将深度平衡模型扩展到点云等离散分布输入，提升效率与性能。
DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows
- 基于Wasserstein梯度流设计新架构，实现对点云的不变性固定点求解
- 在点云分类与补全任务中性能媲美顶尖模型，参数量减少显著
- 适合处理集合或点云数据的高效建模，尤其关注参数效率的场景
深度平衡模型（DEQs）是一类隐式神经网络，在前向传播中求解神经网络的固定点。传统DEQs处理序列输入，但已拓展至多种数据类型。本文提出分布型深度平衡模型（DDEQs），将DEQs扩展至离散测度输入，如集合或点云。我们构建了理论基础框架，利用Wasserstein梯度流，证明可将DEQ前向传播调整为在置换不变性下寻找离散测度的固定点，并推导出适配DDEQs的网络架构。实验表明，其在点云分类与补全任务中表现媲美当前最优模型，同时参数效率显著提升。
原文摘要 · Abstract (English)
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.
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