral patterns of their teachers, providing a new lens for interpreting knowledge distillation dynamics. Our code, pre-trained models, and experimental logs will be made publicly available.