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Understanding what makes high-dimensional data learnable is a fundamental question in machine learning.
Cognitron: A self-organizing multilayered neural network
Fukushima, K · 1975
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Generalization and network design strategies
le Cun, Y · 1989
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Learning curves: Asymptotic values and rate of convergence
Cortes, C., Jackel, L. D., Solla, S., Vapnik, V., and Denker, J · 1993
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Digital image processing
Castleman, K. R · 1996
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Elements of pattern theory
Grenander, U · 1996
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Handbook of Formal Languages
Rozenberg, G. and Salomaa, A · 1997
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Gradient-based learning applied to document recognition
Lecun, Y., Bottou, L., Bengio, Y., and Haffner, P · 1998
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Distance-based classification with lipschitz functions
Luxburg, U. v. and Bousquet, O · 2004
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Invariant scattering convolution networks
Bruna, J. and Mallat, S · 2013
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Learning the irreducible representations of commutative lie groups
Cohen, T. and Welling, M · 2014
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Visualizing and understanding convolutional networks
Zeiler, M. D. and Fergus, R · 2014
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Manitest: Are classifiers really invariant?
Fawzi, A. and Frossard, P · 2015
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Deep learning
LeCun, Y., Bengio, Y., and Hinton, G · 2015
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Very Deep Convolutional Networks for Large-Scale Image Recognition
Simonyan, K. and Zisserman, A · 2015
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Group equivariant convolutional networks
Cohen, T. and Welling, M · 2016
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Exploiting cyclic symmetry in convolutional neural networks
Dieleman, S., De Fauw, J., and Kavukcuoglu, K · 2016
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Deep Residual Learning for Image Recognition
He, K., Zhang, X., Ren, S., and Sun, J · 2016
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Understanding deep convolutional networks
Mallat, S · 2016
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Breaking the curse of dimensionality with convex neural networks
Bach, F · 2017
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The complexity of explaining neural networks through (group) invariants
Ensign, D., Neville, S., Paul, A., and Venkatasubramanian, S · 2017
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Deep learning scaling is predictable, empirically
Hestness, J., Narang, S., Ardalani, N., Diamos, G., Jun, H., Kianinejad, H., Patwary, M., Ali, M., Yang, Y., and Zhou, Y · 2017
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Why and when can deep-but not shallow-networks avoid the curse of dimensionality: a review
Poggio, T., Mhaskar, H., Rosasco, L., Miranda, B., and Liao, Q · 2017
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ADef: an Iterative Algorithm to Construct Adversarial Deformations
Alaifari, R., Alberti, G. S., and Gauksson, T · 2018
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Synthesizing Robust Adversarial Examples
Athalye, A., Engstrom, L., Ilyas, A., and Kwok, K · 2018
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Why do deep convolutional networks generalize so poorly to small image transformations?
Azulay, A. and Weiss, Y · 2018
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Geometric Robustness of Deep Networks: Analysis and Improvement
Kanbak, C., Moosavi-Dezfooli, S.-M., and Frossard, P · 2018
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On the generalization of equivariance and convolution in neural networks to the action of compact groups
Kondor, R. and Trivedi, S · 2018
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A provably correct algorithm for deep learning that actually works, 2018
Asymptotic learning curves of kernel methods: empirical data versus teacher–student paradigm
Spigler, S., Geiger, M., and Wyart, M · 2020
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The staircase property: How hierarchical structure can guide deep learning
Abbe, E., Boix-Adsera, E., Brennan, M. S., Bresler, G., and Nagaraj, D · 2021
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On the sample complexity of learning under invariance and geometric stability, 2021
Bietti, A., Venturi, L., and Bruna, J · 2021
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Provably strict generalisation benefit for invariance in kernel methods
Elesedy, B · 2021
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Provably strict generalisation benefit for equivariant models
Elesedy, B. and Zaidi, S · 2021
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Locality defeats the curse of dimensionality in convolutional teacher-student scenarios
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Malach, E. and Shalev-Shwartz, S · 2018
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Deep learning and hierarchal generative models, 2018
Mossel, E · 2018
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Pooling is neither necessary nor sufficient for appropriate deformation stability in CNNs
Ruderman, A., Rabinowitz, N. C., Morcos, A. S., and Zoran, D · 2018
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Deep learning for computer vision: A brief review
Voulodimos, A., Doulamis, N., Doulamis, A., and Protopapadakis, E · 2018
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Spatially Transformed Adversarial Examples
Xiao, C., Zhu, J.-Y., Li, B., He, W., Liu, M., and Song, D · 2018
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Strike (With) a Pose: Neural Networks Are Easily Fooled by Strange Poses of Familiar Objects
Alcorn, M. A., Li, Q., Gong, Z., Wang, C., Mai, L., Ku, W.-S., and Nguyen, A · 2019
Cited alongside, same era.
Random language model
DeGiuli, E · 2019
Cited alongside, same era.
Favero, A., Cagnetta, F., and Wyart, M · 2021
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A practical method for constructing equivariant multilayer perceptrons for arbitrary matrix groups
Finzi, M., Welling, M., and Wilson, A. G. G · 2021
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Compositionality decomposed: how do neural networks generalise? (extended abstract)
Hupkes, D., Dankers, V., Mul, M., and Bruni, E · 2021
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Learning with invariances in random features and kernel models
Mei, S., Misiakiewicz, T., and Montanari, A · 2021
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Relative stability toward diffeomorphisms indicates performance in deep nets
Petrini, L., Favero, A., Geiger, M., and Wyart, M · 2021
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Approximation and learning with deep convolutional models: a kernel perspective, 2022
Bietti, A · 2022
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Learning single-index models with shallow neural networks, 2022
Bietti, A., Bruna, J., Sanford, C., and Song, M. J · 2022
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On the opportunities and risks of foundation models, 2022
Bommasani, R., Hudson, D. A., Adeli, E., and et al · 2022
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Generalization error of random feature and kernel methods: hypercontractivity and kernel matrix concentration
Mei, S., Misiakiewicz, T., and Montanari, A · 2022
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Eigenspace restructuring: a principle of space and frequency in neural networks
Xiao, L · 2022
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Synergy and symmetry in deep learning: Interactions between the data, model, and inference algorithm
Xiao, L. and Pennington, J · 2022
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How can deep learning performs deep (hierarchical) learning, 2023
Allen-Zhu, Z. and Li, Y · 2023
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Machine learning and invariant theory, 2023
Blum-Smith, B. and Villar, S · 2023
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How deep convolutional neural networks lose spatial information with training
Tomasini, U. M., Petrini, L., Cagnetta, F., and Wyart, M · 2023
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A phase transition in diffusion models reveals the hierarchical nature of data, 2024
Sclocchi, A., Favero, A., and Wyart, M · 2024
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E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J. P., Kornbluth, M., Molinari, N., Smidt, T. E., and Kozinsky, B · 2041
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