CORDS: Continuous Representations of Discrete Structures
This addresses a common challenge in machine learning for applications like scientific inference, though it is an incremental improvement over existing set prediction methods.
The paper tackles the problem of predicting variable-sized sets of objects, such as in object detection or molecular modeling, by introducing CORDS, a method that maps discrete sets to continuous fields for inference, achieving competitive accuracy across multiple tasks.
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.