Deep Learning via Dynamical Systems: An Approximation Perspective

22 December 2019

Papers citing "Deep Learning via Dynamical Systems: An Approximation Perspective"

50 / 62 papers shown

Title
Universal Approximation Theorem for Deep Q-Learning via FBSDE System Qian Qi 29 0 0 09 May 2025
Universal Approximation Theorem of Deep Q-Networks Qian Qi 37 1 0 04 May 2025
Uncertainty propagation in feed-forward neural network models Jeremy Diamzon Daniele Venturi 62 0 0 27 Mar 2025
Finite Samples for Shallow Neural Networks Yu Xia Zhiqiang Xu 43 0 0 17 Mar 2025
Numerical and statistical analysis of NeuralODE with Runge-Kutta time integration Emily C. Ehrhardt Hanno Gottschalk Tobias Riedlinger 41 0 0 13 Mar 2025
Universal approximation property of ODENet and ResNet with a single activation function M. Kimura Kazunori Matsui Yosuke Mizuno 28 0 0 22 Oct 2024
Feedback Favors the Generalization of Neural ODEs Jindou Jia Zihan Yang Meng Wang Kexin Guo Jianfei Yang Xiang Yu Lei Guo OOD AI4CE 43 2 0 14 Oct 2024
Demystifying the Token Dynamics of Deep Selective State Space Models Thieu N. Vo Tung D. Pham Xin T. Tong Tan Minh Nguyen Mamba 49 0 0 04 Oct 2024
Deep Koopman-layered Model with Universal Property Based on Toeplitz Matrices Yuka Hashimoto Tomoharu Iwata 28 0 0 03 Oct 2024
Clustering in pure-attention hardmax transformers and its role in sentiment analysis Albert Alcalde Giovanni Fantuzzi Enrique Zuazua 35 3 0 26 Jun 2024
Graph Neural Aggregation-diffusion with Metastability Kaiyuan Cui Xinyan Wang Zicheng Zhang Weichen Zhao 39 2 0 29 Mar 2024
Diffeomorphic Measure Matching with Kernels for Generative Modeling Biraj Pandey Bamdad Hosseini Pau Batlle H. Owhadi 23 3 0 12 Feb 2024
Interplay between depth and width for interpolation in neural ODEs Antonio Álvarez-López Arselane Hadj Slimane Enrique Zuazua 23 7 0 18 Jan 2024
Differential Equations for Continuous-Time Deep Learning Lars Ruthotto AI4TS AI4CE SyDa BDL 37 7 0 08 Jan 2024
A mathematical perspective on Transformers Borjan Geshkovski Cyril Letrouit Yury Polyanskiy Philippe Rigollet EDL AI4CE 42 36 0 17 Dec 2023
From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond Andi Han Dai Shi Lequan Lin Junbin Gao AI4CE GNN 37 21 0 16 Oct 2023
Minimum width for universal approximation using ReLU networks on compact domain Namjun Kim Chanho Min Sejun Park VLM 29 10 0 19 Sep 2023
Distribution learning via neural differential equations: a nonparametric statistical perspective Youssef Marzouk Zhi Ren Sven Wang Jakob Zech 29 11 0 03 Sep 2023
On the Approximation of Bi-Lipschitz Maps by Invertible Neural Networks Bangti Jin Zehui Zhou Jun Zou 26 3 0 18 Aug 2023
Deep Network Approximation: Beyond ReLU to Diverse Activation Functions Shijun Zhang Jianfeng Lu Hongkai Zhao 27 17 0 13 Jul 2023
A Constructive Approach to Function Realization by Neural Stochastic Differential Equations Tanya Veeravalli Maxim Raginsky 11 0 0 01 Jul 2023
Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes Yuxiao Wen Eric Vanden-Eijnden Benjamin Peherstorfer 24 12 0 27 Jun 2023
Vocabulary for Universal Approximation: A Linguistic Perspective of Mapping Compositions Yongqiang Cai CoGe 80 6 0 20 May 2023
Universal Approximation Property of Hamiltonian Deep Neural Networks M. Zakwan M. d’Angelo Giancarlo Ferrari-Trecate 36 5 0 21 Mar 2023
On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network Shijun Zhang Jianfeng Lu Hongkai Zhao CoGe 33 4 0 29 Jan 2023
Nonlinear controllability and function representation by neural stochastic differential equations Tanya Veeravalli Maxim Raginsky DiffM 13 2 0 01 Dec 2022
Learning Robust State Observers using Neural ODEs (longer version) Keyan Miao Konstantinos Gatsis OOD 11 12 0 01 Dec 2022
On the Universal Approximation Property of Deep Fully Convolutional Neural Networks Ting-Wei Lin Zuowei Shen Qianxiao Li 34 4 0 25 Nov 2022
Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems Lianghao Cao Thomas O'Leary-Roseberry Prashant K. Jha J. Oden Omar Ghattas 28 26 0 06 Oct 2022
Dynamical systems' based neural networks E. Celledoni Davide Murari B. Owren Carola-Bibiane Schönlieb Ferdia Sherry OOD 43 10 0 05 Oct 2022
Achieve the Minimum Width of Neural Networks for Universal Approximation Yongqiang Cai 11 18 0 23 Sep 2022
Neural Generalized Ordinary Differential Equations with Layer-varying Parameters Duo Yu Hongyu Miao Hulin Wu 35 4 0 21 Sep 2022
The Mori-Zwanzig formulation of deep learning D. Venturi Xiantao Li 25 1 0 12 Sep 2022
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems Qianxiao Li T. Lin Zuowei Shen 21 6 0 18 Aug 2022
Analysis of function approximation and stability of general DNNs in directed acyclic graphs using un-rectifying analysis Wonjun Hwang Shih-Shuo Tung 11 4 0 13 Jun 2022
Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems Andrés Felipe Lerma Pineda P. Petersen 26 5 0 02 Jun 2022
Do Residual Neural Networks discretize Neural Ordinary Differential Equations? Michael E. Sander Pierre Ablin Gabriel Peyré 35 25 0 29 May 2022
Neural Network Architecture Beyond Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 3DV MDE 33 13 0 19 May 2022
Universal approximation property of invertible neural networks Isao Ishikawa Takeshi Teshima Koichi Tojo Kenta Oono Masahiro Ikeda Masashi Sugiyama 41 29 0 15 Apr 2022
Learning via nonlinear conjugate gradients and depth-varying neural ODEs George Baravdish Gabriel Eilertsen Rym Jaroudi B. Johansson Lukávs Malý Jonas Unger 18 3 0 11 Feb 2022
Learning High-Dimensional Parametric Maps via Reduced Basis Adaptive Residual Networks Thomas O'Leary-Roseberry Xiaosong Du A. Chaudhuri J. Martins Karen E. Willcox Omar Ghattas 30 22 0 14 Dec 2021
Neural network stochastic differential equation models with applications to financial data forecasting Luxuan Yang Ting Gao Yubin Lu Jinqiao Duan Tao Liu AI4TS 13 37 0 25 Nov 2021
Deep Network Approximation in Terms of Intrinsic Parameters Zuowei Shen Haizhao Yang Shijun Zhang 21 9 0 15 Nov 2021
TaylorSwiftNet: Taylor Driven Temporal Modeling for Swift Future Frame Prediction M. Pourheydari Emad Bahrami Rad Mohsen Fayyaz Gianpiero Francesca M. Noroozi Juergen Gall 22 1 0 27 Oct 2021
Neural Flows: Efficient Alternative to Neural ODEs Marin Bilovs Johanna Sommer Syama Sundar Rangapuram Tim Januschowski Stephan Günnemann AI4TS 21 70 0 25 Oct 2021
Heavy Ball Neural Ordinary Differential Equations Hedi Xia Vai Suliafu H. Ji T. Nguyen Andrea L. Bertozzi Stanley J. Osher Bao Wang 35 56 0 10 Oct 2021
An Optimal Control Framework for Joint-channel Parallel MRI Reconstruction without Coil Sensitivities Wanyu Bian Yunmei Chen X. Ye 44 14 0 20 Sep 2021
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons Zuowei Shen Haizhao Yang Shijun Zhang 56 36 0 06 Jul 2021
Approximation capabilities of measure-preserving neural networks Aiqing Zhu Pengzhan Jin Yifa Tang 21 8 0 21 Jun 2021
Calibrating multi-dimensional complex ODE from noisy data via deep neural networks Kexuan Li Fangfang Wang Ruiqi Liu Fan Yang Zuofeng Shang 29 7 0 07 Jun 2021