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

Oliver Ethan Richardson, Mandana Samiei, Mehran Shakerinava, Joseph D Viviano, Abdessamad El Kabid, Ali Parviz, Yoshua Bengio
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4141-4149, 2026.

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 of these methods 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-richardson26a, title = { Local Inconsistency Resolution: The Interplay between Attention and Control in Probabilistic Models }, author = {Richardson, Oliver Ethan and Samiei, Mandana and Shakerinava, Mehran and Viviano, Joseph D and El Kabid, Abdessamad and Parviz, Ali and Bengio, Yoshua}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4141--4149}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/richardson26a/richardson26a.pdf}, url = {https://proceedings.mlr.press/v300/richardson26a.html}, 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 of these methods 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. } }
Endnote
%0 Conference Paper %T Local Inconsistency Resolution: The Interplay between Attention and Control in Probabilistic Models %A Oliver Ethan Richardson %A Mandana Samiei %A Mehran Shakerinava %A Joseph D Viviano %A Abdessamad El Kabid %A Ali Parviz %A Yoshua Bengio %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-richardson26a %I PMLR %P 4141--4149 %U https://proceedings.mlr.press/v300/richardson26a.html %V 300 %X 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 of these methods 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.
APA
Richardson, O.E., Samiei, M., Shakerinava, M., Viviano, J.D., El Kabid, A., Parviz, A. & Bengio, Y.. (2026). Local Inconsistency Resolution: The Interplay between Attention and Control in Probabilistic Models . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4141-4149 Available from https://proceedings.mlr.press/v300/richardson26a.html.

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