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Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…

Artificial Intelligence · Computer Science 2021-04-30 Vishesh Agarwal , Somak Aditya , Navin Goyal

Transformer based models have shown remarkable capabilities in sequence learning across a wide range of tasks, often performing well on specific task by leveraging input-output examples. Despite their empirical success, a comprehensive…

Machine Learning · Computer Science 2025-06-03 Yifan Hao , Chenlu Ye , Chi Han , Tong Zhang

The widespread 'deeper is better' philosophy has driven the creation of architectures like ResNet and Transformer, which achieve high performance by stacking numerous layers. However, increasing model depth comes with challenges such as…

Machine Learning · Computer Science 2026-02-25 Wei Wang , Xiao-Yong Wei , Qing Li

Transformers have achieved great success in effectively processing sequential data such as text. Their architecture consisting of several attention and feedforward blocks can model relations between elements of a sequence in parallel…

Machine Learning · Computer Science 2025-02-20 Jaemu Heo , Eldor Fozilov , Hyunmin Song , Taehwan Kim

Transformer models yield impressive results on many NLP and sequence modeling tasks. Remarkably, Transformers can handle long sequences which allows them to produce long coherent outputs: full paragraphs produced by GPT-3 or well-structured…

This paper is a review of the developments in Instruction level parallelism. It takes into account all the changes made in speeding up the execution. The various drawbacks and dependencies due to pipelining are discussed and various…

Hardware Architecture · Computer Science 2019-09-17 Taposh Dutta-Roy

Transformer-based encoder-decoder models produce a fused token-wise representation after every encoder layer. We investigate the effects of allowing the encoder to preserve and explore alternative hypotheses, combined at the end of the…

Computation and Language · Computer Science 2021-07-23 Mikhail Burtsev , Anna Rumshisky

The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…

Machine Learning · Computer Science 2026-01-21 Richard E. Turner

The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…

Probability · Mathematics 2016-12-02 G. Budzban , Ph. Feinsilver

Transformers process tokens in parallel but are temporally shallow: at position $t$, each layer attends to key-value pairs computed based on the previous layer, yielding a depth capped by the number of layers. Recurrent models offer…

Machine Learning · Computer Science 2026-04-24 Costin-Andrei Oncescu , Depen Morwani , Samy Jelassi , Alexandru Meterez , Mujin Kwun , Sham Kakade

We construct a model of cell reprogramming (the conversion of fully differentiated cells to a state of pluripotency, known as induced pluripotent stem cells, or iPSCs) which builds on key elements of cell biology viz. cell cycles and cell…

Cell Behavior · Quantitative Biology 2017-09-25 R Hannam , A Annibale , R Kuehn

This paper describes a design that can be used for Explainable AI. The lower level is a nested ensemble of patterns created by self-organisation. The upper level is a hierarchical tree, where nodes are linked through individual concepts, so…

Artificial Intelligence · Computer Science 2020-11-30 Kieran Greer

Pattern recognition based on a high-dimensional predictor is considered. A classifier is defined which is based on a Transformer encoder. The rate of convergence of the misclassification probability of the classifier towards the optimal…

Statistics Theory · Mathematics 2021-11-30 Iryna Gurevych , Michael Kohler , Gözde Gül Sahin

We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…

Programming Languages · Computer Science 2021-11-17 Ningning Xie , Tamara Norman , Dominik Grewe , Dimitrios Vytiniotis

Recent developments in large-scale machine learning suggest that by scaling up data, model size and training time properly, one might observe that improvements in pre-training would transfer favorably to most downstream tasks. In this work,…

Machine Learning · Computer Science 2021-10-06 Samira Abnar , Mostafa Dehghani , Behnam Neyshabur , Hanie Sedghi

Transformers trained in low precision can suffer forward-error amplification. We give a first-order, module-wise theory that predicts when and where errors grow. For self-attention we derive a per-layer bound that factorizes into three…

Machine Learning · Computer Science 2025-10-28 Jinwoo Baek

We investigate multi-scale transformer language models that learn representations of text at multiple scales, and present three different architectures that have an inductive bias to handle the hierarchical nature of language. Experiments…

Computation and Language · Computer Science 2020-05-05 Sandeep Subramanian , Ronan Collobert , Marc'Aurelio Ranzato , Y-Lan Boureau

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

Recent literature suggests that the bigger the model, the more likely it is to converge to similar, ``universal'' representations, despite different training objectives, datasets, or modalities. While this literature shows that there is an…

Computer Vision and Pattern Recognition · Computer Science 2026-01-30 Matéo Mahaut , Marco Baroni

The software development life cycle (SDLC) is a procedure used to develop a software system that meets both the customer s needs and real-world requirements. The first phase of the SDLC involves creating a conceptual model that represents…

Software Engineering · Computer Science 2021-07-30 Sabah Al-Fedaghi