Geometric Space, Architecture and Learning Objective for Large Pre-Trained Models

Abstract

Large pretrained models have reshaped artificial intelligence, yet their Euclidean design assumptions often limit their ability to model hierarchy, curvature, symmetry, and heterogeneous relations in real-world data. The Geometric Space, Architecture and Learning Objective for Large Pre-Trained Models (GALOP) workshop is an accepted half-day KDD 2026 workshop that examines how geometric principles can make large pretrained models more expressive, robust, interpretable, and efficient. The workshop is organized around three complementary themes: (1) Geometric Space, which studies non-Euclidean representation spaces such as hyperbolic, spherical, and mixed-curvature manifolds; (2) Geometric Architecture, which designs model architectures that respect data symmetries, manifold structure, and relational geometry; and (3) Geometric Learning Objective, which develops objectives and optimization methods that preserve distances, angles, curvature, and topology during training. Through two invited talks and four contributed talks, the workshop brings together researchers from machine learning, data mining, and related fields to advance geometrically-informed foundation models for language, vision, graphs, knowledge discovery, and scientific discovery.