Hyperbolic Learning for Structured Data, Knowledge, and Memory: A Tutorial

Abstract

Foundation models are increasingly deployed as agentic data-and-memory systems built on pretrained parameters, retrieval corpora, external knowledge stores, and persistent interaction histories. For the Knowledge Discovery and Data Mining (KDD) community, this matters because recommendation, search, temporal modeling, enterprise knowledge systems, and AI for science are tasked with organizing long-tail, hierarchical, and relational data while supporting retrieval, adaptation, and memory at scale. Yet Euclidean latent spaces can be a limited fit for tree-like or ontology-rich structure. Hyperbolic geometry offers a useful modeling tool: its exponential volume growth supports compact representations of hierarchy, association, and asymmetric neighborhoods. This lecture-style tutorial covers hyperbolic methods for data organization, retrieval, and memory layers in foundation-model systems: manifold operations, scalable neural primitives, retrieval-aware pipelines, recommendation and knowledge systems, agent memory, multimodal and scientific data modeling, and lifecycle operations including fine-tuning, editing, and unlearning. We emphasize when curved geometry can improve KDD systems and how to evaluate and deploy those gains responsibly. Homepage: https://hyperboliclearning.github.io/events/kdd2026tutorial.