Taming Binarized Neural Networks and Mixed-Integer Programs
Johannes Aspman, Georgios Korpas, Jakub Marecek
Abstract
There has been a great deal of recent interest in binarized neural networks, especially because of their explainability. At the same time, automatic differentiation algorithms such as backpropagation fail for binarized neural networks, which limits their applicability. We show that binarized neural networks admit a tame representation by reformulating the problem of training binarized neural networks as a subadditive dual of a mixed-integer program, which we show to have nice properties. This makes it possible to use the framework of Bolte et al. for implicit differentiation, which offers the possibility for practical implementation of backpropagation in the context of binarized neural networks. This approach could also be used for a broader class of mixed-integer programs, beyond the training of binarized neural networks, as encountered in symbolic approaches to AI and beyond.
BibTeX
@article{Aspman_Korpas_Marecek_2024, title={Taming Binarized Neural Networks and Mixed-Integer Programs}, volume={38}, url={https://ojs.aaai.org/index.php/AAAI/article/view/28968}, DOI={10.1609/aaai.v38i10.28968}, abstractNote={There has been a great deal of recent interest in binarized neural networks, especially because of their explainability. At the same time, automatic differentiation algorithms such as backpropagation fail for binarized neural networks, which limits their applicability. We show that binarized neural networks admit a tame representation
by reformulating the problem of training binarized neural networks as a subadditive dual of a mixed-integer program, which we show to have nice properties. This makes it possible to use the framework of Bolte et al. for implicit differentiation, which offers the possibility for practical implementation of backpropagation in the context of binarized neural networks. This approach could also be used for a broader class of mixed-integer programs, beyond the training of binarized neural networks, as encountered in symbolic approaches to AI and beyond.}, number={10}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Aspman, Johannes and Korpas, Georgios and Marecek, Jakub}, year={2024}, month={Mar.}, pages={10935-10943} }