DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915211033706496 |
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| author | Geuter, Jonathan Bonet, Clément Korba, Anna Alvarez-Melis, David |
| author_facet | Geuter, Jonathan Bonet, Clément Korba, Anna Alvarez-Melis, David |
| contents | Deep Equilibrium Models (DEQs) are a class of implicit neural networks that solve for a fixed point of a neural network in their forward pass. Traditionally, DEQs take sequences as inputs, but have since been applied to a variety of data. In this work, we present Distributional Deep Equilibrium Models (DDEQs), extending DEQs to discrete measure inputs, such as sets or point clouds. We provide a theoretically grounded framework for DDEQs. Leveraging Wasserstein gradient flows, we show how the forward pass of the DEQ can be adapted to find fixed points of discrete measures under permutation-invariance, and derive adequate network architectures for DDEQs. In experiments, we show that they can compete with state-of-the-art models in tasks such as point cloud classification and point cloud completion, while being significantly more parameter-efficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows Geuter, Jonathan Bonet, Clément Korba, Anna Alvarez-Melis, David Machine Learning Deep Equilibrium Models (DEQs) are a class of implicit neural networks that solve for a fixed point of a neural network in their forward pass. Traditionally, DEQs take sequences as inputs, but have since been applied to a variety of data. In this work, we present Distributional Deep Equilibrium Models (DDEQs), extending DEQs to discrete measure inputs, such as sets or point clouds. We provide a theoretically grounded framework for DDEQs. Leveraging Wasserstein gradient flows, we show how the forward pass of the DEQ can be adapted to find fixed points of discrete measures under permutation-invariance, and derive adequate network architectures for DDEQs. In experiments, we show that they can compete with state-of-the-art models in tasks such as point cloud classification and point cloud completion, while being significantly more parameter-efficient. |
| title | DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.01140 |