We study the effect of group symmetrization of pre-trained models on conformal prediction (CP), a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, CP uncertainty regions can grow significantly in long horizon missions, rendering the statistical guarantees uninformative. To that end, we propose infusing CP with geometric information via group-averaging of the pretrained predictor to distribute the non-conformity mass across the orbits. Each sample now is treated as a representative of an orbit, thus uncertainty can be mitigated by other samples entangled to it via the orbit inducing elements of the symmetry group. Our approach provably yields contracted non-conformity scores in increasing convex order, implying improved exponential-tail bounds and sharper conformal prediction sets in expectation, especially at high confidence levels. We then propose an experimental design to test these theoretical claims in pedestrian trajectory prediction.

翻译：本研究探讨了预训练模型的群对称化对共形预测（CP）的影响。共形预测是一种后处理、无分布、有限样本的不确定性量化方法，在数据可交换性假设下提供形式化的覆盖保证。然而，在长时程任务中，CP的不确定区域可能显著扩大，导致统计保证的信息量降低。为此，我们提出通过预训练预测器的群平均向CP注入几何信息，从而将非共形质量分布到轨道上。每个样本现在被视为一个轨道的代表，因此可通过对称群中诱导轨道的元素与之纠缠的其他样本来缓解不确定性。我们的方法在理论上能够以递增凸序产生收缩的非共形分数，这意味着改进的指数尾界和期望意义上更尖锐的共形预测集，尤其是在高置信水平下。随后，我们提出了一种实验设计来在行人轨迹预测任务中验证这些理论主张。