Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Intriguing Equivalence Structures of the Embedding Space of Vision Transformers

Shaeke Salman, Md Montasir Bin Shams, Xiuwen Liu

TL;DR

This work analyzes the embedding space of vision transformers by introducing an embedding-matching procedure to probe equivalence classes and local geometry. It reveals that embeddings reside in large piecewise linear subspaces where inputs share representations, alongside local normal directions where small input changes yield large representation changes, as quantified by Jacobian spectra and local Lipschitz constants. The findings demonstrate that semantically related inputs can map to very different embeddings while visually different inputs can map to nearly identical embeddings, implying limited semantic generalization and vulnerability to alignment-based perturbations. The framework is model- and dataset-agnostic, offering a lens to assess robustness and generalization beyond downstream classifiers and suggesting potential mitigations via alignment-sensitive design and Lipschitz-aware training. Overall, it highlights fundamental limitations in current foundation models’ embedding spaces and provides a systematic approach to characterize and potentially improve their reliability in real-world applications.

Abstract

Pre-trained large foundation models play a central role in the recent surge of artificial intelligence, resulting in fine-tuned models with remarkable abilities when measured on benchmark datasets, standard exams, and applications. Due to their inherent complexity, these models are not well understood. While small adversarial inputs to such models are well known, the structures of the representation space are not well characterized despite their fundamental importance. In this paper, using the vision transformers as an example due to the continuous nature of their input space, we show via analyses and systematic experiments that the representation space consists of large piecewise linear subspaces where there exist very different inputs sharing the same representations, and at the same time, local normal spaces where there are visually indistinguishable inputs having very different representations. The empirical results are further verified using the local directional estimations of the Lipschitz constants of the underlying models. Consequently, the resulting representations change the results of downstream models, and such models are subject to overgeneralization and with limited semantically meaningful generalization capability.

Intriguing Equivalence Structures of the Embedding Space of Vision Transformers

TL;DR

This work analyzes the embedding space of vision transformers by introducing an embedding-matching procedure to probe equivalence classes and local geometry. It reveals that embeddings reside in large piecewise linear subspaces where inputs share representations, alongside local normal directions where small input changes yield large representation changes, as quantified by Jacobian spectra and local Lipschitz constants. The findings demonstrate that semantically related inputs can map to very different embeddings while visually different inputs can map to nearly identical embeddings, implying limited semantic generalization and vulnerability to alignment-based perturbations. The framework is model- and dataset-agnostic, offering a lens to assess robustness and generalization beyond downstream classifiers and suggesting potential mitigations via alignment-sensitive design and Lipschitz-aware training. Overall, it highlights fundamental limitations in current foundation models’ embedding spaces and provides a systematic approach to characterize and potentially improve their reliability in real-world applications.

Abstract

Pre-trained large foundation models play a central role in the recent surge of artificial intelligence, resulting in fine-tuned models with remarkable abilities when measured on benchmark datasets, standard exams, and applications. Due to their inherent complexity, these models are not well understood. While small adversarial inputs to such models are well known, the structures of the representation space are not well characterized despite their fundamental importance. In this paper, using the vision transformers as an example due to the continuous nature of their input space, we show via analyses and systematic experiments that the representation space consists of large piecewise linear subspaces where there exist very different inputs sharing the same representations, and at the same time, local normal spaces where there are visually indistinguishable inputs having very different representations. The empirical results are further verified using the local directional estimations of the Lipschitz constants of the underlying models. Consequently, the resulting representations change the results of downstream models, and such models are subject to overgeneralization and with limited semantically meaningful generalization capability.
Paper Structure (15 sections, 7 equations, 20 figures)

This paper contains 15 sections, 7 equations, 20 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Proposed Framework
  5. A Simple and Effective Procedure
  6. Local Algebraic and Geometric Structures
  7. Manifold Structures of the Embedding Space and Their Implications
  8. Experiments
  9. Datasets and Settings
  10. Experimental Results
  11. Discussion
  12. Conclusion
  13. Appendix
  14. More on Vision Transformers
  15. Additional Results

Figures (20)

  • Figure 1: Typical examples from ImageNet obtained using the proposed framework. Three pairs of visually indistinguishable images (a and e, b and f, c and g) have different representations from each other as shown in their low-dimensional projections. In contrast, very similar representations are seen for the images in (e), (f), and (c), despite their substantial semantic differences; similar goes with images in (a) and (g). Note that the arrow in the title ($original \rightarrow target$) signifies a derived image from the original one by aligning the embedding of the original image with the target image using our method. The matrices (d) and (h) show the classification outcomes from the multimodal ImageBind pre-trained model used directly with no modifications.
  • Figure 2: Pixel differences between the two images in each of the three pairs in Fig. \ref{['fig:overall']}; they are multiplied by 50 for visualization.
  • Figure 3: Local structures of the embedding space. (top) The singular values of the Jacobian Matrix for Fig. \ref{['fig:overall']}(a); (bottom) The estimated local directional Lipschitz constant values along the directions given by the right singular vectors, which are consistent with the singular values.
  • Figure 4: The distribution of the estimated local directional Lipschitz constant values along the directions given by random Gaussian vectors (top left), random Gaussian vectors in the null space of singular vectors (top right), and the gradient optimization procedure (bottom).
  • Figure 5: The evolution of loss while matching a target embedding. (left) the loss w.r.t. steps. (right) the cosine similarity between the embeddings of the new input and the target w.r.t. the steps, along with the average pixel value difference between the new input and the original image.
  • ...and 15 more figures