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The development of methods to guide the design of neural networks is an important open challenge for deep learning theory.
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 · 1912
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Positive definite functions on spheres
Schoenberg, I. J · 1942
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Priors for infinite networks
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Solving the n-bit parity problem using neural networks
Hohil, M. E., Liu, D., and Smith, S. H · 1999
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Kernel methods for pattern analysis
Shawe-Taylor, J., Cristianini, N., et al · 2004
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The curse of highly variable functions for local kernel machines
Bengio, Y., Delalleau, O., and Le Roux, N · 2006
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On kernel target alignment
Cristianini, N., Kandola, J., Elisseeff, A., and Shawe-Taylor, J · 2006
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Scaling learning algorithms towards ai
Bengio, Y., LeCun, Y., et al · 2007
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Random features for large-scale kernel machines
Rahimi, A., Recht, B., et al · 2007
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Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning
Rahimi, A. and Recht, B · 2008
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Kernel methods for deep learning
Cho, Y. and Saul, L · 2009
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Learning multiple layers of features from tiny images
Krizhevsky, A · 2009
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Algorithms for learning kernels based on centered alignment
Cortes, C., Mohri, M., and Rostamizadeh, A · 2012
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Random feature maps for dot product kernels
Kar, P. and Karnick, H · 2012
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Analysis of boolean functions
O’Donnell, R · 2014
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Deep learning
LeCun, Y., Bengio, Y., and Hinton, G · 2015
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Spherical random features for polynomial kernels
Pennington, J., Felix, X. Y., and Kumar, S · 2015
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Toward deeper understanding of neural networks: The power of initialization and a dual view on expressivity
Daniely, A., Frostig, R., and Singer, Y · 2016
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Exponential expressivity in deep neural networks through transient chaos
Poole, B., Lahiri, S., Raghu, M., Sohl-Dickstein, J., and Ganguli, S · 2016
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Benefits of depth in neural networks
Telgarsky, M · 2016
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UCI machine learning repository, 2017
Dua, D. and Graff, C · 2017
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Why does deep and cheap learning work so well?
Lin, H. W., Tegmark, M., and Rolnick, D · 2017
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When and why are deep networks better than shallow ones?
Mhaskar, H., Liao, Q., and Poggio, T. A · 2017
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Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review
Poggio, T. A., Mhaskar, H., Rosasco, L., Miranda, B., and Liao, Q · 2017
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Towards understanding the spectral bias of deep learning
Cao, Y., Fang, Z., Wu, Y., Zhou, D.-X., and Gu, Q · 2019
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Gradient descent finds global minima of deep neural networks
Du, S., Lee, J., Li, H., Wang, L., and Zhai, X · 2019
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Asymptotics of wide networks from feynman diagrams
Dyer, E. and Gur-Ari, G · 2019
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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 · 2019
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Yang, G · 2019
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On the expressive power of deep neural networks
Raghu, M., Poole, B., Kleinberg, J. M., Ganguli, S., and Sohl-Dickstein, J · 2017
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Deep information propagation
Schoenholz, S. S., Gilmer, J., Ganguli, S., and Sohl-Dickstein, J · 2017
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JAX: composable transformations of Python+NumPy programs, 2018
Bradbury, J., Frostig, R., Hawkins, P., Johnson, M. J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., and Zhang, Q · 2018
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Neural tangent kernel: Convergence and generalization in neural networks
Jacot, A., Hongler, C., and Gabriel, F · 2018
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Deep neural networks as gaussian processes
Lee, J., Bahri, Y., Novak, R., Schoenholz, S. S., Pennington, J., and Sohl-Dickstein, J · 2018
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Gaussian process behaviour in wide deep neural networks
Matthews, A. G. d. G., Rowland, M., Hron, J., Turner, R. E., and Ghahramani, Z · 2018
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A fine-grained spectral perspective on neural networks
Yang, G. and Salman, H · 2019
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Deep equals shallow for relu networks in kernel regimes
Bietti, A. and Bach, F · 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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Infinite attention: NNGP and NTK for deep attention networks
Hron, J., Bahri, Y., Sohl-Dickstein, J., and Novak, R · 2020
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Kernel alignment risk estimator: risk prediction from training data
Jacot, A., Şimşek, B., Spadaro, F., Hongler, C., and Gabriel, F · 2020
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Finite versus infinite neural networks: an empirical study
Lee, J., Schoenholz, S. S., Pennington, J., Adlam, B., Xiao, L., Novak, R., and Sohl-Dickstein, J · 2020
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Bayesian deep learning and a probabilistic perspective of generalization
Wilson, A. G. and Izmailov, P · 2020
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Learning with convolution and pooling operations in kernel methods
Misiakiewicz, T. and Mei, S · 2021
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Heuristic search for activation functions of neural networks based on gaussian processes
Shi, X., Chen, J., and Wang, L · 2021
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Neural tangent kernel eigenvalues accurately predict generalization
Simon, J. B., Dickens, M., and DeWeese, M. R · 2021
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Eigenspace restructuring: a principle of space and frequency in neural networks
Xiao, L · 2021
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Exact marginal prior distributions of finite bayesian neural networks
Zavatone-Veth, J. and Pehlevan, C · 2021
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