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The poor performance of transformers on arithmetic tasks seems to stem in large part from their inability to keep track of the exact position of each digit inside of a large span of digits.
Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton · 2016
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Decoupled weight decay regularization
Ilya Loshchilov and Frank Hutter · 2017
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Attention is all you need
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Universal transformers
Mostafa Dehghani, Stephan Gouws, Oriol Vinyals, Jakob Uszkoreit, and Lukasz Kaiser · 2018
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Self-attention with relative position representations
Peter Shaw, Jakob Uszkoreit, and Ashish Vaswani · 2018
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Analysing mathematical reasoning abilities of neural models
David Saxton, Edward Grefenstette, Felix Hill, and Pushmeet Kohli · 2019
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Adaptive attention span in transformers
Sainbayar Sukhbaatar, Edouard Grave, Piotr Bojanowski, and Armand Joulin · 2019
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Language models are few-shot learners
Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al · 2020
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Albert: A lite bert for self-supervised learning of language representations
Zhenzhong Lan, Mingda Chen, Sebastian Goodman, Kevin Gimpel, Piyush Sharma, and Radu Soricut · 2020
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Exploring the limits of transfer learning with a unified text-to-text transformer
Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J Liu · 2020
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Glu variants improve transformer
Noam Shazeer · 2020
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Can you learn an algorithm? generalizing from easy to hard problems with recurrent networks
Avi Schwarzschild, Eitan Borgnia, Arjun Gupta, Furong Huang, Uzi Vishkin, Micah Goldblum, and Tom Goldstein · 2021
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End-to-end algorithm synthesis with recurrent networks: Logical extrapolation without overthinking
Arpit Bansal, Avi Schwarzschild, Eitan Borgnia, Zeyad Emam, Furong Huang, Micah Goldblum, and Tom Goldstein · 2022
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Kerple: Kernelized relative positional embedding for length extrapolation
Ta-Chung Chi, Ting-Han Fan, Peter Ramadge, and Alexander Rudnicky · 2022
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A generalist neural algorithmic learner
Borja Ibarz, Vitaly Kurin, George Papamakarios, Kyriacos Nikiforou, Mehdi Bennani, Róbert Csordás, Andrew Joseph Dudzik, Matko Bošnjak, Alex Vitvitskyi, Yulia Rubanova, et al · 2022
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Mega: moving average equipped gated attention
Xuezhe Ma, Chunting Zhou, Xiang Kong, Junxian He, Liangke Gui, Graham Neubig, Jonathan May, and Luke Zettlemoyer · 2022
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In-context learning and induction heads
Catherine Olsson, Nelson Elhage, Neel Nanda, Nicholas Joseph, Nova DasSarma, Tom Henighan, Ben Mann, Amanda Askell, Yuntao Bai, Anna Chen, et al · 2022
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Train short, test long: Attention with linear biases enables input length extrapolation
Ofir Press, Noah Smith, and Mike Lewis · 2022
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Limitations of language models in arithmetic and symbolic induction
Jing Qian, Hong Wang, Zekun Li, Shiyang Li, and Xifeng Yan · 2022
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The clrs algorithmic reasoning benchmark
Petar Veličković, Adrià Puigdomènech Badia, David Budden, Razvan Pascanu, Andrea Banino, Misha Dashevskiy, Raia Hadsell, and Charles Blundell · 2022
Functional interpolation for relative positions improves long context transformers
Shanda Li, Chong You, Guru Guruganesh, Joshua Ainslie, Santiago Ontanon, Manzil Zaheer, Sumit Sanghai, Yiming Yang, Sanjiv Kumar, and Srinadh Bhojanapalli · 2023
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OpenAI · 2023
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Randomized positional encodings boost length generalization of transformers
Anian Ruoss, Grégoire Delétang, Tim Genewein, Jordi Grau-Moya, Róbert Csordás, Mehdi Bennani, Shane Legg, and Joel Veness · 2023
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Positional description matters for transformers arithmetic
Ruoqi Shen, Sébastien Bubeck, Ronen Eldan, Yin Tat Lee, Yuanzhi Li, and Yi Zhang · 2023
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DeepNet: Scaling Transformers to 1,000 Layers
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Scaling vision transformers
Xiaohua Zhai, Alexander Kolesnikov, Neil Houlsby, and Lucas Beyer · 2022
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Dissecting transformer length extrapolation via the lens of receptive field analysis
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Faith and fate: Limits of transformers on compositionality
Nouha Dziri, Ximing Lu, Melanie Sclar, Xiang Lorraine Li, Liwei Jian, Bill Yuchen Lin, Peter West, Chandra Bhagavatula, Ronan Le Bras, Jena D Hwang, et al · 2023
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Cramming: Training a language model on a single gpu in one day
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Looped transformers as programmable computers
Angeliki Giannou, Shashank Rajput, Jy-yong Sohn, Kangwook Lee, Jason D Lee, and Dimitris Papailiopoulos · 2023
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xval: A continuous number encoding for large language models
Siavash Golkar, Mariel Pettee, Michael Eickenberg, Alberto Bietti, Miles Cranmer, Geraud Krawezik, Francois Lanusse, Michael McCabe, Ruben Ohana, Liam Parker, et al · 2023
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Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al · 2023
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What algorithms can transformers learn? a study in length generalization
Hattie Zhou, Arwen Bradley, Etai Littwin, Noam Razin, Omid Saremi, Josh Susskind, Samy Bengio, and Preetum Nakkiran · 2023
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Simulation of graph algorithms with looped transformers
Artur Back de Luca and Kimon Fountoulakis · 2024
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#16: Notes on Arithmetic in GPT-4, February 2024
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Transformers can achieve length generalization but not robustly
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Can neural networks do arithmetic? a survey on the elementary numerical skills of state-of-the-art deep learning models
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