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title={Gaussian processes for machine learning},
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title={Understanding deep learning (still) requires rethinking generalization},
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journal={Communications of the ACM},
volume={64},
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year={2021},
publisher={ACM New York, NY, USA}
}
@inproceedings{zhang2017understanding,
title={Understanding deep learning requires rethinking generalization},
author={Chiyuan Zhang and Samy Bengio and Moritz Hardt and Benjamin Recht and Oriol Vinyals},
booktitle={International Conference on Learning Representations},
year={2017},
}
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title={On exact computation with an infinitely wide neural net},
author={Arora, Sanjeev and Du, Simon S and Hu, Wei and Li, Zhiyuan and Salakhutdinov, Russ R and Wang, Ruosong},
journal={Advances in neural information processing systems},
volume={32},
year={2019}
}
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title={Learning with kernels: support vector machines, regularization, optimization, and beyond},
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year={2002},
publisher={MIT press}
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pages={370--378},
year={2016},
organization={PMLR}
}
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title={Facenet: A unified embedding for face recognition and clustering},
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pages={815--823},
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}
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title={On the expressive power of deep neural networks},
author={Raghu, Maithra and Poole, Ben and Kleinberg, Jon and Ganguli, Surya and Sohl-Dickstein, Jascha},
booktitle={international conference on machine learning},
pages={2847--2854},
year={2017},
organization={PMLR}
}
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title={The geometry of random features},
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booktitle={International Conference on Artificial Intelligence and Statistics},
pages={1--9},
year={2018},
organization={PMLR}
}
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title={Dynamical isometry and a mean field theory of RNNs: Gating enables signal propagation in recurrent neural networks},
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booktitle={International Conference on Machine Learning},
pages={873--882},
year={2018},
organization={PMLR}
}
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title={Siamese neural networks for one-shot image recognition},
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organization={Lille}
}
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title = {On the Impact of the Activation function on Deep Neural Networks Training},
author = {Hayou, Soufiane and Doucet, Arnaud and Rousseau, Judith},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {2672--2680},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/hayou19a/hayou19a.pdf},
abstract = {The weight initialization and the activation function of deep neural networks have a crucial impact on the performance of the training procedure. An inappropriate selection can lead to the loss of information of the input during forward propagation and the exponential vanishing/exploding of gradients during back-propagation. Understanding the theoretical properties of untrained random networks is key to identifying which deep networks may be trained successfully as recently demonstrated by Samuel et al. (2017) who showed that for deep feedforward neural networks only a specific choice of hyperparameters known as the ‘Edge of Chaos’ can lead to good performance. While the work by Samuel et al. (2017) discuss trainability issues, we focus here on training acceleration and overall performance. We give a comprehensive theoretical analysis of the Edge of Chaos and show that we can indeed tune the initialization parameters and the activation function in order to accelerate the training and improve the performance.}
}
@inproceedings{allen2019convergence,
title={A convergence theory for deep learning via over-parameterization},
author={Allen-Zhu, Zeyuan and Li, Yuanzhi and Song, Zhao},
booktitle={International conference on machine learning},
pages={242--252},
year={2019},
organization={PMLR}
}
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title={Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks},
author={Arora, Sanjeev and Du, Simon and Hu, Wei and Li, Zhiyuan and Wang, Ruosong},
booktitle={International Conference on Machine Learning},
pages={322--332},
year={2019},
organization={PMLR}
}
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author = {Latouche, Guy and Ramaswami, Vaidyanathan},
publisher = {SIAM},
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}
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title={Finite-sample properties of the k-class estimators},
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@inproceedings{meterez2024towards,
title={Towards Training Without Depth Limits: Batch Normalization Without Gradient Explosion},
author={Alexandru Meterez and Amir Joudaki and Francesco Orabona and Alexander Immer and Gunnar Ratsch and Hadi Daneshmand},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
}
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author = {Braun, Michael and McAuliffe, Jon},
journal = {Journal of the American Statistical Association},
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year = {2010}
}
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author = {Hazra, Sayan and Banerjee, Soumi and Ghosh, Kripabandhu and Ghosh, Saptarshi and Mehta, Parth},
booktitle = {Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics},
title = {A DET for Natural Language Inference: Generating Natural Language Inference Explanation Trees using Deep Generative Models},
year = {2019}
}
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author = {Chizat, L\'{e}na\"{\i}c and Bach, Francis},
booktitle = {Advances in Neural Information Processing Systems},
journal = {Advances in Neural Information Processing Systems},
title = {On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport},
year = {2018}
}
@inproceedings{chizat2020implicit,
author = {Chizat, Lenaic and Bach, Francis},
booktitle = {Conference on Learning Theory},
pages = {1305--1338},
title = {Implicit bias of gradient descent for wide two-layer neural networks trained with the logistic loss},
year = {2020}
}
@inproceedings{ba2019generalization,
author = {Ba, Jimmy and Erdogdu, Murat and Suzuki, Taiji and Wu, Denny and Zhang, Tianzong},
booktitle = {International Conference on Learning Representations},
title = {Generalization of two-layer neural networks: An asymptotic viewpoint},
year = {2019}
}
@inproceedings{pmlrv9glorot10a,
author = {Glorot, Xavier and Bengio, Yoshua},
booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics},
pages = {249--256},
title = {Understanding the difficulty of training deep feedforward neural networks},
year = {2010}
}
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author = {Hanin, Boris and Nica, Mihai},
journal = {arXiv preprint arXiv:1909.05989},
title = {Finite depth and width corrections to the neural tangent kernel},
year = {2019}
}
@article{hanin2022correlation,
author = {Hanin, Boris},
journal = {arXiv preprint arXiv:2204.01058},
title = {Correlation Functions in Random Fully Connected Neural Networks at Finite Width},
year = {2022}
}
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author = {Rosenthal, Jeffrey S.},
journal = {Journal of the American Statistical Association},
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publisher = {Taylor \& Francis},
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}
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author = {{Jones, Galin L. and Hobert, James P.}},
journal = {Statistical Science},
pages = {312--334},
publisher = {JSTOR},
title = {{Honest exploration of intractable probability distributions via Markov chain Monte Carlo}},
year = {2001}
}
@article{doeblin1938deux,
author = {Doeblin, Wolfgang},
journal = {Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
pages = {210--220},
title = {{Sur deux probl{\`e}mes de M. {K}olmogoroff concernant les cha{\^\i}nes d{\'e}nombrables}},
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author = {Hoffman, Alan J. and Wielandt, Helmut W},
booktitle = {Selected Papers Of Alan J. Hoffman: With Commentary},
pages = {118--120},
publisher = {World Scientific},
title = {The variation of the spectrum of a normal matrix},
year = {2003}
}
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author = {Pastur, LA and Martchenko, VA},
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@article{daneshmand2022polynomial,
title={Polynomial-time Sparse Measure Recovery: From Mean Field Theory to Algorithm Design},
author={Daneshmand, Hadi and Bach, Francis},
journal={arXiv preprint arXiv:2204.07879},
year={2022}
}
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author = {Devroye, Luc and Mehrabian, Abbas and Reddad, Tommy},
journal = {arXiv preprint arXiv:1810.08693},
title = {The total variation distance between high-dimensional {G}aussians},
year = {2018}
}
@article{liu2019roberta,
author = {Liu, Yinhan and Ott, Myle and Goyal, Naman and Du, Jingfei and Joshi, Mandar and Chen, Danqi and Levy, Omer and Lewis, Mike and Zettlemoyer, Luke and Stoyanov, Veselin},
journal = {arXiv preprint arXiv:1907.11692},
title = {{RoBERTa}: A robustly optimized {BERT} pretraining approach},
year = {2019}
}
@article{brown2020language,
author = {Brown, Tom and Mann, Benjamin and Ryder, Nick and Subbiah, Melanie and Kaplan, Jared D and Dhariwal, Prafulla and Neelakantan, Arvind and Shyam, Pranav and Sastry, Girish and Askell, Amanda and Agarwal, Sandhini and Herbert-Voss, Ariel and Krueger, Gretchen and Henighan, Tom and Child, Rewon and Ramesh, Aditya and Ziegler, Daniel and Wu, Jeffrey and Winter, Clemens and Hesse, Chris and Chen, Mark and Sigler, Eric and Litwin, Mateusz and Gray, Scott and Chess, Benjamin and Clark, Jack and Berner, Christopher and McCandlish, Sam and Radford, Alec and Sutskever, Ilya and Amodei, Dario},
journal = {Advances in neural information processing systems},
pages = {1877--1901},
title = {Language models are few-shot learners},
volume = {33},
year = {2020}
}
@article{goyal2021larger,
author = {Goyal, Naman and Du, Jingfei and Ott, Myle and Anantharaman, Giri and Conneau, Alexis},
journal = {arXiv preprint arXiv:2105.00572},
title = {Larger-scale transformers for multilingual masked language modeling},
year = {2021}
}
@article{raffel2020exploring,
author = {Raffel, Colin and Shazeer, Noam and Roberts, Adam and Lee, Katherine and Narang, Sharan and Matena, Michael and Zhou, Yanqi and Li, Wei and Liu, Peter J},
journal = {The Journal of Machine Learning Research},
number = {1},
pages = {5485--5551},
publisher = {JMLRORG},
title = {Exploring the limits of transfer learning with a unified text-to-text transformer},
volume = {21},
year = {2020}
}
@inproceedings{liu2022convnet,
author = {Liu, Zhuang and Mao, Hanzi and Wu, Chao-Yuan and Feichtenhofer, Christoph and Darrell, Trevor and Xie, Saining},
booktitle = {Proceedings of the IEEE/CVF conference on computer vision and pattern recognition},
pages = {11976--11986},
title = {A {ConvNet} for the 2020s},
year = {2022}
}
@inproceedings{woo2023convnext,
author = {Woo, Sanghyun and Debnath, Shoubhik and Hu, Ronghang and Chen, Xinlei and Liu, Zhuang and Kweon, In So and Xie, Saining},
booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
pages = {16133--16142},
title = {{ConvNeXt V2}: Co-designing and scaling convnets with masked autoencoders},
year = {2023}
}
@inproceedings{wu2021cvt,
author = {Wu, Haiping and Xiao, Bin and Codella, Noel and Liu, Mengchen and Dai, Xiyang and Yuan, Lu and Zhang, Lei},
booktitle = {Proceedings of the IEEE/CVF international conference on computer vision},
pages = {22--31},
title = {{Cvt}: Introducing convolutions to vision transformers},
year = {2021}
}
@article{feng2022rank,
author = {Feng, Ruili and Zheng, Kecheng and Huang, Yukun and Zhao, Deli and Jordan, Michael and Zha, Zheng-Jun},
journal = {Advances in Neural Information Processing Systems},
pages = {33054--33065},
title = {Rank diminishing in deep neural networks},
volume = {35},
year = {2022}
}
@article{joudaki2023impact,
title={On the impact of activation and normalization in obtaining isometric embeddings at initialization},
author={Joudaki, Amir and Daneshmand, Hadi and Bach, Francis},
journal={Advances in Neural Information Processing Systems},
volume={36},
pages={39855--39875},
year={2023}
}
@inproceedings{he2016res,
author = {He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
booktitle = {Proceedings of the IEEE conference on computer vision and pattern recognition},
pages = {770--778},
title = {Deep residual learning for image recognition},
year = {2016}
}
@article{burkholz2019initialization,
author = {Burkholz, Rebekka and Dubatovka, Alina},
journal = {Advances in Neural Information Processing Systems},
title = {Initialization of relus for dynamical isometry},
volume = {32},
year = {2019}
}
@article{brock2021characterizing,
author = {Brock, Andrew and De, Soham and Smith, Samuel L},
journal = {arXiv preprint arXiv:2101.08692},
title = {Characterizing signal propagation to close the performance gap in unnormalized resnets},
year = {2021}
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