将可变数量的离散对象转为连续场，实现精准且可逆的预测。
CORDS: Continuous Representations of Discrete Structures
- 用连续密度与特征场表示离散对象集合，避免预设数量。
- 在分子生成、目标检测等任务中表现稳定，精度接近现有方法。
- 适合处理未知数量对象的任务，如物体检测和科学推断。
许多学习任务需要在事先未知对象数量的情况下预测一组对象，例如目标检测、分子建模以及天体物理源检测等科学推理任务。现有方法通常依赖于填充表示或需显式推断集合大小，常带来挑战。我们提出一种新策略，将可变尺寸集合的预测转化为连续推断问题。所提方法CORDS（连续离散结构表征）提供一个可逆映射，将空间对象集合转换为连续场：一个编码对象位置与数量的密度场，以及一个携带其属性的特征场，二者共享相同支撑域。由于映射可逆，模型可在场空间中完全运算，同时精确还原为离散集合。我们在分子生成与回归、目标检测、基于模拟的推断及局部极大值恢复等数学任务上评估CORDS，证明其在未知集合大小下具有鲁棒性，且精度具有竞争力。
原文摘要 · Abstract (English)
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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