Post-Hoc Understanding of Metaphor Processing in Decoder-Only Language Models via Conditional Scale Entropy

TL;DR

This paper introduces conditional scale entropy (CSE), a wavelet-based measure, to analyze how decoder-only language models process metaphors across layers, revealing a consistent spectral breadth signature for metaphorical tokens.

Contribution

The study develops CSE as a novel interpretability tool and demonstrates its effectiveness in identifying metaphor processing signatures across various transformer architectures.

Findings

Metaphorical tokens show higher spectral breadth than literal tokens across models.

The CSE effect persists across different model sizes and architectures.

The spectral breadth signature is not due to semantic complexity or propositional content.

Abstract

Metaphor requires a language model to resolve a token whose contextual meaning diverges from its basic literal sense. Understanding how transformer models organize this reinterpretation across depth remains an open problem in mechanistic interpretability. We introduce conditional scale entropy (CSE), a wavelet-derived measure of how broadly transformer computation engages across frequency scales at each layer position. Two theorems establish that CSE is invariant to update magnitude, isolating the structural pattern of updates from their intensity. Using CSE, we find that metaphorical tokens produce significantly higher spectral breadth than literal tokens at contiguous layer positions on every decoder-only architecture tested, from 124M to 20B parameters (GPT-2 family, LLaMA-2 7B, GPT-oss 20B). The effect survives cluster-based permutation correction, recurs in the early-to-mid relative depth range across models, and converges with an independent analysis of 200 naturalistic VUA pairs. Specificity controls further show that the effect is not explained by semantic complexity or by matched propositional content. These results identify multi-scale coordination as a consistent signature of metaphorical language processing in the decoder-only architectures examined, and establish CSE as a principled tool for characterizing cross-depth structure in transformers.