[论文解读] CORDS: Continuous Representations of Discrete Structures

Tin Hadži Veljković, Erik J. Bekkers+2 more|arXiv (Cornell University)|Jan 29, 2026

Machine Learning in Materials Science被引用 0

一句话总结

CORDS 将对变量大小集合的预测转化为一个连续、可逆的推断问题，将集合编码为密度和特征场，能够被精确解码回离散集合。

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.

研究动机与目标

• 在不预先指定集合大小或填充的情况下处理变量大小集合的预测问题。
• 提供从集合到连续场的可逆映射，以实现完全在场空间中的学习。
• 展示在分子生成、目标检测、基于模拟的推断以及数学恢复任务中的适用性。

提出的方法

• 定义将离散空间对象集合转化为密度场（位置和计数）和在同一支撑上的特征场（属性）的可逆映射。
• 在场空间中操作模型，而非离散集合，同时保证能够精确解码回原始集合。
• 在多个领域评估该方法：分子生成与回归、目标检测、基于模拟的推断，以及涉及局部极值的数学恢复任务。

实验结果

研究问题

• RQ1 是否可以在不显式给出集合大小或填充的情况下，通过使用连续场表示来准确预测变大小集合？
• RQ2 可逆的场空间映射是否能够在多样化任务中实现对离散集合的精确恢复？
• RQ3 与传统填充表示相比，CORDS 在涉及未知集合大小的任务中的表现如何？

主要发现

• CORDS 提供了从离散集合到连续密度和特征场的可逆映射。
• 在场空间中训练的模型可以被精确解码为离散集合。
• 该方法在分子生成与回归、目标检测、基于模拟的推断以及数学任务等领域的评估显示，对未知集合大小具有鲁棒处理能力且精度具有竞争力。