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It has been found that residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODEs). In this paper, we explore a deeper relationship between Transformer and numerical methods of ODEs. We show that a…

Computation and Language · Computer Science 2021-04-07 Bei Li , Quan Du , Tao Zhou , Shuhan Zhou , Xin Zeng , Tong Xiao , Jingbo Zhu

Residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODE). This paper explores a deeper relationship between Transformer and numerical ODE methods. We first show that a residual block of layers in…

Computation and Language · Computer Science 2022-04-13 Bei Li , Quan Du , Tao Zhou , Yi Jing , Shuhan Zhou , Xin Zeng , Tong Xiao , JingBo Zhu , Xuebo Liu , Min Zhang

Recent advancements in large language models (LLMs) based on transformer architectures have sparked significant interest in understanding their inner workings. In this paper, we introduce a novel approach to modeling transformer…

Machine Learning · Computer Science 2025-04-17 Anh Tong , Thanh Nguyen-Tang , Dongeun Lee , Duc Nguyen , Toan Tran , David Hall , Cheongwoong Kang , Jaesik Choi

Pre-trained language models demonstrate general intelligence and common sense, but long inputs quickly become a bottleneck for memorizing information at inference time. We resurface a simple method, Memorizing Transformers (Wu et al.,…

Machine Learning · Computer Science 2024-06-05 Phoebe Klett , Thomas Ahle

While current state-of-the-art NMT models, such as RNN seq2seq and Transformers, possess a large number of parameters, they are still shallow in comparison to convolutional models used for both text and vision applications. In this work we…

Computation and Language · Computer Science 2018-09-06 Ankur Bapna , Mia Xu Chen , Orhan Firat , Yuan Cao , Yonghui Wu

Residual transformations enhance the representational depth and expressive power of large language models (LLMs). However, applying static residual transformations across all tokens in auto-regressive generation leads to a suboptimal…

Computation and Language · Computer Science 2025-02-05 Nikhil Bhendawade , Mahyar Najibi , Devang Naik , Irina Belousova

State-of-the-art results on neural machine translation often use attentional sequence-to-sequence models with some form of convolution or recursion. Vaswani et al. (2017) propose a new architecture that avoids recurrence and convolution…

Artificial Intelligence · Computer Science 2017-11-08 Karim Ahmed , Nitish Shirish Keskar , Richard Socher

Transformer is the state-of-the-art model in recent machine translation evaluations. Two strands of research are promising to improve models of this kind: the first uses wide networks (a.k.a. Transformer-Big) and has been the de facto…

Computation and Language · Computer Science 2019-06-06 Qiang Wang , Bei Li , Tong Xiao , Jingbo Zhu , Changliang Li , Derek F. Wong , Lidia S. Chao

We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…

Machine Learning · Computer Science 2023-07-25 Sören Becker , Michal Klein , Alexander Neitz , Giambattista Parascandolo , Niki Kilbertus

Transformers have become the dominant architecture for sequence modeling tasks such as natural language processing or audio processing, and they are now even considered for tasks that are not naturally sequential such as image…

Machine Learning · Computer Science 2024-03-05 Jorg Bornschein , Yazhe Li , Amal Rannen-Triki

Recently, several types of end-to-end speech recognition methods named transformer-transducer were introduced. According to those kinds of methods, transcription networks are generally modeled by transformer-based neural networks, while…

Machine Learning · Computer Science 2020-11-03 Jae-Jin Jeon , Eesung Kim

In recent years, the connections between deep residual networks and first-order Ordinary Differential Equations (ODEs) have been disclosed. In this work, we further bridge the deep neural architecture design with the second-order ODEs and…

Computer Vision and Pattern Recognition · Computer Science 2021-08-17 Duo Li , Shang-Hua Gao

Model order estimation (MOE) is often a pre-requisite for Direction of Arrival (DoA) estimation. Due to limits imposed by array geometry, it is typically not possible to estimate spatial parameters for an arbitrary number of sources; an…

Signal Processing · Electrical Eng. & Systems 2022-09-05 Jianyuan Yu , William W. Howard , Yue Xu , R. Michael Buehrer

Current Large Language Models (LLMs) face three major challenges: context length limitations, high inference costs, and catastrophic forgetting during continual learning. While Mixture-of-Experts (MoE) architectures mitigate some of these…

Machine Learning · Computer Science 2025-12-23 Zhongpan Tang

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

Machine Learning · Computer Science 2026-04-20 Ethan Mulle , Wei Kang , Qi Gong

Large Language Models (LLMs) based on transformers achieve cutting-edge results on a variety of applications. However, their enormous size and processing requirements hinder deployment on constrained resources. To enhance efficiency,…

Computation and Language · Computer Science 2026-05-13 Wazib Ansar , Saptarsi Goswami , Amlan Chakrabarti

In real-world reinforcement learning (RL) scenarios, agents often encounter partial observability, where incomplete or noisy information obscures the true state of the environment. Partially Observable Markov Decision Processes (POMDPs) are…

Machine Learning · Computer Science 2025-05-19 Ashok Arora , Neetesh Kumar

State-of-the-art neural language models (LMs) represented by Transformers are highly complex. Their use of fixed, deterministic parameter estimates fail to account for model uncertainty and lead to over-fitting and poor generalization when…

Computation and Language · Computer Science 2021-02-10 Boyang Xue , Jianwei Yu , Junhao Xu , Shansong Liu , Shoukang Hu , Zi Ye , Mengzhe Geng , Xunying Liu , Helen Meng

In deep learning, models typically reuse the same parameters for all inputs. Mixture of Experts (MoE) defies this and instead selects different parameters for each incoming example. The result is a sparsely-activated model -- with…

Machine Learning · Computer Science 2022-06-20 William Fedus , Barret Zoph , Noam Shazeer

Mixture-of-Experts (MoE) has emerged as a powerful paradigm for scaling model capacity while preserving computational efficiency. Despite its notable success in large language models (LLMs), existing attempts to apply MoE to Diffusion…

Computer Vision and Pattern Recognition · Computer Science 2026-03-03 Yujie Wei , Shiwei Zhang , Hangjie Yuan , Yujin Han , Zhekai Chen , Jiayu Wang , Difan Zou , Xihui Liu , Yingya Zhang , Yu Liu , Hongming Shan
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