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Although ordinary differential equations (ODEs) provide insights for designing network architectures, its relationship with the non-residual convolutional neural networks (CNNs) is still unclear.
The general problem of the stability of motion
Lyapunov, A. M · 1992
Earlier work this paper cites.
Stability of nonlinear systems
Chen, G · 2001
Earlier work this paper cites.
Identity mappings in deep residual networks
He, K., Zhang, X., Ren, S., and Sun, J · 2016
Earlier work this paper cites.
A proposal on machine learning via dynamical systems
E, W · 2017
Earlier work this paper cites.
Stable architectures for deep neural networks
Haber, E. and Ruthotto, L · 2017
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Aggregated residual transformations for deep neural networks
Xie, S., Girshick, R., Dollár, P., Tu, Z., and He, K · 2017
Earlier work this paper cites.
Reversible architectures for arbitrarily deep residual neural networks
Chang, B., Meng, L., Haber, E., Ruthotto, L., Begert, D., and Holtham, E · 2018
Earlier work this paper cites.
Neural Ordinary Differential Equations
Chen, R. T. Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D · 2018
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Solving high-dimensional partial differential equations using deep learning
Han, J., Jentzen, A., and E, W · 2018
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Visualizing the loss landscape of neural nets
Li, H., Xu, Z., Taylor, G., Studer, C., and Goldstein, T · 2018
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Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations
Lu, Y., Zhong, A., Li, Q., and Dong, B · 2018
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Is robustness the cost of accuracy?–a comprehensive study on the robustness of 18 deep image classification models
Su, D., Zhang, H., Chen, H., Yi, J., Chen, P.-Y., and Gao, Y · 2018
Cited alongside, same era.
Nonlocal neural networks, nonlocal diffusion and nonlocal modeling
Tao, Y., Sun, Q., Du, Q., and Liu, W · 2018
Cited alongside, same era.
Convolutional Neural Networks combined with Runge-Kutta Methods
Augmented neural odes
Dupont, E., Doucet, A., and Teh, Y. W · 2019
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On robustness of neural ordinary differential equations
Hanshu, Y., Jiawei, D., Vincent, T., and Jiashi, F · 2019
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Benchmarking neural network robustness to common corruptions and perturbations
Hendrycks, D. and Dietterich, T · 2019
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Neural sde: Stabilizing neural ode networks with stochastic noise
Liu, X., Si, S., Cao, Q., Kumar, S., and Hsieh, C.-J · 2019
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Understanding and improving transformer from a multi-particle dynamic system point of view
Lu, Y., Li, Z., He, D., Sun, Z., Dong, B., Qin, T., Wang, L., and Liu, T.-Y · 2019
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Zhu, M., Chang, B., and Fu, C · 2018
Cited alongside, same era.
Antisymmetricrnn: A dynamical system view on recurrent neural networks
Chang, B., Chen, M., Haber, E., and Chi, E. H · 2019
Cited alongside, same era.
You only propagate once: Painless adversarial training using maximal principle
Zhang, D., Zhang, T., Lu, Y., Zhu, Z., and Dong, B
Cited in the paper.
Towards robust resnet: A small step but a giant leap
Zhang, J., Han, B., Wynter, L., Low, K. H., and Kankanhalli, M
Cited in the paper.
Reshniak, V. and Webster, C · 2019
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Enresnet: Resnet ensemble via the feynman-kac formalism
Wang, B., Yuan, B., Shi, Z., and Osher, S. J · 2019
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