Local Inconsistency Resolution: The Interplay between Attention and Control in Probabilistic Models

TL;DR

The paper introduces Local Inconsistency Resolution (LIR), a unified framework for learning and inference in probabilistic models that generalizes many existing algorithms by iteratively focusing on and resolving model inconsistencies.

Contribution

LIR provides a flexible, unified approach to approximate inference and learning in probabilistic models, encompassing algorithms like EM, belief propagation, GANs, and GFlowNets.

Findings

LIR unifies various inference algorithms under a single framework.

Applying LIR to GFlowNets improves convergence.

LIR's properties are validated on synthetic probabilistic dependency graphs.

Abstract

We present a generic algorithm for learning and approximate inference with an intuitive epistemic interpretation: iteratively focus on a subset of the model and resolve inconsistencies using the parameters under control. This framework, which we call Local Inconsistency Resolution (LIR) is built upon Probabilistic Dependency Graphs (PDGs), which provide a flexible representational foundation capable of capturing inconsistent beliefs. We show how LIR unifies and generalizes a wide variety of important algorithms in the literature, including the Expectation-Maximization (EM) algorithm, belief propagation, adversarial training, GANs, and GFlowNets. In the last case, LIR actually suggests a more natural loss, which we demonstrate improves GFlowNet convergence. Each method can be recovered as a specific instance of LIR by choosing a procedure to direct focus (attention and control). We implement this algorithm for discrete PDGs and study its properties on synthetically generated PDGs, comparing its behavior to the global optimization semantics of the full PDG.