The Geometry of Numerical Reasoning: Language Models Compare Numeric Properties in Linear Subspaces (2025.naacl-short)
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| Challenge: | Existing studies have focused on simple factual recall, but we have not explored how this is used in more complex queries. |
| Approach: | They propose to identify low-dimensional subspaces which encode numerical attributes associated with entities in comparison prompts. |
| Outcome: | The proposed model can answer numeric comparison questions using a low-dimensional subspace of theembedding space. |
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| Challenge: | Large language models (LLMs) have impressive proficiency in basic arithmetic, but little attention has been given to how they perform when numerical expressions deviate from the prevailing conventions present in their training corpora. |
| Approach: | They investigate numerical reasoning across a wide range of numeral scripts and formats . they show that LLM accuracy drops substantially when numerical inputs are rendered in underrepresented scripts or formats despite the underlying mathematical reasoning being identical . |
| Outcome: | The proposed methods can narrow the gap between LLMs and human models when they deviate from prevailing numerical conventions. |
The Geometry of Multilingual Language Model Representations (2022.emnlp-main)
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| Challenge: | XLM-R models encode language-sensitive information in each language, allowing them to extract features for downstream tasks and cross-lingual transfer learning. |
| Approach: | They evaluate how multilingual language models maintain a shared multilingual representation space while still encoding language-sensitive information in each language. |
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Language Models Learn Universal Representations of Numbers and Here’s Why You Should Care (2026.acl-long)
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Michal Štefánik, Timothee Mickus, Marek Kadlčík, Bertram Højer, Michal Spiegel, Raúl Vázquez, Aman Sinha, Josef Kuchař, Philipp Mondorf, Pontus Stenetorp
| Challenge: | Prior work has shown that large language models (LLMs) often converge to accurate input embedding for numbers, based on sinusoidal representations. |
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Language Models Encode the Value of Numbers Linearly (2025.coling-main)
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| Challenge: | Existing studies show that large language models encode the value of numbers linearly. |
| Approach: | They construct a large language model and use linear probes to read out input numbers from hidden states. |
| Outcome: | The proposed model encodes the value of numbers linearly, and can store the outputs via simple vector additions. |
LLMs Know More About Numbers than They Can Say (2026.eacl-short)
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| Challenge: | Large language models (LLMs) are increasingly used in mathematical, scientific, financial and engineering domains. |
| Approach: | They probe the hidden states of several smaller open-source LLMs to find out how big they are . |
| Outcome: | The proposed model improves verbalized accuracy by 3.22% over base models. |
LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages (2025.findings-naacl)
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| Challenge: | Large Language Models (LLMs) have demonstrated strong performance across various natural language processing tasks, but their proficiency in mathematical reasoning remains a key challenge. |
| Approach: | They propose a process-oriented framework to evaluate LLMs' ability to construct mathematical models, using solvers to compare outputs with ground truth. |
| Outcome: | The proposed framework evaluates LLMs' ability to construct mathematical models, using solvers to compare outputs with ground truth. |
Ranking Entities along Conceptual Space Dimensions with LLMs: An Analysis of Fine-Tuning Strategies (2024.findings-acl)
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| Challenge: | Conceptual spaces represent entities in terms of their primitive semantic features. |
| Approach: | They argue that conceptual spaces should be used alongside knowledge graphs in many settings to model entities in terms of their primitive semantic features. |
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Knowing the Facts but Choosing the Shortcut: Understanding How Large Language Models Compare Entities (2026.eacl-long)
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| Challenge: | Large Language Models (LLMs) are increasingly used for knowledge-based reasoning tasks, yet understanding when they rely on genuine knowledge versus superficial heuristics remains challenging. |
| Approach: | They propose to ask LLMs to compare numerical attributes to find out which country has the highest population, France or Germany. |
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Concept Space Alignment in Multilingual LLMs (2024.emnlp-main)
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| Challenge: | Multilingual large language models generalize somewhat across languages, but it is unclear whether this is a result of improved, implicit alignment, or of something else, e.g., linguistic overlap or semi-parallel subsets of training data. |
| Approach: | They hypothesize that implicit alignment is the reason for generalization in multilingual large language models. |
| Outcome: | The proposed model generalizes well across languages, but lacks linearity. |
Causal Inference with Large Language Model: A Survey (2025.findings-naacl)
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| Challenge: | Existing causal inference frameworks do not match human judgment in several key areas, such as domain knowledge, logical inference, and cultural context. |
| Approach: | They propose to apply large language models to causal inference tasks . they summarize the main causal problems and approaches and compare their results . |
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