通过准算术神经网络改进集合函数近似
Improving Set Function Approximation with Quasi-Arithmetic Neural Networks
AI总结：
本文提出准算术神经网络（QUANNs），通过引入神经化的柯尔莫戈罗夫均值（NKM）作为可学习的聚合函数，改进集合函数近似，提升模型的表达能力和迁移能力。
摘要：
集合在许多类型的数据中代表了基本的抽象。为了处理集合结构数据的无序性质，模型如DeepSets和PointNet依赖于固定且不可学习的池化操作（例如求和或求最大值）-- 这种设计选择可能会阻碍学习到的嵌入的可迁移性，并限制模型的表达能力。最近，可学习的聚合函数已被提出作为更具表达力的替代方案。在本工作中，我们通过引入神经化的柯尔莫戈罗夫均值（NKM）-- 一种新的可训练框架，通过可逆的神经函数学习通用的集中趋势度量，来推进这一研究领域。我们进一步提出准算术神经网络（QUANNs），其中将NKM作为可学习的聚合函数进行整合。我们提供了理论分析，证明QUANNs是广泛类别集合函数分解的通用近似器，并且由于其可逆的神经组件，能够学习更具结构的潜在表示。实验上，QUANNs在多样化的基准测试中优于最先进的基线模型，同时学习到的嵌入能够有效地迁移到不涉及集合的任务中。
英文摘要：
Sets represent a fundamental abstraction across many types of data. To handle the unordered nature of set-structured data, models such as DeepSets and PointNet rely on fixed, non-learnable pooling operations (e.g., sum or max) -- a design choice that can hinder the transferability of learned embeddings and limits model expressivity. More recently, learnable aggregation functions have been proposed as more expressive alternatives. In this work, we advance this line of research by introducing the Neuralized Kolmogorov Mean (NKM) -- a novel, trainable framework for learning a generalized measure of central tendency through an invertible neural function. We further propose quasi-arithmetic neural networks (QUANNs), which incorporate the NKM as a learnable aggregation function. We provide a theoretical analysis showing that, QUANNs are universal approximators for a broad class of common set-function decompositions and, thanks to their invertible neural components, learn more structured latent representations. Empirically, QUANNs outperform state-of-the-art baselines across diverse benchmarks, while learning embeddings that transfer effectively even to tasks that do not involve sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
