[论文] Hyper Input Convex Neural Networks for Shape Constrained Learning and ...

论文概要

研究领域: ML 作者: Shayan Hundrieser, Insung Kong, Johannes Schmidt-Hieber 发布时间: 2025-04-30 arXiv: 2504.20796

中文摘要

我们提出超输入凸神经网络（HyCNNs），一种专为学习凸函数而设计的新型神经网络架构。HyCNNs将Maxout网络的原理与输入凸神经网络（ICNNs）相结合，构建了一种对输入始终凸的神经网络，理论上能够利用深度优势，且在大规模训练时比ICNNs表现更可靠。具体而言，我们证明了HyCNNs在近似二次函数达到给定精度时，所需参数数量比ICNNs少指数级。在一系列合成实验中，我们展示了HyCNNs在凸回归和插值任务的预测性能上优于现有ICNNs和MLPs。我们进一步将HyCNNs应用于学习高维最优传输映射，在合成示例和单细胞RNA测序数据上，它们在广泛设置下经常优于基于ICNN的神经最优传输方法和其他基线。

原文摘要

We introduce Hyper Input Convex Neural Networks (HyCNNs), a novel neural network architecture designed for learning convex functions. HyCNNs combine the principles of Maxout networks with input convex neural networks (ICNNs) to create a neural network that is always convex in the input, theoretically capable of leveraging depth, and performs reliable when trained at scale compared to ICNNs. Concretely, we prove that HyCNNs require exponentially fewer parameters than ICNNs to approximate quadratic functions up to a given精度. Throughout a series of synthetic experiments, we demonstrate that HyCNNs outperform existing ICNNs and MLPs in terms of predictive performance for convex regression and interpolation tasks. We further apply HyCNNs to learn high-dimensional optimal transport maps for synt...

自动采集于 2026-05-01

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