Learning Iterative Reasoning through Energy Diffusion
This work addresses the need for flexible reasoning systems that can handle out-of-distribution problems, such as more complex Sudoku puzzles and larger graphs, though it is incremental in its approach.
The paper tackles the problem of learning to reason for various tasks by introducing the IRED framework, which uses energy-based optimization to adapt inference steps based on problem difficulty, achieving superior performance in continuous-space reasoning, discrete-space reasoning, and planning tasks, especially in challenging scenarios.
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/