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Transformers have achieved state-of-the-art performance in language modeling tasks. However, the reasons behind their tremendous success are still unclear. In this paper, towards a better understanding, we train a Transformer model on a…

Machine Learning · Statistics 2024-06-06 Michael E. Sander , Raja Giryes , Taiji Suzuki , Mathieu Blondel , Gabriel Peyré

Chain-of-Thought (CoT) reasoning is known to improve Large Language Models both empirically and in terms of theoretical approximation power. However, our understanding of the inner workings and conditions of apparition of CoT capabilities…

Machine Learning · Computer Science 2024-10-29 Vivien Cabannes , Charles Arnal , Wassim Bouaziz , Alice Yang , Francois Charton , Julia Kempe

Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of…

Machine Learning · Computer Science 2026-04-01 Penghao Yu , Haotian Jiang , Zeyu Bao , Ruoxi Yu , Qianxiao Li

Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can…

Machine Learning · Computer Science 2026-02-27 Joshua S. Schiffman

Associative memory has long underpinned the design of sequential models. Beyond recall, humans reason by projecting future states and selecting goal-directed actions, a capability that modern language models increasingly require but do not…

Machine Learning · Computer Science 2026-03-11 Peihao Wang , Shan Yang , Xijun Wang , Tesi Xiao , Xin Liu , Changlong Yu , Yu Lou , Pan Li , Zhangyang Wang , Ming Lin , René Vidal

We propose Re-FORC, an adaptive reward prediction method that, given a context, enables prediction of the expected future rewards as a function of the number of future thinking tokens. Re-FORC trains a lightweight adapter on reasoning…

Artificial Intelligence · Computer Science 2025-11-05 Renos Zabounidis , Aditya Golatkar , Michael Kleinman , Alessandro Achille , Wei Xia , Stefano Soatto

Few-shot Chain-of-Thought (CoT) prompting has demonstrated strong performance in improving the reasoning capabilities of large language models (LLMs). While theoretical investigations have been conducted to understand CoT, the underlying…

Computation and Language · Computer Science 2024-10-23 Yingqian Cui , Pengfei He , Xianfeng Tang , Qi He , Chen Luo , Jiliang Tang , Yue Xing

Scaling large language models by increasing parameters and training data is increasingly constrained by limited high-quality corpora and rising communication costs. This work explores an alternative axis: increasing per-token computation…

Computation and Language · Computer Science 2026-03-11 Boyi Zeng , Yiqin Hao , He Li , Shixiang Song , Feichen Song , Zitong Wang , Siyuan Huang , Yi Xu , ZiWei He , Xinbing Wang , Zhouhan Lin

Pre-trained language models demonstrate general intelligence and common sense, but long inputs quickly become a bottleneck for memorizing information at inference time. We resurface a simple method, Memorizing Transformers (Wu et al.,…

Machine Learning · Computer Science 2024-06-05 Phoebe Klett , Thomas Ahle

Large reasoning models (LRMs) excel on complex problems but face a critical barrier to efficiency: reinforcement learning (RL) training requires long rollouts for outcome-based rewards, where autoregressive decoding dominates time and…

Machine Learning · Computer Science 2026-02-20 Zeliang Zhang , Xiaodong Liu , Hao Cheng , Hao Sun , Chenliang Xu , Jianfeng Gao

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

Transformers architecture apply self-attention to tokens represented as vectors, before a fully connected (neuronal network) layer. These two parts can be layered many times. Traditionally, self-attention is seen as a mechanism for…

Computation and Language · Computer Science 2025-01-22 Evgeniy Shin , Heinrich Matzinger

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This…

Contemporary autoregressive transformers operate in open loop: each hidden state is computed in a single forward pass and never revised, causing errors to propagate uncorrected through the sequence. We identify this open-loop bottleneck as…

Machine Learning · Computer Science 2025-12-01 Akbar Anbar Jafari , Gholamreza Anbarjafari

Recent studies on transformer-based language models show that they can answer questions by reasoning over knowledge provided as part of the context (i.e., in-context reasoning). However, since the available knowledge is often not filtered…

Computation and Language · Computer Science 2023-11-07 Zeming Chen , Gail Weiss , Eric Mitchell , Asli Celikyilmaz , Antoine Bosselut

Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored. In this paper, we…

Machine Learning · Computer Science 2025-06-06 Kevin Xu , Issei Sato

Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning…

Machine Learning · Computer Science 2023-05-03 Bingbin Liu , Jordan T. Ash , Surbhi Goel , Akshay Krishnamurthy , Cyril Zhang

The self-attention mechanism, a cornerstone of Transformer-based state-of-the-art deep learning architectures, is largely heuristic-driven and fundamentally challenging to interpret. Establishing a robust theoretical foundation to explain…

Computer Vision and Pattern Recognition · Computer Science 2026-02-10 Laziz U. Abdullaev , Maksim Tkachenko , Tan M. Nguyen

We propose a new architectural change, and post-training pipeline, for making LLMs more verbose reasoners by teaching a model to truncate forward passes early. We augment an existing transformer architecture with an early-exit mechanism at…

Artificial Intelligence · Computer Science 2026-03-25 Elizabeth Pavlova , Mariia Koroliuk , Karthik Viswanathan , Cameron Tice , Edward James Young , Puria Radmard

Transformers have exhibited exceptional capabilities in sequence modeling tasks, leveraging self-attention and in-context learning. Critical to this success are induction heads, attention circuits that enable copying tokens based on their…

Machine Learning · Computer Science 2025-09-11 Francesco D'Angelo , Francesco Croce , Nicolas Flammarion