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.
Jiahong Liu, Menglin Yang, Irwin King· Proceedings of the 32nd ACM...· 0 citations
Federated learning enables privacy-preserving collaborative training, but highly heterogeneous client data remain challenging, especially in graph federated learning where clients possess structurally diverse graphs. Existing personalized federated learning (PFL) methods ignore the intrinsic geometric properties of diverse graph structures. We propose FlatLand, a novel personalized federated learning method that embeds different clients'data in tailored Lorentz space of hyperbolic geometry. Our key insight is that hyperbolic geometry naturally accommodates the intrinsic negative curvature prevalent in real-world graphs, while the time-like dimension in Lorentz space provides a principled way to encode client-specific heterogeneity. We develop a parameter decoupling strategy that separates heterogeneous information (captured in time-like parameters) from common knowledge (preserved in space-like parameters), enabling direct aggregation without requiring client similarity estimation and extra calculation modules. Empirical results on diverse federated graph learning tasks demonstrate that FlatLand achieves superior performance, particularly in low-dimensional settings.
Jiahong Liu, Ram Samarth, Xinyu Fu et al.· 0 citations
Evaluation of long-context Large Language Models (LLMs) has advanced rapidly. However, most existing benchmarks are limited to the document level and focus mainly on high-resource languages, leaving many fine-grained challenges insufficiently evaluated. To address this gap, we present MGAL, the first multilingual, granularity- and position-aware long-context benchmark. MGAL is constructed from United Nations (UN) reports spanning 8K to 128K tokens across the six official UN languages. It covers four coherent levels of linguistic granularity (word, sentence, paragraph, and document) and further stratifies entries by their position within the document (begin, middle, and end), indexed at both the document and paragraph levels. This design enables systematic diagnosis of multilingual long-context comprehension across different granularities. Through extensive experiments and analyses, we find that: (1) LLMs perform well at word-level tasks but struggle with coarser-grained ones; and (2) Closed-source models retain a clear performance advantage in lower-resource languages. We further identify two new challenges: (1) Under local semantic crowding, where neighboring sentences share topics and entities, models tend to follow surface cues (e.g., connectives like ``however''or repeated entities) rather than the discourse role of the sentence in surrounding context (e.g., background, outcome); and (2) A gap between fluency and consistency in generated outputs, where models produce text that reads smoothly but drifts from the source facts. In addition, we observe several patterns in line with prior studies, including reliance on nearby evidence and reuse of options under uncertainty.
Chunhan Li, Chenglin Xu, Zongyang Zhang et al.· 0 citations