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We approach the problem of implicit regularization in deep learning from a geometrical viewpoint. We highlight a regularization effect induc… (see more)ed by a dynamical alignment of the neural tangent features introduced by Jacot et al, along a small number of task-relevant directions. This can be interpreted as a combined mechanism of feature selection and compression. By extrapolating a new analysis of Rademacher complexity bounds for linear models, we motivate and study a heuristic complexity measure that captures this phenomenon, in terms of sequences of tangent kernel classes along optimization paths.
We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent … (see more)over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.
2018-07-02
International Conference on Machine Learning (unknown)
It is well known that over-parametrized deep neural networks (DNNs) are an overly expressive class of functions that can memorize even rando… (see more)m data with
This paper presents a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size. MINE… (see more) is back-propable and we prove that it is strongly consistent. We illustrate a handful of applications in which MINE is succesfully applied to enhance the property of generative models in both unsupervised and supervised settings. We apply our framework to estimate the information bottleneck, and apply it in tasks related to supervised classification problems. Our results demonstrate substantial added flexibility and improvement in these settings.
Recent research showed that deep neural networks are highly sensitive to so-called adversarial perturbations, which are tiny perturbations o… (see more)f the input data purposely designed to fool a machine learning classifier. Most classification models, including deep learning models, are highly vulnerable to adversarial attacks. In this work, we investigate a procedure to improve adversarial robustness of deep neural networks through enforcing representation invariance. The idea is to train the classifier jointly with a discriminator attached to one of its hidden layer and trained to filter the adversarial noise. We perform preliminary experiments to test the viability of the approach and to compare it to other standard adversarial training methods.