Local Inconsistency Resolution: The Interplay between Attention and Control in Probabilistic Models
Provides a unified framework for diverse algorithms, offering new insights and improvements for probabilistic modeling.
The paper introduces Local Inconsistency Resolution (LIR), a generic algorithm for learning and inference in probabilistic models that unifies EM, belief propagation, adversarial training, GANs, and GFlowNets. LIR improves GFlowNet convergence by suggesting a more natural loss.
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.