41 lines
1.5 KiB
Markdown
41 lines
1.5 KiB
Markdown
---
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title: "预测不变区间 (Prediction-Invariant Intervals)"
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created: 2026-07-04
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updated: 2026-07-04
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type: concept
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tags: [certification, interval, prediction, semantics]
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sources: ["arXiv:2606.18839"]
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---
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# 预测不变区间 (Prediction-Invariant Intervals)
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语义鲁棒性认证的输出：将语义 extent 范围 $[\varphi_a, \varphi_{a'}]$ 切分为若干子区间，在每个区间内 VLM 预测类别保持不变。
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## 计算过程
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1. **闭式 margin**：将语义变换 $\gamma(\varphi)$ 代入 pairwise margin
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$$m_{c,c'}(\varphi) = A_{c,c'} \cos\varphi + B_{c,c'} \sin\varphi + C_{c,c'}$$
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2. **求解穿越点**：$m_{c,c'}(\varphi) = 0$ 的闭式解
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3. **收集排序**：所有类别对的穿越点集合 $\{\varphi_\ell\}_{\ell=0}^L$
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4. **区间划分**：$(\varphi_\ell, \varphi_{\ell+1})$ 内预测恒定
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## 证书输出
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$$\mathcal{S} = \{((\varphi_\ell, \varphi_{\ell+1}), y_\ell) : \ell = 0, \ldots, L-1\}$$
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- 每个区间标注预测类别 $y_\ell$
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- 区间边界对应类别翻转点（class flip）
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## 聚合指标：预测不变概率
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$$\mathbb{P}(f(\gamma(\varphi)) = \hat{y}) = \frac{1}{\varphi_{a'} - \varphi_a} \sum_{\ell: y_\ell = \hat{y}} (\varphi_{\ell+1} - \varphi_\ell)$$
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度量整个语义 extent 范围内预测保持不变的**总比例**。
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## 参考
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- [[semantic-robustness-certification|语义鲁棒性认证]]
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- [[semantic-extent|语义 extent]]
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- [[voronoi-decision-regions|Voronoi 决策区域]]
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- [[semantic-robustness-certification-vlm-2026|论文原文]]
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