Challenge: Recent work has shown that large pretrained Language Models (LMs) can perform remarkably well on a range of NLP tasks but they have limitations on basic symbolic manipulation tasks such as copy, reverse, and addition.
Approach: They propose to use explicit positional markers, fine-grained computation steps, and LMs with callable programs to teach large pretrained Language Models.
Outcome: The proposed model can perform 100% accuracy in OOD and repeating symbols.

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Challenge: Recent success of pre-trained language models has spurred widespread interest in their capabilities.
Approach: They propose an evaluation protocol that includes zero-shot evaluation and no fine-tuning . they propose to compare the learning curve of a fine- tuned LM to the learning of multiple controls .
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Do Large Language Models Truly Grasp Addition? A Rule-Focused Diagnostic Using Two-Integer Arithmetic (2025.emnlp-main)

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Challenge: Large language models (LLMs) excel at complex math but fail on basic addition, raising the question of whether they grasp rules or are merely reproducing patterns.
Approach: They systematically probe LLMs’ understanding of two-integer addition by testing three crucial properties: commutativity (A+B=B+A), representation invariance via symbolic remapping and consistent accuracy scaling with operand length.
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Language Models Implement Simple Word2Vec-style Vector Arithmetic (2024.naacl-long)

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Challenge: a primary criticism of language models is their inscrutability.
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Pre-trained Language Models Learn Remarkably Accurate Representations of Numbers (2025.emnlp-main)

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Challenge: Existing work showed limited success in probing numeric values from models’ representations, indicating that these errors can be attributed to the inherent unreliability of distributionally learned embeddings in representing exact quantities.
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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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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 Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks (2024.acl-short)

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Challenge: Despite the generality and far-reaching consequences of large language models, there are still significant limitations making it difficult to apply them to certain tasks.
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Working Memory Identifies Reasoning Limits in Language Models (2024.emnlp-main)

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Challenge: Using large language models, we examine the limitations of their cognitive capabilities and their working memory.
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Lower Bounds on the Expressivity of Recurrent Neural Language Models (2024.naacl-long)

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Challenge: Recent studies of the representational capacity of neural LMs have focused on their ability to recognize formal languages.
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A Comprehensive Evaluation of Inductive Reasoning Capabilities and Problem Solving in Large Language Models (2024.findings-eacl)

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Challenge: Inductive reasoning is fundamental to both human and artificial intelligence.
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What do Large Language Models Learn beyond Language? (2022.findings-emnlp)

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Challenge: Pretraining on text confers models with useful ‘inductive biases’ for non-linguistic reasoning.
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