CORDS: Continuous Representations of Discrete Structures

TL;DR

CORDS introduces a novel continuous inference framework that transforms variable-sized set prediction problems into continuous field representations, enabling exact decoding and robust handling of unknown set sizes across diverse tasks.

Contribution

The paper proposes CORDS, a new invertible mapping that encodes sets as continuous fields, allowing models to operate in field space and decode sets without explicit size inference.

Findings

Effective in molecular generation and object detection

Handles unknown set sizes with high accuracy

Demonstrates robustness across multiple tasks

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.