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Related papers: Length Generalization in Arithmetic Transformers

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Transformers, central to the successes in modern Natural Language Processing, often falter on arithmetic tasks despite their vast capabilities --which paradoxically include remarkable coding abilities. We observe that a crucial challenge is…

Computation and Language · Computer Science 2023-11-28 Ruoqi Shen , Sébastien Bubeck , Ronen Eldan , Yin Tat Lee , Yuanzhi Li , Yi Zhang

Despite the empirical success of prompt tuning in adapting pretrained language models to new tasks, theoretical analyses of its capabilities remain limited. Existing theoretical work primarily addresses universal approximation properties,…

Machine Learning · Computer Science 2025-09-03 Maxime Meyer , Mario Michelessa , Caroline Chaux , Vincent Y. F. Tan

This paper introduces a novel training methodology that enables a Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation…

Machine Learning · Computer Science 2024-06-13 Alexandre Galvao Patriota

Length generalization (LG) is a challenging problem in learning to reason. It refers to the phenomenon that when trained on reasoning problems of smaller lengths or sizes, the resulting model struggles with problems of larger sizes or…

Artificial Intelligence · Computer Science 2024-04-02 Changnan Xiao , Bing Liu

In Transformers, Position Embeddings (PEs) significantly influence Length Generalization (LG) performance, yet their fundamental role remains unclear. In this work, we investigate the limitations and capabilities of PEs in achieving LG. We…

Machine Learning · Computer Science 2025-10-07 Yang Chen , Yitao Liang , Zhouchen Lin

We study the performance of transformers as a function of the number of repetitions of training examples with algorithmically generated datasets. On three problems of mathematics: the greatest common divisor, modular multiplication, and…

Machine Learning · Computer Science 2024-10-10 François Charton , Julia Kempe

Effectively training language models on long inputs poses many technical challenges. As a cost consideration, languages models are pretrained on a fixed sequence length before being adapted to longer sequences. We explore various methods…

Computation and Language · Computer Science 2024-06-21 Petros Karypis , Julian McAuley , George Karypis

Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token…

Machine Learning · Computer Science 2023-07-10 Nayoung Lee , Kartik Sreenivasan , Jason D. Lee , Kangwook Lee , Dimitris Papailiopoulos

Recently, many datasets have been proposed to test the systematic generalization ability of neural networks. The companion baseline Transformers, typically trained with default hyper-parameters from standard tasks, are shown to fail…

Machine Learning · Computer Science 2022-02-15 Róbert Csordás , Kazuki Irie , Jürgen Schmidhuber

It is a widely known issue that Transformers, when trained on shorter sequences, fail to generalize robustly to longer ones at test time. This raises the question of whether Transformer models are real reasoning engines, despite their…

Machine Learning · Computer Science 2025-04-04 Ruining Li , Gabrijel Boduljak , Jensen , Zhou

Pre-trained language models have recently emerged as a powerful tool for fine-tuning a variety of language tasks. Ideally, when models are pre-trained on large amount of data, they are expected to gain implicit knowledge. In this paper, we…

Computation and Language · Computer Science 2023-06-22 Mohamad Ballout , Ulf Krumnack , Gunther Heidemann , Kai-Uwe Kühnberger

Training large language models to predict beyond their training context lengths has drawn much attention in recent years, yet the principles driving such behavior of length generalization remain underexplored. We propose a new theoretical…

Machine Learning · Computer Science 2025-02-25 Noah Golowich , Samy Jelassi , David Brandfonbrener , Sham M. Kakade , Eran Malach

It has become common practice now to use random initialization schemes, rather than the pre-trained embeddings, when training transformer based models from scratch. Indeed, we find that pre-trained word embeddings from GloVe, and some…

Computation and Language · Computer Science 2024-07-18 Ha Young Kim , Niranjan Balasubramanian , Byungkon Kang

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long…

Machine Learning · Computer Science 2025-10-14 Ricardo Buitrago Ruiz , Albert Gu

We study length generalization in sequence models on a composite problem involving both state tracking and associative recall. Prior work finds that recurrent networks handle state tracking well but struggle with recall, whereas…

Machine Learning · Computer Science 2025-10-02 Buu Phan , Reza Ebrahimi , Sanjay Haresh , Roland Memisevic

The Transformer model has a tendency to overfit various aspects of the training data, such as the overall sequence length. We study elementary string edit functions using a defined set of error indicators to interpret the behaviour of the…

Machine Learning · Computer Science 2024-10-18 Patrik Zavoral , Dušan Variš , Ondřej Bojar

Length Generalization is the essential capacity of autonomous agents to perform tasks in longer contexts than those encountered during training. To systematically study this feat, we test how well models can approximate the next token…

Transformers have the capacity to act as supervised learning algorithms: by properly encoding a set of labeled training ("in-context") examples and an unlabeled test example into an input sequence of vectors of the same dimension, the…

Machine Learning · Computer Science 2024-12-16 Spencer Frei , Gal Vardi

Length generalization is a key property of a learning algorithm that enables it to make correct predictions on inputs of any length, given finite training data. To provide such a guarantee, one needs to be able to compute a length…

Machine Learning · Computer Science 2026-03-04 Andy Yang , Pascal Bergsträßer , Georg Zetzsche , David Chiang , Anthony W. Lin

Transformers are widely deployed in large language models (LLMs), yet most models still fail on basic arithmetic tasks such as multidigit addition. In contrast, we show that small transformers trained from scratch can solve n-digit addition…

Machine Learning · Computer Science 2025-10-06 Philip Quirke , Clement Neo , Fazl Barez