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Statistical Test for Attention Map in Vision Transformer

Tomohiro Shiraishi, Daiki Miwa, Teruyuki Katsuoka, Vo Nguyen Le Duy, Kouichi Taji, Ichiro Takeuchi

TL;DR

This work tackles the problem of interpreting Vision Transformer attentions as reliable evidence in high-stakes tasks by formulating a selective-inference-based statistical test. It develops a new computational approach to obtain selective $p$-values for attention regions, accounting for the data-driven selection process and providing a uniform null distribution for valid inference. The method combines a 1D conditional data-space reduction, adaptive grid search, and implementation strategies for differentiating ViT attention maps, and it demonstrates controlled false positive rates and improved power on synthetic data and brain-image diagnostics. The approach enables principled, quantitatively reliable interpretation of ViT decisions with potential impact on clinical and safety-critical deployments.

Abstract

The Vision Transformer (ViT) demonstrates exceptional performance in various computer vision tasks. Attention is crucial for ViT to capture complex wide-ranging relationships among image patches, allowing the model to weigh the importance of image patches and aiding our understanding of the decision-making process. However, when utilizing the attention of ViT as evidence in high-stakes decision-making tasks such as medical diagnostics, a challenge arises due to the potential of attention mechanisms erroneously focusing on irrelevant regions. In this study, we propose a statistical test for ViT's attentions, enabling us to use the attentions as reliable quantitative evidence indicators for ViT's decision-making with a rigorously controlled error rate. Using the framework called selective inference, we quantify the statistical significance of attentions in the form of p-values, which enables the theoretically grounded quantification of the false positive detection probability of attentions. We demonstrate the validity and the effectiveness of the proposed method through numerical experiments and applications to brain image diagnoses.

Statistical Test for Attention Map in Vision Transformer

TL;DR

This work tackles the problem of interpreting Vision Transformer attentions as reliable evidence in high-stakes tasks by formulating a selective-inference-based statistical test. It develops a new computational approach to obtain selective -values for attention regions, accounting for the data-driven selection process and providing a uniform null distribution for valid inference. The method combines a 1D conditional data-space reduction, adaptive grid search, and implementation strategies for differentiating ViT attention maps, and it demonstrates controlled false positive rates and improved power on synthetic data and brain-image diagnostics. The approach enables principled, quantitatively reliable interpretation of ViT decisions with potential impact on clinical and safety-critical deployments.

Abstract

The Vision Transformer (ViT) demonstrates exceptional performance in various computer vision tasks. Attention is crucial for ViT to capture complex wide-ranging relationships among image patches, allowing the model to weigh the importance of image patches and aiding our understanding of the decision-making process. However, when utilizing the attention of ViT as evidence in high-stakes decision-making tasks such as medical diagnostics, a challenge arises due to the potential of attention mechanisms erroneously focusing on irrelevant regions. In this study, we propose a statistical test for ViT's attentions, enabling us to use the attentions as reliable quantitative evidence indicators for ViT's decision-making with a rigorously controlled error rate. Using the framework called selective inference, we quantify the statistical significance of attentions in the form of p-values, which enables the theoretically grounded quantification of the false positive detection probability of attentions. We demonstrate the validity and the effectiveness of the proposed method through numerical experiments and applications to brain image diagnoses.
Paper Structure (36 sections, 3 theorems, 46 equations, 27 figures, 1 table, 1 algorithm)

This paper contains 36 sections, 3 theorems, 46 equations, 27 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Statistical Test for ViT's Attentions
  3. Notations.
  4. Statistical Inference.
  5. Conditional Distribution.
  6. Selective $p$-value.
  7. Computing Selective $p$-values
  8. Characterization of the Conditional Data Space.
  9. Reformulation of the Truncated Region.
  10. Selective $p$-value Computation by Adaptive Grid Search.
  11. Implementation Teqniques.
  12. Derivative of the Attention Map.
  13. Numerical Experiments
  14. Methods for Comparison.
  15. Experimental Setup.
  16. ...and 21 more sections

Key Result

Theorem 1

Under the null hypothesis $\mathrm{H}_0$ in eq:hypothesis_testing, for any $\alpha\in(0,1)$, the selective $p$-value in eq:selective_pvalue satisfies the following property

Figures (27)

  • Figure 1: Brain image with tumor. The naive $p$-value is 0.000 (true positive) and the selective $p$-value is 0.000 (true positive).
  • Figure 2: Brain image without tumor. The naive $p$-value is 0.000 (false positive) and the selective $p$-value is 0.801 (true negative).
  • Figure 4: Schematic illustration of Lipschitz continuity.
  • Figure 5: Schematic illustration of the introduced heuristics.
  • Figure 6: Independence
  • ...and 22 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Lemma 1