用球面坐标系让模型输出自动满足约束，安全又高效。
Constrained Machine Learning Through Hyperspherical Representation
- 将输出空间转为球面坐标，只允许可行点存在
- 实验显示100%满足约束，推理开销极小
- 适合需要绝对安全的工业或医疗场景
确保机器学习模型输出满足约束条件对许多应用至关重要，尤其在安全关键领域。现有方法依赖训练时的惩罚项，无法保证不违反约束；或使用特定结构（如单调性）；或通过输出投影，需解优化问题，计算成本高。本文提出超球面约束表示法，适用于凸且有界的可行区域（可推广至星形域）。该方法在不同表示系统中运作，将欧氏坐标转换为相对于约束区域的超球坐标，仅能表示可行点。在合成数据集和真实世界数据集上的实验表明，该方法预测性能与现有方法相当，可保证100%约束满足，且推理时计算开销极小。
原文摘要 · Abstract (English)
The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do not guarantee to avoid constraints violations; or constraint-specific model architectures (e.g., for monotonocity); or on output projection, which requires to solve an optimization problem that might be computationally demanding. We present the Hypersherical Constrained Representation, a novel method to enforce constraints in the output space for convex and bounded feasibility regions (generalizable to star domains). Our method operates on a different representation system, where Euclidean coordinates are converted into hyperspherical coordinates relative to the constrained region, which can only inherently represent feasible points. Experiments on a synthetic and a real-world dataset show that our method has predictive performance comparable to the other approaches, can guarantee 100% constraint satisfaction, and has a minimal computational cost at inference time.
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