A Differentiable Bayesian Relaxation for Latent Partial-Order Inference

Rank-data and action-trace datasets are typically recorded as linear sequences, although the constraints governing valid outcomes are often only partially ordered. These constraints may be temporal or process-based [24, 23, 16], causal [5], or dominance-based [28], and are usually not observed directly. Inferring them is important because they encode interpretable structure and support feasibility evaluation on new sequences. In these settings, however, the underlying relation is often incomplete: the latent structure is a partial order, or poset, in which pairs of items that can occur in either order have no precedence relation. Consequently, an observed order need not imply a true prerequisite relation; it may reflect scheduling, logging, or a single valid linearization of the latent partial order. Treating all observed precedences as real can therefore produce overly sequential and unrealistic structures, especially in workflow or LLM-agent settings where unnecessary ordering induces extra execution steps and compute.