When and How Does Known Class Help Discover Unknown Ones? Provable Understanding Through Spectral Analysis

TL;DR

This paper provides a theoretical framework for Novel Class Discovery (NCD), introducing spectral analysis and a novel loss function that helps understand when and how known classes aid in discovering unknown ones.

Contribution

It introduces a graph-theoretic spectral contrastive loss for NCD, offering theoretical guarantees and conditions for effective novel class discovery.

Findings

NSCL matches or outperforms strong baselines

Provides a provable error bound for NCD

Offers necessary and sufficient conditions for NCD success

Abstract

Novel Class Discovery (NCD) aims at inferring novel classes in an unlabeled set by leveraging prior knowledge from a labeled set with known classes. Despite its importance, there is a lack of theoretical foundations for NCD. This paper bridges the gap by providing an analytical framework to formalize and investigate when and how known classes can help discover novel classes. Tailored to the NCD problem, we introduce a graph-theoretic representation that can be learned by a novel NCD Spectral Contrastive Loss (NSCL). Minimizing this objective is equivalent to factorizing the graph's adjacency matrix, which allows us to derive a provable error bound and provide the sufficient and necessary condition for NCD. Empirically, NSCL can match or outperform several strong baselines on common benchmark datasets, which is appealing for practical usage while enjoying theoretical guarantees.