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Discrete-Space Reasoning
Our approach can also solve discrete reasoning tasks such as Sudoku. Below, we illustrate the predicted solutions to the Sudoku problem as we run optimization over additional energy landscapes.
Predicted Sudoku Solutions Over Energy Landscape.
Illustration of predicted sudoku boards across optimized energy landscapes. Incorrect entries are highlighted in red. At later landscapes, predicted sudoku boards are more accurate.
When generalizing to harder variants of Sudoku (with fewer numerical entries given), we can leverage additional test-time optimization iterations to obtain the final more accurate answer.
Generalization Performance with Per Landscape Optimization Steps.
By increasing the number of optimization steps run at each energy landscape, IRED is able to leverage additional computational steps to improve the final performance on harder variants of Sudoku.
Planning
Finally, our approach can also solve planning problems. Below, we illustrate how IRED enables us to find the correct next action to take in a graph given start node (green) to a goal node (red).
Optimized Plans Across Landscapes.
Plot of next action prediction in plans across energy landscapes. In each visualization, the green/red nodes indicate start/goal nodes with connections between nodes indicated with arrows. The darkness of a node indicates the score for selecting the corresponding node as the next node to move to in the predicted plan. As landscapes are sequentially optimized, the correct next action is selected.
Related Projects
Check out a list of our related papers on compositional generation and energy based models. A full list can be found here!We propose energy optimization as an approach to add iterative reasoning into neural network. We illustrate how this procedure enables generalization to harder instances of problems unseen at training time on both continuous, discrete and image processing tasks.
We propose new samplers, inspired by MCMC, to enable successful compositional generation. Further, we propose an energy-based parameterization of diffusion models which enables the use of new compositional operators and more sophisticated, Metropolis-corrected samplers.
BibTeX
@InProceedings{Du_2024_ICML,
author = {Du, Yilun and Mao, Jiayuan and Tenenbaum, Joshua B.},
title = {Learning Iterative Reasoning through Energy Diffusion},
booktitle = {International Conference on Machine Learning (ICML)},
year = {2024}
}