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This paper studies how Transformer models with Rotary Position Embeddings (RoPE) develop emergent, wavelet-like properties that compensate for the positional encoding's theoretical limitations. Through an analysis spanning model scales,…

Machine Learning · Computer Science 2025-06-06 Valeria Ruscio , Umberto Nanni , Fabrizio Silvestri

We propose a synthetic reasoning task, LEGO (Learning Equality and Group Operations), that encapsulates the problem of following a chain of reasoning, and we study how the Transformer architectures learn this task. We pay special attention…

Machine Learning · Computer Science 2023-02-21 Yi Zhang , Arturs Backurs , Sébastien Bubeck , Ronen Eldan , Suriya Gunasekar , Tal Wagner

Recent advances in Transformer models allow for unprecedented sequence lengths, due to linear space and time complexity. In the meantime, relative positional encoding (RPE) was proposed as beneficial for classical Transformers and consists…

Machine Learning · Computer Science 2021-06-11 Antoine Liutkus , Ondřej Cífka , Shih-Lun Wu , Umut Şimşekli , Yi-Hsuan Yang , Gaël Richard

Consider the problem of learning, from non-experimental data, the causal (Markov equivalence) structure of the true, unknown causal Bayesian network (CBN) on a given, fixed set of (categorical) variables. This learning problem is known to…

Machine Learning · Statistics 2025-02-26 Hanti Lin , Jiji Zhang

Transformer-based language models excel at both recall (retrieving memorized facts) and reasoning (performing multi-step inference), but whether these abilities rely on distinct internal mechanisms remains unclear. Distinguishing recall…

Machine Learning · Computer Science 2026-03-16 Harshwardhan Fartale , Ashish Kattamuri , Rahul Raja , Arpita Vats , Ishita Prasad , Akshata Kishore Moharir

Non-stationary sequences arise naturally in control, forecasting, and decision-making. The data-generating process shifts at unknown times, and models must detect the change, discard or downweight obsolete evidence, and adapt to new…

Machine Learning · Computer Science 2026-04-21 Carson Dudley , Yutong Bi , Xiaofeng Liu , Samet Oymak

There is mounting evidence that existing neural network models, in particular the very popular sequence-to-sequence architecture, struggle to systematically generalize to unseen compositions of seen components. We demonstrate that one of…

Computation and Language · Computer Science 2022-03-23 Hao Zheng , Mirella Lapata

Standard attention-based transformers are known to exhibit instability under learning rate overspecification during training, particularly at high learning rates. While various methods have been proposed to improve resilience to such…

Machine Learning · Computer Science 2026-02-02 Shyam Venkatasubramanian , Sean Moushegian , Michael Lin , Mir Park , Ankit Singhal , Connor Lee

There have been several post-hoc explanation approaches developed to explain pre-trained black-box neural networks. However, there is still a gap in research efforts toward designing neural networks that are inherently explainable. In this…

Computer Vision and Pattern Recognition · Computer Science 2022-07-01 Subash Khanal , Benjamin Brodie , Xin Xing , Ai-Ling Lin , Nathan Jacobs

Transformer-based neural decoders have emerged as a promising approach to error correction coding, combining data-driven adaptability with efficient modeling of long-range dependencies. This paper presents a novel decoder architecture that…

Information Theory · Computer Science 2025-09-22 Chin Wa Lau , Xiang Shi , Ziyan Zheng , Haiwen Cao , Nian Guo

Transformer architectures are now central to sequence modeling tasks. At its heart is the attention mechanism, which enables effective modeling of long-term dependencies in a sequence. Recently, transformers have been successfully applied…

Computer Vision and Pattern Recognition · Computer Science 2022-06-16 Lin Zheng , Huijie Pan , Lingpeng Kong

Transformers, and the attention mechanism in particular, have become ubiquitous in machine learning. Their success in modeling nonlocal, long-range correlations has led to their widespread adoption in natural language processing, computer…

Machine Learning · Computer Science 2025-12-23 Edoardo Calvello , Nikola B. Kovachki , Matthew E. Levine , Andrew M. Stuart

Circuit discovery and activation steering in transformers have developed as separate research threads, yet both operate on the same representational space. Are they two views of the same underlying structure? We show they follow a single…

Machine Learning · Computer Science 2026-02-11 Andres Saurez , Neha Sengar , Dongsoo Har

In-context learning refers to the ability of a model to condition on a prompt sequence consisting of in-context examples (input-output pairs corresponding to some task) along with a new query input, and generate the corresponding output.…

Computation and Language · Computer Science 2023-08-15 Shivam Garg , Dimitris Tsipras , Percy Liang , Gregory Valiant

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a…

Machine Learning · Computer Science 2023-09-01 Simon Geisler , Yujia Li , Daniel Mankowitz , Ali Taylan Cemgil , Stephan Günnemann , Cosmin Paduraru

In this paper, we try to understand neural machine translation (NMT) via simplifying NMT architectures and training encoder-free NMT models. In an encoder-free model, the sums of word embeddings and positional embeddings represent the…

Computation and Language · Computer Science 2019-07-19 Gongbo Tang , Rico Sennrich , Joakim Nivre

The Transformer is a highly successful deep learning model that has revolutionised the world of artificial neural networks, first in natural language processing and later in computer vision. This model is based on the attention mechanism…

Machine Learning · Computer Science 2023-05-09 Riccardo Ughi , Eugenio Lomurno , Matteo Matteucci

Self-attention is essential to Transformer architectures, yet how information is embedded in the self-attention matrices and how different objective functions impact this process remains unclear. We present a mathematical framework to…

Machine Learning · Computer Science 2025-06-04 Matteo Saponati , Pascal Sager , Pau Vilimelis Aceituno , Thilo Stadelmann , Benjamin Grewe

Understanding how information propagates through Transformer models is a key challenge for interpretability. In this work, we study the effects of minimal token perturbations on the embedding space. In our experiments, we analyze the…

Machine Learning · Computer Science 2025-06-24 Eddie Conti , Alejandro Astruc , Alvaro Parafita , Axel Brando

In a conventional circuit for quantum machine learning, the quantum gates used to encode the input parameters and the variational parameters are constructed with a fixed order. The resulting output function, which can be expressed in the…

Quantum Physics · Physics 2024-03-07 Nannan Ma , P. Z. Zhao , Jiangbin Gong
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