Manifold Contrastive Learning with Variational Lie Group Operators

Self-supervised learning of deep neural networks has become a prevalent paradigm for learning representations that transfer to a variety of downstream tasks. Similar to proposed models of the ventral stream of biological vision, it is observed that these networks lead to a separation of category manifolds in the representations of the penultimate layer. Although this observation matches the manifold hypothesis of representation learning, current self-supervised approaches are limited in their ability to explicitly model this manifold. Indeed, current approaches often only apply augmentations from a pre-specified set of "positive pairs" during learning. In this work, we propose a contrastive learning approach that directly models the latent manifold using Lie group operators parameterized by coefficients with a sparsity-promoting prior. A variational distribution over these coefficients provides a generative model of the manifold, with samples which provide feature augmentations applicable both during contrastive training and downstream tasks. Additionally, learned coefficient distributions provide a quantification of which transformations are most likely at each point on the manifold while preserving identity. We demonstrate benefits in self-supervised benchmarks for image datasets, as well as a downstream semi-supervised task. In the former case, we demonstrate that the proposed methods can effectively apply manifold feature augmentations and improve learning both with and without a projection head. In the latter case, we demonstrate that feature augmentations sampled from learned Lie group operators can improve classification performance when using few labels

Active Learning of Ordinal Embeddings: A User Study on Football Data

Humans innately measure distance between instances in an unlabeled dataset using an unknown similarity function. Distance metrics can only serve as proxy for similarity in information retrieval of similar instances. Learning a good similarity function from human annotations improves the quality of retrievals. This work uses deep metric learning to learn these user-defined similarity functions from few annotations for a large football trajectory dataset. We adapt an entropy-based active learning method with recent work from triplet mining to collect easy-to-answer but still informative annotations from human participants and use them to train a deep convolutional network that generalizes to unseen samples. Our user study shows that our approach improves the quality of the information retrieval compared to a previous deep metric learning approach that relies on a Siamese network. Specifically, we shed light on the strengths and weaknesses of passive sampling heuristics and active learners alike by analyzing the participants' response efficacy. To this end, we collect accuracy, algorithmic time complexity, the participants' fatigue and time-to-response, qualitative self-assessment and statements, as well as the effects of mixed-expertise annotators and their consistency on model performance and transfer-learning.Comment: 23 pages, 17 figure