@inproceedings{civelli-etal-2026-shared,
title = "A Shared Geometry of Difficulty in Multilingual Language Models",
author = "Civelli, Stefano and
Bernardelle, Pietro and
Brunello, Nicol{\`o} and
Demartini, Gianluca",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 2: Short Papers)",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.acl-short.66/",
pages = "796--807",
ISBN = "979-8-89176-391-3",
abstract = "Large language models (LLMs) encode problem difficulty as an internal signal that can be linearly decoded from their residuals. Given their multilingual capabilities, we investigate whether this meta-cognitive signal is language-agnostic and how it is organized across the model{'}s layers by training linear probes on the AMC subset of the Easy2Hard benchmark, translated into 21 languages. We found that difficulty-related signals emerge at two distinct stages of the model internals, corresponding to shallow (early-layers) and deep (later-layers) internal representations, that exhibit functionally different behaviors. Probes trained on deep representations achieve high accuracy when evaluated on the same language but exhibit weaker cross-lingual transfer. In contrast, probes trained on shallow representations generalize better across languages, despite achieving lower within-language performance. This closely aligns with existing findings in LLM interpretability, showing that models tend to operate in an abstract conceptual space before producing language-specific outputs. Our results suggest that this two-stage organizational principle extends beyond simple semantic processing to meta-cognitive properties such as problem difficulty, highlighting an internal control signal that is not tied to surface meaning."
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<abstract>Large language models (LLMs) encode problem difficulty as an internal signal that can be linearly decoded from their residuals. Given their multilingual capabilities, we investigate whether this meta-cognitive signal is language-agnostic and how it is organized across the model’s layers by training linear probes on the AMC subset of the Easy2Hard benchmark, translated into 21 languages. We found that difficulty-related signals emerge at two distinct stages of the model internals, corresponding to shallow (early-layers) and deep (later-layers) internal representations, that exhibit functionally different behaviors. Probes trained on deep representations achieve high accuracy when evaluated on the same language but exhibit weaker cross-lingual transfer. In contrast, probes trained on shallow representations generalize better across languages, despite achieving lower within-language performance. This closely aligns with existing findings in LLM interpretability, showing that models tend to operate in an abstract conceptual space before producing language-specific outputs. Our results suggest that this two-stage organizational principle extends beyond simple semantic processing to meta-cognitive properties such as problem difficulty, highlighting an internal control signal that is not tied to surface meaning.</abstract>
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%0 Conference Proceedings
%T A Shared Geometry of Difficulty in Multilingual Language Models
%A Civelli, Stefano
%A Bernardelle, Pietro
%A Brunello, Nicolò
%A Demartini, Gianluca
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-391-3
%F civelli-etal-2026-shared
%X Large language models (LLMs) encode problem difficulty as an internal signal that can be linearly decoded from their residuals. Given their multilingual capabilities, we investigate whether this meta-cognitive signal is language-agnostic and how it is organized across the model’s layers by training linear probes on the AMC subset of the Easy2Hard benchmark, translated into 21 languages. We found that difficulty-related signals emerge at two distinct stages of the model internals, corresponding to shallow (early-layers) and deep (later-layers) internal representations, that exhibit functionally different behaviors. Probes trained on deep representations achieve high accuracy when evaluated on the same language but exhibit weaker cross-lingual transfer. In contrast, probes trained on shallow representations generalize better across languages, despite achieving lower within-language performance. This closely aligns with existing findings in LLM interpretability, showing that models tend to operate in an abstract conceptual space before producing language-specific outputs. Our results suggest that this two-stage organizational principle extends beyond simple semantic processing to meta-cognitive properties such as problem difficulty, highlighting an internal control signal that is not tied to surface meaning.
%U https://aclanthology.org/2026.acl-short.66/
%P 796-807
Markdown (Informal)
[A Shared Geometry of Difficulty in Multilingual Language Models](https://aclanthology.org/2026.acl-short.66/) (Civelli et al., ACL 2026)
ACL
- Stefano Civelli, Pietro Bernardelle, Nicolò Brunello, and Gianluca Demartini. 2026. A Shared Geometry of Difficulty in Multilingual Language Models. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 796–807, San Diego, California, United States. Association for Computational Linguistics.