mlsanityData to 14 Oct 2026

DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows

arXiv 2503.01140 ↗First posted 3 Mar 2025cs.LG stat.MLcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 61 of its 82 references that are in the map. First posted on arXiv 3 Mar 2025.

Builds on

61 of 82 references.

References · 61

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38 more
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50 most cited of 61 All 61 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2026Measure-to-measure Regression with Transformerscited by 2
  2. 2025Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicingcited by 1
  3. 2026Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approachcited by 1
  4. 2026Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimizationcited by 0