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The training dynamics and generalization properties of neural networks (NN) can be precisely characterized in function space via the neural tangent kernel (NTK).
A rigorous framework for the mean field limit of multilayer neural networks
Nguyen, P.-M. and Pham, H. T · 2001
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Algorithms for learning kernels based on centered alignment
Cortes, C., Mohri, M., and Rostamizadeh, A · 2012
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Exact solutions to the nonlinear dynamics of learning in deep linear neural networks
Saxe, A. M., McClelland, J. L., and Ganguli, S · 2014
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Deep learning
LeCun, Y., Bengio, Y., and Hinton, G · 2015
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Zagoruyko, S. and Komodakis, N · 2017
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On the optimization of deep networks: Implicit acceleration by overparameterization
Arora, S., Cohen, N., and Hazan, E · 2018
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Algorithmic regularization in learning deep homogeneous models: Layers are automatically balanced, 2018
Du, S. S., Hu, W., and Lee, J. D · 2018
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Spurious local minima are common in two-layer relu neural networks
Safran, I. and Shamir, O · 2018
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On the inductive bias of neural tangent kernels, 2019
Bietti, A. and Mairal, J · 2019
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On lazy training in differentiable programming
Chizat, L., Oyallon, E., and Bach, F · 2019
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Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit
Mei, S., Misiakiewicz, T., and Montanari, A · 2019
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Mean field limit of the learning dynamics of multilayer neural networks, 2019
Nguyen, P.-M · 2019
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High-dimensional dynamics of generalization error in neural networks
Advani, M. S., Saxe, A. M., and Sompolinsky, H · 2020
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On the asymptotics of wide networks with polynomial activations, 2020
Aitken, K. and Gur-Ari, G · 2020
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Spectrum dependent learning curves in kernel regression and wide neural networks
Bordelon, B., Canatar, A., and Pehlevan, C · 2020
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Asymptotics of wide networks from feynman diagrams
Dyer, E. and Gur-Ari, G · 2020
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Convex geometry of two-layer relu networks: Implicit autoencoding and interpretable models
Ergen, T. and Pilanci, M · 2020
Mean field analysis of neural networks: A law of large numbers
Sirignano, J. and Spiliopoulos, K · 2020
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A fine-grained spectral perspective on neural networks, 2020
Yang, G. and Salman, H · 2020
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Neural networks as kernel learners: The silent alignment effect
Atanasov, A., Bordelon, B., and Pehlevan, C · 2021
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Explaining neural scaling laws
Bahri, Y., Dyer, E., Kaplan, J., Lee, J., and Sharma, U · 2021
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Implicit regularization via neural feature alignment
Baratin, A., George, T., Laurent, C., Devon Hjelm, R., Lajoie, G., Vincent, P., and Lacoste-Julien, S · 2021
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When do neural networks outperform kernel methods?*
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Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the neural tangent kernel, 2020
Fort, S., Dziugaite, G. K., Paul, M., Kharaghani, S., Roy, D. M., and Ganguli, S · 2020
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Disentangling feature and lazy training in deep neural networks
Geiger, M., Spigler, S., Jacot, A., and Wyart, M · 2020
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Dynamics of deep neural networks and neural tangent hierarchy
Huang, J. and Yau, H.-T · 2020
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Wide neural networks of any depth evolve as linear models under gradient descent
Lee, J., Xiao, L., Schoenholz, S. S., Bahri, Y., Novak, R., Sohl-Dickstein, J., and Pennington, J · 2020
Cited alongside, same era.
Neural tangents: Fast and easy infinite neural networks in python
Novak, R., Xiao, L., Hron, J., Lee, J., Alemi, A. A., Sohl-Dickstein, J., and Schoenholz, S. S · 2020
Cited alongside, same era.
Neural tangent kernel: Convergence and generalization in neural networks, 2020a
Jacot, A., Gabriel, F., and Hongler, C
Cited in the paper.
Ghorbani, B., Mei, S., Misiakiewicz, T., and Montanari, A · 2021
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Phase diagram for two-layer relu neural networks at infinite-width limit
Luo, T., Xu, Z.-Q. J., Ma, Z., and Zhang, Y · 2021
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Geometric compression of invariant manifolds in neural networks
Paccolat, J., Petrini, L., Geiger, M., Tyloo, K., and Wyart, M · 2021
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The principles of deep learning theory
Roberts, D. A., Yaida, S., and Hanin, B · 2021
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Feature learning in infinite-width neural networks, 2021
Yang, G. and Hu, E. J · 2021
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