CORDS: Continuous Representations of Discrete Structures
cs.LG
Submitted: 2026-01-29
Updated: 2026-09-17
Comments: Published as a conference paper at ICLR 2026. 38 pages, including appendix. Code: https://github.com/stases/CORDS
Journal ref: Proceedings of the International Conference on Learning Representations (ICLR), 2026
Code: https://github.com/stases/CORDS
License: http://creativecommons.org/licenses/by/4.0/
The gist: Many learning problems require predicting sets of objects when the number of objects is not known beforehand.
Terminology
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.
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