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Quantitative and numerical comprehension in language is an important task in many fields like education and finance, but still remains a challenging task for language models. While tool and calculator usage has shown to be helpful to…

Computation and Language · Computer Science 2024-06-27 Vishruth Veerendranath , Vishwa Shah , Kshitish Ghate

We propose a generalization of neural network sequence models. Instead of predicting one symbol at a time, our multi-scale model makes predictions over multiple, potentially overlapping multi-symbol tokens. A variation of the byte-pair…

Machine Learning · Statistics 2017-07-06 Bart van Merriënboer , Amartya Sanyal , Hugo Larochelle , Yoshua Bengio

The ability to extrapolate from short problem instances to longer ones is an important form of out-of-distribution generalization in reasoning tasks, and is crucial when learning from datasets where longer problem instances are rare. These…

Computation and Language · Computer Science 2022-11-15 Cem Anil , Yuhuai Wu , Anders Andreassen , Aitor Lewkowycz , Vedant Misra , Vinay Ramasesh , Ambrose Slone , Guy Gur-Ari , Ethan Dyer , Behnam Neyshabur

Large Language Models (LLMs) have recently developed new advanced functionalities. Their effectiveness relies on statistical learning and generalization capabilities. However, they face limitations in internalizing the data they process and…

Machine Learning · Computer Science 2026-01-14 Farah Ben Slama , Frédéric Armetta

Many NLP applications, such as biomedical data and technical support, have 10-100 million tokens of in-domain data and limited computational resources for learning from it. How should we train a language model in this scenario? Most…

Computation and Language · Computer Science 2020-10-01 Charles Welch , Rada Mihalcea , Jonathan K. Kummerfeld

Subword tokenization introduces a computational layer in language models where many distinct token sequences decode to the same surface form and preserve meaning, yet induce different internal computations. Despite this non-uniqueness,…

Computation and Language · Computer Science 2026-01-14 Adrian Cosma , Stefan Ruseti , Emilian Radoi , Mihai Dascalu

Speech tokenization serves as the foundation of speech language model (LM), enabling them to perform various tasks such as spoken language modeling, text-to-speech, speech-to-text, etc. Most speech tokenizers are trained independently of…

Computation and Language · Computer Science 2024-09-11 Arnon Turetzky , Yossi Adi

Supervised deep learning is most commonly applied to difficult problems defined on large and often extensively curated datasets. Here we demonstrate the ability of deep representation learning to address problems of classification and…

Machine Learning · Computer Science 2022-11-30 Benjamin L. Badger

Language prediction is constrained by informational entropy intrinsic to language, such that there exists a limit to how accurate any language model can become and equivalently a lower bound to language compression. The most efficient…

Computation and Language · Computer Science 2025-11-14 Benjamin L. Badger , Matthew Neligeorge

We propose a method to teach multiple large language models (LLM) to collaborate by interleaving their generations at the token level. We model the decision of which LLM generates the next token as a latent variable. By optimizing the…

Computation and Language · Computer Science 2024-08-28 Shannon Zejiang Shen , Hunter Lang , Bailin Wang , Yoon Kim , David Sontag

Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical…

Artificial Intelligence · Computer Science 2025-12-15 Shubhra Mishra , Gabriel Poesia , Noah D. Goodman

Language model (LM) pre-training is useful in many language processing tasks. But can pre-trained LMs be further leveraged for more general machine learning problems? We propose an approach for using LMs to scaffold learning and…

Large language models (LLM) such as OpenAI's ChatGPT and GPT-3 offer unique testbeds for exploring the translation challenges of turning literacy into numeracy. Previous publicly-available transformer models from eighteen months prior and…

Computation and Language · Computer Science 2023-02-01 David Noever , Forrest McKee

We investigate whether internal activations in language models can be used to detect arithmetic errors. Starting with a controlled setting of 3-digit addition, we show that simple probes can accurately decode both the model's predicted…

Computation and Language · Computer Science 2025-07-17 Yucheng Sun , Alessandro Stolfo , Mrinmaya Sachan

Large language models are powerful systems that excel at many tasks, ranging from translation to mathematical reasoning. Yet, at the same time, these models often show unhuman-like characteristics. In the present paper, we address this gap…

Computation and Language · Computer Science 2023-06-08 Marcel Binz , Eric Schulz

Large language models (LLMs) have demonstrated impressive capabilities, yet their internal mechanisms for handling reasoning-intensive tasks remain underexplored. To advance the understanding of model-internal processing mechanisms, we…

Computation and Language · Computer Science 2026-04-20 Tanja Baeumel , Josef van Genabith , Simon Ostermann

Tokenization -- the process of decomposing a given text into a sequence of subwords called tokens -- is one of the key components in the development of language models. Particularly, auto-regressive language models generate texts token by…

Computation and Language · Computer Science 2026-02-19 Daiki Chijiwa , Taku Hasegawa , Kyosuke Nishida , Shin'ya Yamaguchi , Tomoya Ohba , Tamao Sakao , Susumu Takeuchi

In this paper, we study the ability of large language models to learn specific mathematical rules such as distributivity or simplifying equations. We present an empirical analysis of their ability to generalize these rules, as well as to…

Computation and Language · Computer Science 2024-10-28 Antoine Gorceix , Bastien Le Chenadec , Ahmad Rammal , Nelson Vadori , Manuela Veloso

Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on broadening the training set with various data augmentation…

Computation and Language · Computer Science 2024-10-08 Zhihan Zhang , Tao Ge , Zhenwen Liang , Wenhao Yu , Dian Yu , Mengzhao Jia , Dong Yu , Meng Jiang

Learning to construct text representations in end-to-end systems can be difficult, as natural languages are highly compositional and task-specific annotated datasets are often limited in size. Methods for directly supervising language…

Computation and Language · Computer Science 2018-11-15 Marek Rei , Anders Søgaard