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

arXiv: https://arxiv.org/abs/2605.21391 · HTML: https://mlsanity.com/paper/2605.21391/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Information-Theoretic Probing with Minimum Description Length](https://mlsanity.com/paper/2003.12298/) (2020)
- [A mathematical perspective on Transformers](https://mlsanity.com/paper/2312.10794/) (2023)
- [Stabilizing Transformer Training by Preventing Attention Entropy Collapse](https://mlsanity.com/paper/2303.06296/) (2023)
- [PUB: A Pragmatics Understanding Benchmark for Assessing LLMs' Pragmatics Capabilities](https://mlsanity.com/paper/2401.07078/) (2024)
- [Transformer Layers as Painters](https://mlsanity.com/paper/2407.09298/) (2024)
- [MelBERT: Metaphor Detection via Contextualized Late Interaction using Metaphorical Identification Theories](https://mlsanity.com/paper/2104.13615/) (2021)
- [Neural Metaphor Detection in Context](https://mlsanity.com/paper/1808.09653/) (2018)
- [Metaphors in Pre-Trained Language Models: Probing and Generalization Across Datasets and Languages](https://mlsanity.com/paper/2203.14139/) (2022)

## Abstract (arXiv)

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.