# Learning Iterative Reasoning through Energy Diffusion

Source: [Learning Iterative Reasoning through Energy Diffusion](<https://www.sota2.com/research/paper/68fa73a51e209131cea5da69>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T02:54:13.197Z

Authors: Yilun Du, Jiayuan Mao, Joshua B. Tenenbaum

Published: 2024-06-17T03:36:47.000Z

## Abstract

We introduce iterative reasoning through energy diffusion (IRED), a novel framework for learning to reason for a variety of tasks by formulating reasoning and decision-making problems with energy-based optimization. IRED learns energy functions to represent the constraints between input conditions and desired outputs. After training, IRED adapts the number of optimization steps during inference based on problem difficulty, enabling it to solve problems outside its training distribution -- such as more complex Sudoku puzzles, matrix completion with large value magnitudes, and pathfinding in larger graphs. Key to our method's success is two novel techniques: learning a sequence of annealed energy landscapes for easier inference and a combination of score function and energy landscape supervision for faster and more stable training. Our experiments show that IRED outperforms existing methods in continuous-space reasoning, discrete-space reasoning, and planning tasks, particularly in more challenging scenarios. Code and visualizations at https://energy-based-model.github.io/ired/

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Sudoku Solving on Sudoku OOD - RRN (test)](<https://www.sota2.com/research/sota/sudoku-solving-on-sudoku-ood-rrn-test.md>): Sudoku Solving; Sudoku OOD - RRN (test); Instance Solved Rate: 62.1.

- [Sudoku Solving on Sudoku Hard](<https://www.sota2.com/research/sota/sudoku-solving-on-sudoku-hard.md>): Sudoku Solving; Sudoku Hard; Success Rate: 62.1.

- [Sudoku Solving on Sudoku In-distribution (test)](<https://www.sota2.com/research/sota/sudoku-solving-on-sudoku-in-distribution-test.md>): Sudoku Solving; Sudoku In-distribution (test); Accuracy: 99.4.

- [Sudoku Solving on Sudoku Easy](<https://www.sota2.com/research/sota/sudoku-solving-on-sudoku-easy.md>): Sudoku Solving; Sudoku Easy; Accuracy: 99.4.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2406.11179>)

[PDF](<https://arxiv.org/pdf/2406.11179.pdf>)