Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods.

Our framework is based on a generalization of Angluin's equivalence query model

Differentiable structure learning is a novel line of causal discovery research that transforms the combinatorial optimization of structural models into a continuous optimization problem. However, the field has lacked feasible methods to integrate partial order constraints, a critical prior information typically used in real-world scenarios, into the differentiable structure learning framework. The main difficulty lies in adapting these constraints, typically suited for the space of total orderings, to the continuous optimization context of structure learning in the graph space. To bridge this gap, this paper formalizes a set of equivalent constraints that map partial orders onto graph spaces and introduces a plug-and-play module for their efficient application. This module preserves the equivalent effect of partial order constraints in the graph space, backed by theoretical validations of correctness and completeness. It significantly enhances the quality of recovered structures while maintaining good efficiency, which learns better structures using 90% fewer samples than the data-based method on a real-world dataset. This result, together with a comprehensive evaluation on synthetic cases, demonstrates our method's ability to effectively improve differentiable structure learning with partial orders.

NTP is limited, with existing studies focusing mainly on asymptotic performance. This paper provides a fine-grained non-asymptotic analysis of the training dynamics of a one-layer transformer consisting of a self-attention module followed by a feed-forward layer.

Mixtures of ranking models have been widely used for heterogeneous preferences. However, learning a mixture model is highly nontrivial, especially when the dataset consists of partial orders.

The motivating example comes from e-commerce, where a customer typically has a greater appetence for items of a specific well-identified but unknown category than any other one.