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Why do modern language models, trained to do well on next-word prediction, appear to generate coherent documents and capture long-range structure? Here we show that next-token prediction is provably powerful for learning longer-range…

Machine Learning · Computer Science 2025-12-09 Xinyuan Cao , Santosh S. Vempala

Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…

Computation and Language · Computer Science 2026-02-13 Michelle Yuan , Weiyi Sun , Amir H. Rezaeian , Jyotika Singh , Sandip Ghoshal , Yao-Ting Wang , Miguel Ballesteros , Yassine Benajiba

Attention-based transformers have been remarkably successful at modeling generative processes across various domains and modalities. In this paper, we study the behavior of transformers on data drawn from \kth Markov processes, where the…

Machine Learning · Computer Science 2024-07-26 Nived Rajaraman , Marco Bondaschi , Kannan Ramchandran , Michael Gastpar , Ashok Vardhan Makkuva

Can a mere next-token predictor faithfully model human intelligence? We crystallize this emerging concern and correct popular misconceptions surrounding it, and advocate a simple multi-token objective. As a starting point, we argue that the…

Computation and Language · Computer Science 2025-07-30 Gregor Bachmann , Vaishnavh Nagarajan

LLMs are statistical models of language learning through stochastic gradient descent with a next token prediction objective. Prompting a popular view among AI modelers: LLMs are just next token predictors. While LLMs are engineered using…

Computation and Language · Computer Science 2024-08-12 Stephen M. Downes , Patrick Forber , Alex Grzankowski

We introduce Transfusion, a recipe for training a multi-modal model over discrete and continuous data. Transfusion combines the language modeling loss function (next token prediction) with diffusion to train a single transformer over…

Artificial Intelligence · Computer Science 2024-08-21 Chunting Zhou , Lili Yu , Arun Babu , Kushal Tirumala , Michihiro Yasunaga , Leonid Shamis , Jacob Kahn , Xuezhe Ma , Luke Zettlemoyer , Omer Levy

The next-token prediction (NTP) objective trains language models to predict a single token at each step, even though many continuations can express the same meaning. For example, in the sentence ``this sticker can be placed here'',…

Computation and Language · Computer Science 2026-05-26 Christine Zhang , Dan Jurafsky , Chen Shani

We introduce a new family of toy problems that combine features of linear-regression-style continuous in-context learning (ICL) with discrete associative recall. We pretrain transformer models on sample traces from this toy, specifically…

Machine Learning · Computer Science 2025-07-03 Sultan Daniels , Dylan Davis , Dhruv Gautam , Wentinn Liao , Gireeja Ranade , Anant Sahai

We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and…

Information Theory · Computer Science 2019-01-14 Michal Hledík , Thomas R. Sokolowski , Gašper Tkačik

Large language models such as GPT and Llama are trained with a next-token prediction loss. In this work, we suggest that training language models to predict multiple future tokens at once results in higher sample efficiency. More…

Computation and Language · Computer Science 2026-03-03 Athul Radhakrishnan , Siddhant Mohan , Mahima Sachdeva

Transformers have been successfully applied to sequential, auto-regressive tasks despite being feedforward networks. Unlike recurrent neural networks, Transformers use attention to capture temporal relations while processing input tokens in…

Machine Learning · Computer Science 2021-01-26 Angela Fan , Thibaut Lavril , Edouard Grave , Armand Joulin , Sainbayar Sukhbaatar

We initiate an investigation into the optimization properties of next-token prediction (NTP), the dominant training paradigm for modern language models. Specifically, we study the structural properties of the solutions selected by…

Machine Learning · Computer Science 2024-11-01 Christos Thrampoulidis

Transformers predict over a representation of a sequence. The same data can be written as bytes, characters, or subword tokens, and these representations may be lossless. Yet, under a fixed context window, they need not expose the same…

Machine Learning · Computer Science 2026-05-14 Amirmehdi Jafari Fesharaki , Mohammadamin Rami , Aslan Tchamkerten

Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed…

Machine Learning · Computer Science 2025-09-08 Arash Behboodi , Alvaro H. C. Correia , Fabio Valerio Massoli , Christos Louizos

In this technical note, we study the problem of inverse permutation learning in decoder-only transformers. Given a permutation and a string to which that permutation has been applied, the model is tasked with producing the original…

Machine Learning · Computer Science 2025-12-11 Rohan Alur , Chris Hays , Manish Raghavan , Devavrat Shah

Large language models such as GPT and Llama are trained with a next-token prediction loss. In this work, we suggest that training language models to predict multiple future tokens at once results in higher sample efficiency. More…

Computation and Language · Computer Science 2024-05-01 Fabian Gloeckle , Badr Youbi Idrissi , Baptiste Rozière , David Lopez-Paz , Gabriel Synnaeve

The diverse nature of protein prediction tasks has traditionally necessitated specialized models, hindering the development of broadly applicable and computationally efficient Protein Language Models (PLMs). In this work, we introduce…

Transformers achieve unrivalled performance in modelling language, but remain inefficient in terms of memory and time complexity. A possible remedy is to reduce the sequence length in the intermediate layers by pooling fixed-length segments…

Computation and Language · Computer Science 2023-10-25 Piotr Nawrot , Jan Chorowski , Adrian Łańcucki , Edoardo M. Ponti

We propose a new encoder-decoder approach to learn distributed sentence representations that are applicable to multiple purposes. The model is learned by using a convolutional neural network as an encoder to map an input sentence into a…

Computation and Language · Computer Science 2017-07-28 Zhe Gan , Yunchen Pu , Ricardo Henao , Chunyuan Li , Xiaodong He , Lawrence Carin

With the attention mechanism, transformers achieve significant empirical successes. Despite the intuitive understanding that transformers perform relational inference over long sequences to produce desirable representations, we lack a…

Machine Learning · Computer Science 2024-04-02 Yufeng Zhang , Boyi Liu , Qi Cai , Lingxiao Wang , Zhaoran Wang