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Transform coding is routinely used for lossy compression of discrete sources with memory. The input signal is divided into N-dimensional vectors, which are transformed by means of a linear mapping. Then, transform coefficients are quantized…

Information Theory · Computer Science 2016-09-13 Marco Tagliasacchi , Marco Visentini-Scarzanella , Pier Luigi Dragotti , Stefano Tubaro

Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…

Programming Languages · Computer Science 2023-04-21 Brando Miranda , Avi Shinnar , Vasily Pestun , Barry Trager

As the usage of deep learning becomes increasingly popular in mobile and embedded solutions, it is necessary to convert the framework-specific network representations into executable code for these embedded platforms. This paper consists of…

Programming Languages · Computer Science 2021-04-13 Max Sponner , Bernd Waschneck , Akash Kumar

In this note we construct a quantum Fourier transform circuit in a recursive way, by directly copying the 'divide and conquer' construction of the fast Fourier transform algorithm, rather than using the explicit formula that is given in…

Quantum Physics · Physics 2007-05-23 Gloria Paradisi , Hugues Randriam

Transformer-based models have demonstrated state-of-the-art performance in many intelligent coding tasks such as code comment generation and code completion. Previous studies show that deep learning models are sensitive to the input…

Software Engineering · Computer Science 2025-06-10 Yaoxian Li , Shiyi Qi , Cuiyun Gao , Yun Peng , David Lo , Zenglin Xu , Michael R. Lyu

Recent advances in the area of long document matching have primarily focused on using transformer-based models for long document encoding and matching. There are two primary challenges associated with these models. Firstly, the performance…

Computation and Language · Computer Science 2023-02-09 Akshita Jha , Adithya Samavedhi , Vineeth Rakesh , Jaideep Chandrashekar , Chandan K. Reddy

In this paper, we aim to build the global convergence theory of encoder-only shallow Transformers under a realistic setting from the perspective of architectures, initialization, and scaling under a finite width regime. The difficulty lies…

Machine Learning · Computer Science 2023-11-06 Yongtao Wu , Fanghui Liu , Grigorios G Chrysos , Volkan Cevher

Trained transformer models have been found to implement interpretable procedures for tasks like arithmetic and associative recall, but little is understood about how the circuits that implement these procedures originate during training. To…

Machine Learning · Computer Science 2024-10-08 Ziqian Zhong , Jacob Andreas

This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…

Computer Vision and Pattern Recognition · Computer Science 2020-08-10 Jyoti Maggu , Angshul Majumdar

Understanding the inner workings of machine learning models like Transformers is vital for their safe and ethical use. This paper provides a comprehensive analysis of a one-layer Transformer model trained to perform n-digit integer…

Machine Learning · Computer Science 2024-04-25 Philip Quirke , Fazl Barez

This document provides a brief introduction to the attention mechanism used in modern language models based on the Transformer architecture. We first illustrate how text is encoded as vectors and how the attention mechanism processes these…

Numerical Analysis · Mathematics 2026-04-02 Michel Fabrice Serret

Training transformer-based encoder-decoder models for long document summarization poses a significant challenge due to the quadratic memory consumption during training. Several approaches have been proposed to extend the input length at…

Computation and Language · Computer Science 2025-06-30 Rohit Saxena , Hao Tang , Frank Keller

People enjoy food photography because they appreciate food. Behind each meal there is a story described in a complex recipe and, unfortunately, by simply looking at a food image we do not have access to its preparation process. Therefore,…

Computer Vision and Pattern Recognition · Computer Science 2019-06-18 Amaia Salvador , Michal Drozdzal , Xavier Giro-i-Nieto , Adriana Romero

Code pre-trained models (CodePTMs) have recently demonstrated a solid capacity to process various software intelligence tasks, e.g., code clone detection, code translation, and code summarization. The current mainstream method that deploys…

Software Engineering · Computer Science 2024-05-10 Qiushi Sun , Nuo Chen , Jianing Wang , Xiang Li , Ming Gao

This paper proposes a novel approach to word embeddings in Transformer models by utilizing spinors from geometric algebra. Spinors offer a rich mathematical framework capable of capturing complex relationships and transformations in…

Machine Learning · Computer Science 2024-10-02 Rick White

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for…

Machine Learning · Computer Science 2024-07-02 Jannik Brinkmann , Abhay Sheshadri , Victor Levoso , Paul Swoboda , Christian Bartelt

In this work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps…

Machine Learning · Computer Science 2022-07-22 Sankalan Pal Chowdhury , Adamos Solomou , Avinava Dubey , Mrinmaya Sachan

We introduce a new construction of embeddings of arbitrary recursive data structures into high dimensional vectors. These embeddings provide an interpretable model for the latent state vectors of transformers. We demonstrate that these…

Machine Learning · Computer Science 2023-11-22 Joshua Maher

The Transformer architecture is shown to provide a powerful framework as an end-to-end model for building expression trees from online handwritten gestures corresponding to glyph strokes. In particular, the attention mechanism was…

Computation and Language · Computer Science 2022-11-07 Mirco Ramo , Guénolé C. M. Silvestre

In the Hydro project we are designing a compiler toolkit that can optimize for the concerns of distributed systems, including scale-up and scale-down, availability, and consistency of outcomes across replicas. This invited paper overviews…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-05-25 Joseph M. Hellerstein , Shadaj Laddad , Mae Milano , Conor Power , Mingwei Samuel