Built on

M. Stone, The generalized Weierstrass approximation theorem
1948
Earlier work this paper cites.
Herbert Federer, Geometric measure theory
1969
Earlier work this paper cites.
A. van der Schaafa and J.H. van Haterena, Modelling the power spectra of natural images: Statistics and information
1996
Earlier work this paper cites.
Gilbert Strang and Truong Nguyen, Wavelets and filter banks
1996
Earlier work this paper cites.
A. Srivastava, A. Lee, E. Simoncelli and S.-C. Zhu, On advances in statistical modeling of natural images
2003
Earlier work this paper cites.
M. B. Wakin, D. L. Donoho, H. Choi, and R. G. Baraniuk, The multiscale structure of non-differentiable image manifolds
2005
Earlier work this paper cites.
David S. Dean and Satya N. Majumdar, Large deviations of extreme eigenvalues of random matrices
2006
Earlier work this paper cites.
A. J. Bray and D. S. Dean, Statistics of critical points of gaussian fields on large-dimensional spaces
2007
Earlier work this paper cites.
Jean-Pierre Dedieu and Gregorio Malajovich, On the number of minima of a random polynomial
2008
Earlier work this paper cites.
Anna Choromanska, Mikael Henaff, Michael Mathieu, Gérard Ben Arous and Yann LeCun, The loss surfaces of multilayer networks
Original
2014
Earlier work this paper cites.

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Later among the works it cites.
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2018

High Dimensional Spaces, Deep Learning and Adversarial Examples

Dube, Simant

Understand

In this paper, we analyze deep learning from a mathematical point of view and derive several novel results.

The results are based on intriguing mathematical properties of high dimensional spaces.
We first look at perturbation based adversarial examples and show how they can be understood using topological and geometrical arguments in high dimensions.
We point out mistake in an argument presented in prior published literature, and we present a more rigorous, general and correct mathematical result to explain adversarial examples in terms of topology of image manifolds.

Built on

M. Stone, The generalized Weierstrass approximation theorem
1948
Earlier work this paper cites.
Herbert Federer, Geometric measure theory
1969
Earlier work this paper cites.
A. van der Schaafa and J.H. van Haterena, Modelling the power spectra of natural images: Statistics and information
1996
Earlier work this paper cites.
Gilbert Strang and Truong Nguyen, Wavelets and filter banks
1996
Earlier work this paper cites.
A. Srivastava, A. Lee, E. Simoncelli and S.-C. Zhu, On advances in statistical modeling of natural images
2003
Earlier work this paper cites.
M. B. Wakin, D. L. Donoho, H. Choi, and R. G. Baraniuk, The multiscale structure of non-differentiable image manifolds
2005
Earlier work this paper cites.
David S. Dean and Satya N. Majumdar, Large deviations of extreme eigenvalues of random matrices
2006
Earlier work this paper cites.
A. J. Bray and D. S. Dean, Statistics of critical points of gaussian fields on large-dimensional spaces
2007
Earlier work this paper cites.
Jean-Pierre Dedieu and Gregorio Malajovich, On the number of minima of a random polynomial
2008
Earlier work this paper cites.
Anna Choromanska, Mikael Henaff, Michael Mathieu, Gérard Ben Arous and Yann LeCun, The loss surfaces of multilayer networks
Original
2014
Earlier work this paper cites.

Similar

Yann N. Dauphin, Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli and Yoshua Bengio, Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
Original
2014
Cited alongside, same era.
Guido Montúfar, Razvan Pascanu, Kyunghyun Cho and Yoshua Bengio, On the number of linear regions of deep neural networks
2014
Cited alongside, same era.
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian J. Goodfellow and Rob Fergus, Intriguing properties of neural networks
Original
2014
Cited alongside, same era.
Ian J. Goodfellow, Jonathon Shlens and Christian Szegedy, Explaining and harnessing adversarial examples
Original
2015
Cited alongside, same era.
A. Nguyen, J.Yosinski and J. Clune, Deep neural networks are easily fooled: High confidence predictions for unrecognizable images

Then

Alexey Kurakin, Ian J. Goodfellow and Samy Bengio, Adversarial examples in the physical world
Original
2017
Later among the works it cites.
Qianli Liao and Tomaso Poggio, Theory II: Landscape of the empirical risk in deep learning
Original
2017
Later among the works it cites.
Quynh Nguyen and Matthias Hein, The loss surface of deep and wide neural networks
Original
2017
Later among the works it cites.
Tomaso Poggio, Kenji Kawaguchi, Qianli Liao, Brando Miranda, Lorenzo Rosasco, Xavier Boix, Jack Hidary and Hrushikesh Mhaskar, Theory of deep learning III: explaining the non-overfitting puzzle
Original
2017
Later among the works it cites.
Sara Sabour, Nicholas Frosst and Geoffrey E Hinton, Dynamic routing between capsules

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2015

Cited alongside, same era.

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2016

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Thomas Tanay and Lewis Griffin, A boundary tilting persepective on the phenomenon of adversarial examples

Original

2016

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Laurent Amsaleg, James Bailey, Dominique Barbe, Sarah Erfani, Michael E. Houle, Vinh Nguyen, and Milos Radovanovic, The vulnerability of learning to adversarial perturbation increases with ? intrinsic dimensionality

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