GFlowRule: Detailed-balance GFlowNets for diverse symbolic rule selection in neuro-symbolic image classification
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Abstract
We propose a neuro-symbolic image-classification framework that combines CNN representations, Random-Forest-derived symbolic rules, and a Detailed-Balance GFlowNet for diverse rule-set selection. The GFlowNet optimizes a multi-component reward based on macro accuracy, correct and incorrect coverage, and inter-rule conflict, while the selected rules regularize CNN fine-tuning through either a fixed rule set or stochastic marginalization over ???? = 32 sampled rule sets. On a 12 class Vietnamese cultural-heritage dataset with 10,674 images, four backbones, and five random seeds, GFlowNet consistently obtains the highest matched-budget rule-set reward compared with Top-???? Confidence, Greedy Coverage, and Random selection. Rule regularization generally matches or improves the CNN baseline, achieving its largest Macro-F1 gain of +0.73 percentage points on MobileNetV3-S. The learned policy also yields highly diverse rule sets, with a 100% unique-sample ratio over 5,000 draws. Overall, the results indicate that GFlowNet is effective at learning a diverse distribution of high-reward symbolic rule sets, while the downstream benefit of rule regularization remains dependent on the CNN backbone and regularization strategy.
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© 2026 The authors. This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License.
References
Bengio, Y., Lahlou, S., Deleu, T., Hu, E. J., Tiwari, M., & Bengio, E. (2023). GFlowNet foundations. Journal of Machine Learning Research, 24(210), 1–55. https://jmlr.org/papers/v24/22-0364.html
Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324
Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., & Houlsby, N. (2021). An image is worth 16×16 words: Transformers for image recognition at scale. International Conference on Learning Representations. https://doi.org/10.48550/arXiv.2010.11929
Howard, A., Sandler, M., Chu, G., Chen, L.-C., Chen, B., Tan, M., Wang, W., Zhu, Y., Pang, R., Vasudevan, V., Le, Q. V., & Adam, H. (2019). Searching for MobileNetV3. Proceedings of the IEEE/CVF International Conference on Computer Vision (pp. 1314–1324). https://doi.org/10.1109/ICCV.2019.00140
Kingma, D. P., & Ba, J. (2015). Adam: A method for stochastic optimization. International Conference on Learning Representations. https://doi.org/10.48550/arXiv.1412.6980
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2012). ImageNet classification with deep convolutional neural networks. Advances in Neural Information Processing Systems, 25, 1097–1105.
Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., & Guo, B. (2021). Swin Transformer: Hierarchical vision Transformer using shifted windows. Proceedings of the IEEE/CVF International Conference on Computer Vision (pp. 10012–10022). https://doi.org/10.1109/ICCV48922.2021.00986
Mao, J., Tenenbaum, J. B., & Wu, J. (2025). Neuro-symbolic concepts [Preprint]. arXiv. https://arxiv.org/abs/2505.06191.
Seo, S., Arık, S. Ö., Yoon, J., Zhang, X., Sohn, K., & Pfister, T. (2021). Controlling neural networks with rule representations. Advances in Neural Information Processing Systems, 34, 11196-11207. https://doi.org/10.48550/arXiv.2106.07804
Simonyan, K., & Zisserman, A. (2015). Very deep convolutional networks for large-scale image recognition. International Conference on Learning Representations. https://doi.org/10.48550/arXiv.1409.1556