When LRP Diverges from Leave-One-Out in Transformers

TL;DR

This paper investigates the divergence between Layer-Wise Relevance Propagation (LRP) and Leave-One-Out (LOO) importance measures in Transformers, revealing theoretical and empirical issues affecting LRP's reliability.

Contribution

It analytically demonstrates violations of axiomatic properties in LRP for Transformers and proposes a simple relevance backpropagation modification that improves alignment with LOO.

Findings

Bilinear propagation rules violate implementation invariance.

Softmax layer relevance backpropagation improves LRP-LOO alignment.

Sensitivity to bilinear factorization affects LRP accuracy.

Abstract

Leave-One-Out (LOO) provides an intuitive measure of feature importance but is computationally prohibitive. While Layer-Wise Relevance Propagation (LRP) offers a potentially efficient alternative, its axiomatic soundness in modern Transformers remains largely under-examined. In this work, we first show that the bilinear propagation rules used in recent advances of AttnLRP violate the implementation invariance axiom. We prove this analytically and confirm it empirically in linear attention layers. Second, we also revisit CP-LRP as a diagnostic baseline and find that bypassing relevance propagation through the softmax layer -- backpropagating relevance only through the value matrices -- significantly improves alignment with LOO, particularly in middle-to-late Transformer layers. Overall, our results suggest that (i) bilinear factorization sensitivity and (ii) softmax propagation error potentially jointly undermine LRP's ability to approximate LOO in Transformers.