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Mathematical reasoning is one of the most impressive achievements of human intellect but remains a formidable challenge for artificial intelligence systems. In this work we explore whether modern deep learning architectures can learn to…

Machine Learning · Computer Science 2022-07-07 Samuel Cognolato , Alberto Testolin

The complexity of a learning task is increased by transformations in the input space that preserve class identity. Visual object recognition for example is affected by changes in viewpoint, scale, illumination or planar transformations.…

Computer Vision and Pattern Recognition · Computer Science 2017-03-16 Andrea Tacchetti , Stephen Voinea , Georgios Evangelopoulos

Transformer-based models have brought a radical change to neural machine translation. A key feature of the Transformer architecture is the so-called multi-head attention mechanism, which allows the model to focus simultaneously on different…

Computation and Language · Computer Science 2020-10-06 Alessandro Raganato , Yves Scherrer , Jörg Tiedemann

Mechanisms for encoding positional information are central for transformer-based language models. In this paper, we analyze the position embeddings of existing language models, finding strong evidence of translation invariance, both for the…

Computation and Language · Computer Science 2021-06-04 Ulme Wennberg , Gustav Eje Henter

Auto-regressive neural sequence models have been shown to be effective across text generation tasks. However, their left-to-right decoding order prevents generation from being parallelized. Insertion Transformer (Stern et al., 2019) is an…

Computation and Language · Computer Science 2023-02-01 Zhisong Zhang , Yizhe Zhang , Bill Dolan

Prior works have demonstrated that implicit representations trained only for reconstruction tasks typically generate encodings that are not useful for semantic tasks. In this work, we propose a method that contextualises the encodings of…

Computer Vision and Pattern Recognition · Computer Science 2023-05-23 Theo W. Costain , Kejie Li , Victor A. Prisacariu

Graph Transformers (GTs) facilitate the comprehension of graph-structured data by calculating the self-attention of node pairs without considering node position information. To address this limitation, we introduce an innovative and…

Machine Learning · Computer Science 2023-12-12 Kushal Bose , Swagatam Das

Rotary positional embedding has become the state-of-the-art approach to encode position information in transformer-based models. While it is often succinctly expressed in complex linear algebra, we note that the actual implementation of…

Machine Learning · Computer Science 2026-04-02 Beicheng Lou , Zifei Xu , Vivian W. H. Wong

Positional encodings are employed to capture the high frequency information of the encoded signals in implicit neural representation (INR). In this paper, we propose a novel positional encoding method which improves the reconstruction…

Computer Vision and Pattern Recognition · Computer Science 2023-11-13 Bharath Bhushan Damodaran , Francois Schnitzler , Anne Lambert , Pierre Hellier

An important aspect subtending language understanding and production is the ability to independently encode positional and symbolic information of the words within a sentence. In Transformers, positional information is typically encoded…

Machine Learning · Computer Science 2025-11-18 Felipe Urrutia , Jorge Salas , Alexander Kozachinskiy , Cristian Buc Calderon , Hector Pasten , Cristobal Rojas

Transformers have demonstrated outstanding performance in many applications of deep learning. When applied to time series data, transformers require effective position encoding to capture the ordering of the time series data. The efficacy…

Machine Learning · Computer Science 2024-02-21 Navid Mohammadi Foumani , Chang Wei Tan , Geoffrey I. Webb , Mahsa Salehi

In this paper, we investigate the inherent capabilities of transformer models in learning arithmetic algorithms, such as addition and parity. Through experiments and attention analysis, we identify a number of crucial factors for achieving…

Machine Learning · Computer Science 2024-05-13 Shaoxiong Duan , Yining Shi , Wei Xu

Owing to success in the data-rich domain of natural images, Transformers have recently become popular in medical image segmentation. However, the pairing of Transformers with convolutional blocks in varying architectural permutations leaves…

Computer Vision and Pattern Recognition · Computer Science 2023-04-11 Saikat Roy , Gregor Koehler , Michael Baumgartner , Constantin Ulrich , Jens Petersen , Fabian Isensee , Klaus Maier-Hein

Positional Encodings (PEs) are essential for injecting structural information into Graph Neural Networks (GNNs), particularly Graph Transformers, yet their empirical impact remains insufficiently understood. We introduce a unified…

Machine Learning · Computer Science 2026-01-15 Florian Grötschla , Jiaqing Xie , Roger Wattenhofer

Language models are increasingly capable, yet still fail at a seemingly simple task of multi-digit multiplication. In this work, we study why, by reverse-engineering a model that successfully learns multiplication via \emph{implicit…

Machine Learning · Computer Science 2025-10-02 Xiaoyan Bai , Itamar Pres , Yuntian Deng , Chenhao Tan , Stuart Shieber , Fernanda Viégas , Martin Wattenberg , Andrew Lee

Foundation language models learn from their finetuning input context in different ways. In this paper, we reformulate inputs during finetuning for challenging translation tasks, leveraging model strengths from pretraining in novel ways to…

Computation and Language · Computer Science 2026-01-05 Brian Yu , Hansen Lillemark , Kurt Keutzer

Transformers achieve remarkable performance in various domains, including NLP, CV, audio processing, and graph analysis. However, they do not scale well on long sequence tasks due to their quadratic complexity w.r.t. the inputs length.…

Machine Learning · Computer Science 2022-02-24 Maksim Zubkov , Daniil Gavrilov

Position embeddings, encoding the positional relationships among tokens in text sequences, make great contributions to modeling local context features in Transformer-based pre-trained language models. However, in Extractive Question…

Computation and Language · Computer Science 2023-11-21 Mingxu Tao , Yansong Feng , Dongyan Zhao

Numerous studies have demonstrated that the Transformer architecture possesses the capability for in-context learning (ICL). In scenarios involving function approximation, context can serve as a control parameter for the model, endowing it…

Machine Learning · Computer Science 2025-11-11 Qian Ma , Ruoxiang Xu , Yongqiang Cai

Multilingual neural machine translation has shown the capability of directly translating between language pairs unseen in training, i.e. zero-shot translation. Despite being conceptually attractive, it often suffers from low output quality.…

Computation and Language · Computer Science 2021-07-02 Danni Liu , Jan Niehues , James Cross , Francisco Guzmán , Xian Li