分析LRP归因方法的数值特性，揭示其收敛性与权重无关的稳定性。
Value bounds and Convergence Analysis for Averages of LRP attributions
- 将LRP归因表示为修正梯度矩阵乘积，类比链式法则的雅可比矩阵
- 推导出归因值的分量级上界，证明其在数据增强下均值收敛于期望
- 发现LRP-beta的收敛常数不依赖权重范数，优于传统梯度方法
我们通过将层间重要性传播（LRP）型归因方法表示为修正梯度矩阵的乘积，分析其数值性质。这一表示形式类比了微分链式法则中出现的雅可比矩阵。为理解归因值的分布，我们推导了奇异值的上界，并得到了归因图值的分量级上界。作为主要结果，我们将这些分量级上界应用于获得乘法常数，这些常数控制了归因经验均值向归因图期望值的收敛速度。该发现对应用多种非几何数据增强的场景以及Smoothgrad型归因方法具有重要意义。特别地，我们的分析表明，LRP-beta的收敛常数不随权重范数变化，这与基于梯度的方法和LRP-epsilon有显著区别。
原文摘要 · Abstract (English)
We analyze numerical properties of Layer-wise relevance propagation (LRP)-type attribution methods by representing them as a product of modified gradient matrices. This representation creates an analogy to matrix multiplications of Jacobi-matrices which arise from the chain rule of differentiation. In order to shed light on the distribution of attribution values, we derive upper bounds for singular values. Furthermore we derive component-wise bounds for attribution map values. As a main result, we apply these component-wise bounds to obtain multiplicative constants. These constants govern the convergence of empirical means of attributions to expectations of attribution maps. This finding has important implications for scenarios where multiple non-geometric data augmentations are applied to individual test samples, as well as for Smoothgrad-type attribution methods. In particular, our analysis reveals that the constants for LRP-beta remain independent of weight norms, a significant distinction from both gradient-based methods and LRP-epsilon.
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