Many ranking and agent trace datasets are recorded as linear orders even though their latent structure is only partially ordered. This is especially common in agent and workflow traces, where observed order may reflect arbitrary linearization rather than true prerequisites. We introduce a differentiable relaxation for latent partial-order inference from such traces. Starting from a hard frontier-constrained model of noisy linear extensions, we replace discontinuous product-order precedence and binary frontier feasibility with smooth surrogates, yielding a continuous posterior that preserves closure-level partial-order semantics and supports gradient-based MCMC and variational inference. We prove soft transitivity, sharp-limit frontier recovery, and convergence to the hard likelihood. Experiments on synthetic data, records of social dominance relations, and cloud-agent traces show close posterior fidelity to hard MCMC on small instances and improved runtime--accuracy trade-offs on larger problems.

翻译：许多排序和智能体追踪数据集是以线性顺序记录的，但其潜在结构仅为偏序。这在智能体和工作流轨迹中尤为常见，观察到的顺序可能反映的是任意线性化而非真实先决条件。我们提出一种可微松弛方法，用于从此类轨迹中推断潜在偏序。从噪声线性扩展的硬前沿约束模型出发，我们用光滑替代函数替换不连续的产品序优先关系和二元前沿可行性，从而得到一种连续后验，该后验保留了闭包级偏序语义，并支持基于梯度的MCMC和变分推理。我们证明了软传递性、尖锐极限前沿恢复以及向硬似然的收敛性。在合成数据、社会支配关系记录以及云智能体轨迹上的实验表明，该方法在小型实例上与硬MCMC的后验保真度接近，并在较大问题上改善了运行时间-精度权衡。