arXiv:2604.27529cs.CV2026-04被引 1

揭示卷积网络分类依赖像素级相消干涉,而非简单筛选特征。

Adjoint Inversion Reveals Holographic Superposition and Destructive Interference in CNN Classifiers

论文配图:Adjoint Inversion Reveals Holographic Superposition and Destructive Interference in CNN Classifiers
图 1 · 摘自论文原文
  • 通过无幻觉反演框架,首次在像素层面发现通道间全息叠加现象。
  • 正负权重重建视觉能量相同,但代数和聚焦前景,证明分类靠相消干涉。
  • 适用于注意力结构,可解释模型对异常输入的失效机制。

CNN可解释性的一个基础假设——深层编码器抑制背景像素,分类器仅从净化后的特征池中选择(空间漏斗假说)——因现有可视化工具存在空间幻觉而长期未被验证。本文提出一种无幻觉反演框架,基于幅度-相位解耦与局部伴随校正器,数学上保证每个重构的空间梯度支持严格源自真正激活的通道。以此为几何探针,我们首次获得视觉编码器中强叠加的像素级证据。发现各通道反演具有均匀全息性:正负权重重建在视觉和能量上无法区分。但其代数和强烈聚焦于前景,证实分类通过相消干涉实现——分类权重在像素空间抵消共享背景方向,同时构建类别判别残差,直接证伪空间漏斗假说。该干涉模型将允许干涉子空间体积定义为决定通道需求的几何量。我们证明该体积与全局平均池化协方差行列式互为对偶,由此导出一个具有(1−1/e)近似保证的协方差-体积通道选择算法。该算法数学揭示了分布外(OOD)失败是干涉必需的协方差体积坍缩所致。本框架无需重训练即可无缝扩展至基于注意力的头。

原文摘要 · Abstract (English)

A foundational assumption in CNN interpretability -- that deep encoders suppress background pixels while classifiers merely select from a cleaned feature pool (the Spatial Funnel Hypothesis) -- remains untested due to spatial hallucinations in existing visualization tools. We address this by introducing a hallucination-free inversion framework built on magnitude-phase decoupling and Local Adjoint Correctors. Our method mathematically guarantees that the spatial gradient support of every reconstruction stems strictly from genuinely active channels. Using this framework as a geometric probe, we uncover the first pixel-level evidence of strong superposition in vision encoders. We show that per-channel inversions are uniformly holographic: positive and negative weight reconstructions are visually and energetically indistinguishable. However, their algebraic sum sharply concentrates on the foreground. This proves classification operates via destructive interference -- classifier weights cancel a shared background direction in pixel space and constructively assemble class-discriminative residuals, directly falsifying the Spatial Funnel Hypothesis. This interference model identifies the volume of the admissible interference subspace as the geometric quantity governing channel requirements. We prove this volume is dual to the GAP covariance determinant, yielding a covariance-volume channel selection algorithm with a $(1-1/e)$ approximation guarantee. This algorithm mathematically reveals out-of-distribution (OOD) failure as a measurable collapse of the covariance volume essential for interference-based classification. Our framework extends seamlessly to attention-based heads without retraining.

CNN可解释性相消干涉通道选择反演框架

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。