Distance Learner: Incorporating Manifold Prior to Model Training

Published: 29 Nov 2023, Last Modified: 29 Nov 2023NeurReps 2023 PosterEveryoneRevisionsBibTeX
Submission Track: Proceedings
Keywords: Manifold Learning, Manifold Hypothesis, Adversarial Robustness, Deep Learning
TL;DR: We propose Distance Learner, a new way to incorporate the manifold hypothesis as a prior for DNN training. Distance Learner is trained to predict distance of points from the underlying data manifold, rather than class labels.
Abstract: The manifold hypothesis (real-world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high-dimensional problems that are common in domains such as vision and speech. Multiple methods have been proposed to explicitly incorporate the manifold hypothesis as a prior in modern Deep Neural Networks (DNNs), with varying success. In this paper, we propose a new method, Distance Learner, to incorporate this prior for DNN-based classifiers. Distance Learner is trained to predict the distance of a point from the underlying manifold of each class, rather than the class label. For classification, Distance Learner then chooses the class corresponding to the closest predicted class manifold. Distance Learner can also identify points as being out of distribution (belonging to neither class), if the distance to the closest manifold is higher than a threshold. We evaluate our method on multiple synthetic datasets and show that Distance Learner learns much more meaningful classification boundaries compared to a standard classifier. We also evaluate our method on the task of adversarial robustness and find that it not only outperforms standard classifiers by a large margin but also performs at par with classifiers trained via well-accepted standard adversarial training.
Submission Number: 50