CORDS - Continuous Representations of Discrete Structures

ICLR 2026 Conference Submission25519 Authors

Keywords: Continuous set representations, Neural fields, Variable-cardinality prediction, Invertible encoding/decoding, Diffusion and flow matching, Object detection, Molecular generation, Simulation-based inference

TL;DR: We turn discrete objects into continuous fields that implicitly encode their count, offering a simple way to handle variable cardinality across tasks and domains.

Abstract: Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection. Existing methods often rely on padded representations or must explicitly infer the set size, which often poses challenges. We present a novel strategy for addressing this challenge by casting prediction of variable-sized sets as a continuous inference problem. Our approach, CORDS (Continuous Representations of Discrete Structures), provides an invertible mapping that transforms a set of spatial objects into continuous fields: a density field that encodes object locations and count, and a feature field that carries their attributes over the same support. Because the mapping is invertible, models operate entirely in field space while remaining exactly decodable to discrete sets. We evaluate CORDS across molecular generation and regression, object detection, simulation-based inference, and a mathematical task involving recovery of local maxima, demonstrating robust handling of unknown set sizes with competitive accuracy.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 25519