Timezone: »
Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still largely unknown. This paper studies this fundamental problem in deep learning from a so-called ``neural tangent kernel'' perspective. Specifically, we first show that under proper conditions, as the width goes to infinity, training deep ResNets can be viewed as learning reproducing kernel functions with some kernel function. We then compare the kernel of deep ResNets with that of deep FFNets and discover that the class of functions induced by the kernel of FFNets is asymptotically not learnable, as the depth goes to infinity. In contrast, the class of functions induced by the kernel of ResNets does not exhibit such degeneracy. Our discovery partially justifies the advantages of deep ResNets over deep FFNets in generalization abilities. Numerical results are provided to support our claim.
Author Information
Kaixuan Huang (Princeton University)
Yuqing Wang (Georgia Institute of Technology)
Molei Tao (Georgia Institute of Technology)
Tuo Zhao (Georgia Tech)
More from the Same Authors
-
2022 : Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian »
Oswin So · Gongjie Li · Evangelos Theodorou · Molei Tao -
2022 : Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint »
Hao Liu · Minshuo Chen · Siawpeng Er · Wenjing Liao · Tong Zhang · Tuo Zhao -
2023 Poster: Deep Momentum Multi-Marginal Schrödinger Bridge »
Tianrong Chen · Guan-Horng Liu · Molei Tao · Evangelos Theodorou -
2023 Poster: Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms »
Shenao Zhang · Boyi Liu · Zhaoran Wang · Tuo Zhao -
2023 Poster: Mirror Diffusion Models for Constrained and Watermarked Generation »
Guan-Horng Liu · Tianrong Chen · Evangelos Theodorou · Molei Tao -
2023 Poster: Module-wise Adaptive Distillation for Multimodality Foundation Models »
Chen Liang · Jiahui Yu · Ming-Hsuan Yang · Matthew Brown · Yin Cui · Tuo Zhao · Boqing Gong · Tianyi Zhou -
2023 Poster: Robust Multi-Agent Reinforcement Learning via Adversarial Regularization: Theoretical Foundation and Stable Algorithms »
Alexander Bukharin · Yan Li · Yue Yu · Qingru Zhang · Zhehui Chen · Simiao Zuo · Chao Zhang · Songan Zhang · Tuo Zhao -
2022 Poster: Alternating Mirror Descent for Constrained Min-Max Games »
Andre Wibisono · Molei Tao · Georgios Piliouras -
2022 Poster: On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds »
Biraj Dahal · Alexander Havrilla · Minshuo Chen · Tuo Zhao · Wenjing Liao -
2021 Poster: Pessimism Meets Invariance: Provably Efficient Offline Mean-Field Multi-Agent RL »
Minshuo Chen · Yan Li · Ethan Wang · Zhuoran Yang · Zhaoran Wang · Tuo Zhao -
2021 Poster: Going Beyond Linear RL: Sample Efficient Neural Function Approximation »
Baihe Huang · Kaixuan Huang · Sham Kakade · Jason Lee · Qi Lei · Runzhe Wang · Jiaqi Yang -
2021 Poster: Fast Federated Learning in the Presence of Arbitrary Device Unavailability »
Xinran Gu · Kaixuan Huang · Jingzhao Zhang · Longbo Huang -
2021 Poster: Optimal Gradient-based Algorithms for Non-concave Bandit Optimization »
Baihe Huang · Kaixuan Huang · Sham Kakade · Jason Lee · Qi Lei · Runzhe Wang · Jiaqi Yang -
2020 Session: Orals & Spotlights Track 34: Deep Learning »
Tuo Zhao · Jimmy Ba -
2020 Poster: Differentiable Top-k with Optimal Transport »
Yujia Xie · Hanjun Dai · Minshuo Chen · Bo Dai · Tuo Zhao · Hongyuan Zha · Wei Wei · Tomas Pfister -
2020 Poster: Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function »
Lingkai Kong · Molei Tao -
2020 Poster: Towards Understanding Hierarchical Learning: Benefits of Neural Representations »
Minshuo Chen · Yu Bai · Jason Lee · Tuo Zhao · Huan Wang · Caiming Xiong · Richard Socher -
2019 : Poster and Coffee Break 2 »
Karol Hausman · Kefan Dong · Ken Goldberg · Lihong Li · Lin Yang · Lingxiao Wang · Lior Shani · Liwei Wang · Loren Amdahl-Culleton · Lucas Cassano · Marc Dymetman · Marc Bellemare · Marcin Tomczak · Margarita Castro · Marius Kloft · Marius-Constantin Dinu · Markus Holzleitner · Martha White · Mengdi Wang · Michael Jordan · Mihailo Jovanovic · Ming Yu · Minshuo Chen · Moonkyung Ryu · Muhammad Zaheer · Naman Agarwal · Nan Jiang · Niao He · Nikolaus Yasui · Nikos Karampatziakis · Nino Vieillard · Ofir Nachum · Olivier Pietquin · Ozan Sener · Pan Xu · Parameswaran Kamalaruban · Paul Mineiro · Paul Rolland · Philip Amortila · Pierre-Luc Bacon · Prakash Panangaden · Qi Cai · Qiang Liu · Quanquan Gu · Raihan Seraj · Richard Sutton · Rick Valenzano · Robert Dadashi · Rodrigo Toro Icarte · Roshan Shariff · Roy Fox · Ruosong Wang · Saeed Ghadimi · Samuel Sokota · Sean Sinclair · Sepp Hochreiter · Sergey Levine · Sergio Valcarcel Macua · Sham Kakade · Shangtong Zhang · Sheila McIlraith · Shie Mannor · Shimon Whiteson · Shuai Li · Shuang Qiu · Wai Lok Li · Siddhartha Banerjee · Sitao Luan · Tamer Basar · Thinh Doan · Tianhe Yu · Tianyi Liu · Tom Zahavy · Toryn Klassen · Tuo Zhao · Vicenç Gómez · Vincent Liu · Volkan Cevher · Wesley Suttle · Xiao-Wen Chang · Xiaohan Wei · Xiaotong Liu · Xingguo Li · Xinyi Chen · Xingyou Song · Yao Liu · YiDing Jiang · Yihao Feng · Yilun Du · Yinlam Chow · Yinyu Ye · Yishay Mansour · · Yonathan Efroni · Yongxin Chen · Yuanhao Wang · Bo Dai · Chen-Yu Wei · Harsh Shrivastava · Hongyang Zhang · Qinqing Zheng · SIDDHARTHA SATPATHI · Xueqing Liu · Andreu Vall -
2019 : Poster Spotlight 2 »
Aaron Sidford · Mengdi Wang · Lin Yang · Yinyu Ye · Zuyue Fu · Zhuoran Yang · Yongxin Chen · Zhaoran Wang · Ofir Nachum · Bo Dai · Ilya Kostrikov · Dale Schuurmans · Ziyang Tang · Yihao Feng · Lihong Li · Denny Zhou · Qiang Liu · Rodrigo Toro Icarte · Ethan Waldie · Toryn Klassen · Rick Valenzano · Margarita Castro · Simon Du · Sham Kakade · Ruosong Wang · Minshuo Chen · Tianyi Liu · Xingguo Li · Zhaoran Wang · Tuo Zhao · Philip Amortila · Doina Precup · Prakash Panangaden · Marc Bellemare -
2019 Poster: Towards Understanding the Importance of Shortcut Connections in Residual Networks »
Tianyi Liu · Minshuo Chen · Mo Zhou · Simon Du · Enlu Zhou · Tuo Zhao -
2018 Poster: Provable Gaussian Embedding with One Observation »
Ming Yu · Zhuoran Yang · Tuo Zhao · Mladen Kolar · Zhaoran Wang