In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.

A: Shortest path distance in random k-nearest neighbor graphs
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Q: Despite being so vital to success of Support Vector Machines, the principle of separating margin maximisation is not used in deep learning. We show that minimisation of margin variance and not maximisation of the margin is more suitable for improving generalisation in deep architectures. We propose the Halfway loss function that minimises the Normalised Margin Variance (NMV) at the output of a deep learning models and evaluate its performance against the Softmax Cross-Entropy loss on the MNIST, smallNORB and CIFAR-10 datasets.

A: Effects of the optimisation of the margin distribution on generalisation in deep architectures
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Q: Feature squeezing is a recently-introduced framework for mitigating and detecting adversarial examples. In previous work, we showed that it is effective against several earlier methods for generating adversarial examples. In this short note, we report on recent results showing that simple feature squeezing techniques also make deep learning models significantly more robust against the Carlini/Wagner attacks, which are the best known adversarial methods discovered to date.

A:
Feature Squeezing Mitigates and Detects Carlini/Wagner Adversarial Examples
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