# Margin Preservation of Deep Neural Networks

@article{Sokoli2016MarginPO, title={Margin Preservation of Deep Neural Networks}, author={Jure Sokoli{\'c} and Raja Giryes and Guillermo Sapiro and Miguel R. D. Rodrigues}, journal={ArXiv}, year={2016}, volume={abs/1605.08254} }

The generalization error of deep neural networks via their classification margin is studied in this work, providing novel generalization error bounds that are independent of the network depth, thereby avoiding the common exponential depth-dependency which is unrealistic for current networks with hundreds of layers. We show that a large margin linear classifier operating at the output of a deep neural network induces a large classification margin at the input of the network, provided that the…

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## References

SHOWING 1-10 OF 23 REFERENCES

### Large Margin Deep Neural Networks: Theory and Algorithms

- Computer ScienceArXiv
- 2015

A new margin bound for DNN is derived, in which the expected0-1 error of a DNN model is upper bounded by its empirical margin plus a Rademacher Average based capacity term, which is consistent with the empirical behaviors of DNN models.

### Deep Neural Networks with Random Gaussian Weights: A Universal Classification Strategy?

- Computer ScienceIEEE Transactions on Signal Processing
- 2016

It is formally proved that these networks with random Gaussian weights perform a distance-preserving embedding of the data, with a special treatment for in-class and out-of-class data.

### Deep Learning using Linear Support Vector Machines

- Computer Science
- 2013

The results using L2-SVMs show that by simply replacing softmax with linear SVMs gives significant gains on popular deep learning datasets MNIST, CIFAR-10, and the ICML 2013 Representation Learning Workshop's face expression recognition challenge.

### Deep Residual Learning for Image Recognition

- Computer Science2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
- 2016

This work presents a residual learning framework to ease the training of networks that are substantially deeper than those used previously, and provides comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth.

### Breaking the Curse of Dimensionality with Convex Neural Networks

- Computer ScienceJ. Mach. Learn. Res.
- 2017

This work considers neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units and shows that they are adaptive to unknown underlying linear structures, such as the dependence on the projection of the input variables onto a low-dimensional subspace.

### Contractive Rectifier Networks for Nonlinear Maximum Margin Classification

- Computer Science2015 IEEE International Conference on Computer Vision (ICCV)
- 2015

Experimental results demonstrate that the proposed contractive rectifier networks consistently outperform their conventional unconstrained rectifier network counterparts.

### Discriminative Robust Transformation Learning

- Computer ScienceNIPS
- 2015

A framework for learning features that are robust to data variation, which is particularly important when only a limited number of training samples are available, is proposed, thereby providing theoretical justification for reductions in generalization error observed in experiments.

### On the Number of Linear Regions of Deep Neural Networks

- Computer ScienceNIPS
- 2014

We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep…

### ImageNet classification with deep convolutional neural networks

- Computer ScienceCommun. ACM
- 2012

A large, deep convolutional neural network was trained to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes and employed a recently developed regularization method called "dropout" that proved to be very effective.

### Global Optimality in Tensor Factorization, Deep Learning, and Beyond

- Computer ScienceArXiv
- 2015

This framework derives sufficient conditions to guarantee that a local minimum of the non-convex optimization problem is a global minimum and shows that if the size of the factorized variables is large enough then from any initialization it is possible to find a global minimizer using a purely local descent algorithm.