Deep Flow Networks

Ozan Candogan, Ayoub Foussoul
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:11044-11062, 2026.

Abstract

We introduce Deep Flow Networks (DFNs), a new class of discrete function approximators. DFNs are inspired by and generalize minimum-cost flow value functions that map node imbalances on a subset of nodes to the optimal flow cost. Such functions are known to be M-convex (Murota2003) and admit efficient optimization. On the theoretical side, we prove that DFNs are universal approximators for discrete functions on $\mathbb{Z}^d$ that admit convex extensions to $\mathbb{R}^d$, and characterize their optimization complexity in terms of their deviation from the M-convex regime. Guided by these results, we develop a practical DFN implementation for learning from data. Finally, we evaluate our implementation empirically on data from different ground-truth functions, showing that DFNs achieve strong approximation accuracy while being substantially faster to optimize than benchmark approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-candogan26b, title = {Deep Flow Networks}, author = {Candogan, Ozan and Foussoul, Ayoub}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {11044--11062}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/candogan26b/candogan26b.pdf}, url = {https://proceedings.mlr.press/v306/candogan26b.html}, abstract = {We introduce Deep Flow Networks (DFNs), a new class of discrete function approximators. DFNs are inspired by and generalize minimum-cost flow value functions that map node imbalances on a subset of nodes to the optimal flow cost. Such functions are known to be M-convex (Murota2003) and admit efficient optimization. On the theoretical side, we prove that DFNs are universal approximators for discrete functions on $\mathbb{Z}^d$ that admit convex extensions to $\mathbb{R}^d$, and characterize their optimization complexity in terms of their deviation from the M-convex regime. Guided by these results, we develop a practical DFN implementation for learning from data. Finally, we evaluate our implementation empirically on data from different ground-truth functions, showing that DFNs achieve strong approximation accuracy while being substantially faster to optimize than benchmark approaches.} }
Endnote
%0 Conference Paper %T Deep Flow Networks %A Ozan Candogan %A Ayoub Foussoul %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-candogan26b %I PMLR %P 11044--11062 %U https://proceedings.mlr.press/v306/candogan26b.html %V 306 %X We introduce Deep Flow Networks (DFNs), a new class of discrete function approximators. DFNs are inspired by and generalize minimum-cost flow value functions that map node imbalances on a subset of nodes to the optimal flow cost. Such functions are known to be M-convex (Murota2003) and admit efficient optimization. On the theoretical side, we prove that DFNs are universal approximators for discrete functions on $\mathbb{Z}^d$ that admit convex extensions to $\mathbb{R}^d$, and characterize their optimization complexity in terms of their deviation from the M-convex regime. Guided by these results, we develop a practical DFN implementation for learning from data. Finally, we evaluate our implementation empirically on data from different ground-truth functions, showing that DFNs achieve strong approximation accuracy while being substantially faster to optimize than benchmark approaches.
APA
Candogan, O. & Foussoul, A.. (2026). Deep Flow Networks. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:11044-11062 Available from https://proceedings.mlr.press/v306/candogan26b.html.

Related Material