mlsanityData to 14 Oct 2026

Value bounds and Convergence Analysis for Averages of LRP attributions

arXiv 2509.08963 ↗First posted 10 Sep 2025cs.LG cs.CVcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 41 of its 57 references that are in the map. First posted on arXiv 10 Sep 2025.

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References · 41

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