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Deep learning involves navigating a high-dimensional loss landscape over the neural network parameter space. Over the course of training, complex computational structures form and re-form inside the neural network, leading to shifts in…

Machine Learning · Computer Science 2025-08-04 Jesse Hoogland , George Wang , Matthew Farrugia-Roberts , Liam Carroll , Susan Wei , Daniel Murfet

Sequential decision-making algorithms such as reinforcement learning (RL) in real-world scenarios inevitably face environments with partial observability. This paper scrutinizes the effectiveness of a popular architecture, namely…

Machine Learning · Computer Science 2024-05-31 Chenhao Lu , Ruizhe Shi , Yuyao Liu , Kaizhe Hu , Simon S. Du , Huazhe Xu

We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise…

Machine Learning · Computer Science 2026-01-29 Faruk Alpay , Bugra Kilictas

In this paper, we describe the use of recurrent neural networks to capture sequential information from the self-attention representations to improve the Transformers. Although self-attention mechanism provides a means to exploit long…

Computation and Language · Computer Science 2021-04-06 Tze Yuang Chong , Xuyang Wang , Lin Yang , Junjie Wang

In many real-world scenarios, data to train machine learning models becomes available over time. Unfortunately, these models struggle to continually learn new concepts without forgetting what has been learnt in the past. This phenomenon is…

Computation and Language · Computer Science 2023-01-16 Beyza Ermis , Giovanni Zappella , Martin Wistuba , Aditya Rawal , Cedric Archambeau

Decoding in a Transformer based language model is inherently sequential as a token's embedding needs to pass through all the layers in the network before the generation of the next token can begin. In this work, we propose a new…

Machine Learning · Computer Science 2025-08-27 Dylan Cutler , Arun Kandoor , Nishanth Dikkala , Nikunj Saunshi , Xin Wang , Rina Panigrahy

In this work, we address two main shortcomings of transformer architectures: input corruption and rank collapse in their output representation. We unveil self-attention as an autonomous state-space model that inherently promotes smoothness…

Artificial Intelligence · Computer Science 2024-02-27 Tam Nguyen , César A. Uribe , Tan M. Nguyen , Richard G. Baraniuk

Transformers are widely used across data modalities, and yet the principles distilled from text models often transfer imperfectly to models trained to other modalities. In this paper, we analyze Transformers through the lens of rank…

Incremental models that process sentences one token at a time will sometimes encounter points where more than one interpretation is possible. Causal models are forced to output one interpretation and continue, whereas models that can revise…

Computation and Language · Computer Science 2024-06-04 Brielen Madureira , Patrick Kahardipraja , David Schlangen

Transformer networks have lead to important progress in language modeling and machine translation. These models include two consecutive modules, a feed-forward layer and a self-attention layer. The latter allows the network to capture long…

Machine Learning · Computer Science 2019-07-03 Sainbayar Sukhbaatar , Edouard Grave , Guillaume Lample , Herve Jegou , Armand Joulin

We introduce a new way of learning to encode position information for non-recurrent models, such as Transformer models. Unlike RNN and LSTM, which contain inductive bias by loading the input tokens sequentially, non-recurrent models are…

Machine Learning · Computer Science 2020-03-23 Xuanqing Liu , Hsiang-Fu Yu , Inderjit Dhillon , Cho-Jui Hsieh

Transformer architectures, capable of capturing sequential dependencies in the history of user interactions, have become the dominant approach in sequential recommender systems. Despite their success, such models consider sequence elements…

Information Retrieval · Computer Science 2026-03-02 Artur Gimranov , Viacheslav Yusupov , Elfat Sabitov , Tatyana Matveeva , Anton Lysenko , Ruslan Israfilov , Evgeny Frolov

In this work, we present a generalized formulation of the Transformer algorithm by reinterpreting its core mechanisms within the framework of Path Integral formalism. In this perspective, the attention mechanism is recast as a process that…

High Energy Physics - Phenomenology · Physics 2025-05-02 Won-Gi Paeng , Daesuk Kwon , Kyungwon Jeong , Honggyo Suh

Deep learning has achieved remarkable success in modeling sequential data, including event sequences, temporal point processes, and irregular time series. Recently, transformers have largely replaced recurrent networks in these tasks.…

Machine Learning · Computer Science 2025-08-05 Ivan Karpukhin , Andrey Savchenko

Transformers have been established as the de-facto backbones for most recent advances in sequence modeling, mainly due to their growing memory capacity that scales with the context length. While plausible for retrieval tasks, it causes…

Machine Learning · Computer Science 2026-03-02 Ali Behrouz , Zeman Li , Yuan Deng , Peilin Zhong , Meisam Razaviyayn , Vahab Mirrokni

Transformer-based language models have achieved impressive success in various natural language processing tasks due to their ability to capture complex dependencies and contextual information using self-attention mechanisms. However, they…

Computation and Language · Computer Science 2023-06-26 Kaushik Roy , Yuxin Zi , Vignesh Narayanan , Manas Gaur , Amit Sheth

A world model matters to an agent only through the state it constructs. That state must preserve some information, discard other information, and support some future function: prediction, control, planning, memory, grounding, or…

Artificial Intelligence · Computer Science 2026-05-05 Keon Woo Kim

In contrast to RNNs, which compress their history into a single hidden state, Transformers can attend to all past tokens directly. However, standard Transformers rely solely on the hidden state from the previous layer to represent the…

Machine Learning · Computer Science 2025-05-29 Gleb Gerasimov , Yaroslav Aksenov , Nikita Balagansky , Viacheslav Sinii , Daniil Gavrilov

One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence diagrams are intrinsically (multi-)sets of points in…

Machine Learning · Computer Science 2022-09-27 Raphael Reinauer , Matteo Caorsi , Nicolas Berkouk

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

Machine Learning · Computer Science 2025-08-04 Saleh Nikooroo , Thomas Engel