A Differentiable Bayesian Relaxation for Latent Partial-Order Inference

TL;DR

This paper introduces a differentiable relaxation method for inferring latent partial orders from linear order data, enabling efficient gradient-based inference while preserving partial order semantics.

Contribution

It presents a novel smooth surrogate for partial order inference that supports gradient-based methods and guarantees theoretical properties like transitivity and convergence.

Findings

Close posterior fidelity to hard MCMC on small instances.

Improved runtime-accuracy trade-offs on larger problems.

Supports gradient-based MCMC and variational inference.

Abstract

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.