Distribution Disagreement via Lorentzian Focal Representation

Error disagreement-based active learning (AL) selects the data that maximally update the error of a classification hypothesis. However, poor human supervision (e.g., few labels, improper classifier parameters) may weaken or clutter this update; moreover, the computational cost of performing a greedy search to estimate the errors using a deep neural network is intolerable. In this paper, a novel disagreement coefficient based on distribution, not error, provides a tighter bound on label complexity, which further guarantees its generalization in hyperbolic space. The focal points derived from the squared Lorentzian distance, present more effective hyperbolic representations on aspherical distribution from geometry, replacing the typical euclidean, kernelized, and Poincaré centroids. Experiments on different deep AL tasks show that, the focal representation adopted in a tree-likeliness splitting, significantly performs better than typical baselines of centroid representations and error disagreement, and state-of-the-art neural network architectures-based AL, dramatically accelerating the learning process.