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

arXiv: https://arxiv.org/abs/2604.17140 · HTML: https://mlsanity.com/paper/2604.17140/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 18 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Are adversarial examples inevitable?](https://mlsanity.com/paper/1809.02104/) (2018)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [VarGrad: A Low-Variance Gradient Estimator for Variational Inference](https://mlsanity.com/paper/2010.10436/) (2020)
- [Loss as the Inconsistency of a Probabilistic Dependency Graph: Choose Your Model, Not Your Loss Function](https://mlsanity.com/paper/2202.11862/) (2022)
- [Inference for Probabilistic Dependency Graphs](https://mlsanity.com/paper/2311.05580/) (2023)

## Built on by (most cited first, 2 of 2)

- [Inverting the Bellman Equation: From Q-Values to World Models](https://mlsanity.com/paper/2606.21173/) (2026)
- [Mixture of GFlowNets](https://mlsanity.com/paper/2610.17007/) (2026)

## Abstract (arXiv)

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.