Title: Improving Set Function Approximation with Quasi-Arithmetic Neural Networks
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: representation learning, set function learning

Abstract: 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. In this work, we break from this paradigm 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.

TL;DR: We introduce quasi-arithmetic neural networks (QUANNs), which use Neuralized Kolmogorov Mean---newly introduced trainable pooling mechanism---to improve set functions approximation.