提出可学习的集合聚合方法，提升模型表达力与迁移性
Improving Set Function Approximation with Quasi-Arithmetic Neural Networks
- 用可逆神经网络构建新型可学习聚合函数
- 在多个基准上超越现有最优模型表现
- 学习到的嵌入能有效迁移到非集合任务
集合是多种数据的基本抽象。当前如DeepSets和PointNet等模型依赖固定不可学习的池化操作（如求和或取最大值），限制了嵌入的迁移性和模型表达能力。本文提出神经化柯尔莫哥洛夫均值（NKM），一种通过可逆神经函数学习广义中心趋势的新框架，并进一步设计准算术神经网络（QUANNs），将NKM作为可学习聚合函数。理论分析表明，QUANNs是广泛常见集合函数分解的通用逼近器；其可逆组件有助于学习更结构化的潜在表示。实验显示，QUANNs在多样基准上优于现有最先进模型，且学习的嵌入能有效迁移至不涉及集合的任务。
原文摘要 · Abstract (English)
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.
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