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To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…

Dynamical Systems · Mathematics 2020-10-19 Pipi Hu , Wuyue Yang , Yi Zhu , Liu Hong

With the rise of deep learning technology in practical applications, Convolutional Neural Networks (CNNs) have been able to assist humans in solving many real-world problems. To enhance the performance of CNNs, numerous network…

Machine Learning · Computer Science 2024-09-10 Qi Wang , Zijun Gao , Mingxiu Sui , Taiyuan Mei , Xiaohan Cheng , Iris Li

Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…

Machine Learning · Computer Science 2026-03-20 Yifan Zhang , Wei Bi , Kechi Zhang , Dongming Jin , Jie Fu , Zhi Jin

Deep learning has emerged as a compelling framework for scientific and engineering computing, motivating growing interest in neural network-based solvers for partial differential equations (PDEs). Within this landscape, network…

Numerical Analysis · Mathematics 2026-04-06 Tao Cheng , Lili Ju , Zhonghua Qiao , Xiaoping Zhang

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

Machine Learning · Statistics 2025-08-27 Yuji Okamoto , Tomoya Takeuchi , Yusuke Sakemi

In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide accurate and reliable analysis of a plethora of phenomena. Most notably, Physics-informed…

Machine Learning · Computer Science 2023-06-21 Mattia Silvestri , Federico Baldo , Eleonora Misino , Michele Lombardi

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Machine Learning · Computer Science 2024-10-28 Mikko Lehtimäki , Lassi Paunonen , Marja-Leena Linne

Order-agnostic autoregressive distribution (density) estimation (OADE), i.e., autoregressive distribution estimation where the features can occur in an arbitrary order, is a challenging problem in generative machine learning. Prior work on…

Machine Learning · Computer Science 2021-07-13 Michael A. Alcorn , Anh Nguyen

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…

Machine Learning · Statistics 2020-06-12 Luca Falorsi , Patrick Forré

Conditional computation and modular networks have been recently proposed for multitask learning and other problems as a way to decompose problem solving into multiple reusable computational blocks. We propose a new approach for learning…

Machine Learning · Computer Science 2021-07-26 Andrey Zhmoginov , Dina Bashkirova , Mark Sandler

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

Machine Learning · Computer Science 2022-03-04 Hanshu Yan , Jiawei Du , Vincent Y. F. Tan , Jiashi Feng

Transformers have achieved state-of-the-art performance in numerous tasks. In this paper, we propose a continuous-time formulation of transformers. Specifically, we consider a dynamical system whose governing equation is parametrized by…

Machine Learning · Computer Science 2025-02-03 Kelvin Kan , Xingjian Li , Stanley Osher

Although attention-based Neural Machine Translation has achieved remarkable progress in recent layers, it still suffers from issue of making insufficient use of the output of each layer. In transformer, it only uses the top layer of encoder…

Computation and Language · Computer Science 2021-08-02 GuoLiang Li , Yiyang Li

Neural networks have the ability to serve as universal function approximators, but they are not interpretable and don't generalize well outside of their training region. Both of these issues are problematic when trying to apply standard…

Machine Learning · Computer Science 2023-08-21 Colby Fronk , Linda Petzold

Time-series data in real-world medical settings typically exhibit long-range dependencies and are observed at non-uniform intervals. In such contexts, traditional sequence-based recurrent models struggle. To overcome this, researchers…

Machine Learning · Statistics 2024-03-18 Fernando Moreno-Pino , Álvaro Arroyo , Harrison Waldon , Xiaowen Dong , Álvaro Cartea

We show that Neural Ordinary Differential Equations (ODEs) learn representations that preserve the topology of the input space and prove that this implies the existence of functions Neural ODEs cannot represent. To address these…

Machine Learning · Statistics 2019-10-29 Emilien Dupont , Arnaud Doucet , Yee Whye Teh

Transformer models achieve remarkable success in Neural Machine Translation. Many efforts have been devoted to deepening the Transformer by stacking several units (i.e., a combination of Multihead Attentions and FFN) in a cascade, while the…

Computation and Language · Computer Science 2020-10-26 Jianhao Yan , Fandong Meng , Jie Zhou

Neural machine translation (NMT) is nowadays commonly applied at the subword level, using byte-pair encoding. A promising alternative approach focuses on character-level translation, which simplifies processing pipelines in NMT…

Computation and Language · Computer Science 2020-05-25 Nikolay Banar , Walter Daelemans , Mike Kestemont

To model the dependencies between utterances in multi-party conversations, we propose a simple and generic framework based on the dependency parsing results of utterances. Particularly, we present an approach to encoding the dependencies in…

Computation and Language · Computer Science 2023-02-22 Weizhou Shen , Xiaojun Quan , Ke Yang

Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…

Optimization and Control · Mathematics 2021-02-24 Peiyuan Zhang , Antonio Orvieto , Hadi Daneshmand , Thomas Hofmann , Roy Smith