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[2505.24403] On the Lipschitz Continuity of Set Aggregation Functions and Neural Networks for Sets
Summary
This paper explores the Lipschitz continuity of set aggregation functions and neural networks designed for set data, providing insights into their robustness and generalization capabilities.
Why It Matters
Understanding Lipschitz continuity is crucial for assessing the stability and performance of neural networks, especially those processing unordered sets. This research contributes to the theoretical foundation of neural network design, impacting applications in various domains where set data is prevalent.
Key Takeaways
- Lipschitz continuity is linked to the robustness and generalization of neural networks.
- Aggregation functions like sum, mean, and max are Lipschitz continuous with respect to specific distance functions.
- Attention-based aggregation functions may lack Lipschitz continuity, affecting their stability.
- The paper provides empirical verification of theoretical findings through experiments on diverse datasets.
- Upper bounds on Lipschitz constants for neural networks processing multisets are derived.
Computer Science > Machine Learning arXiv:2505.24403 (cs) [Submitted on 30 May 2025 (v1), last revised 26 Feb 2026 (this version, v3)] Title:On the Lipschitz Continuity of Set Aggregation Functions and Neural Networks for Sets Authors:Giannis Nikolentzos, Konstantinos Skianis View a PDF of the paper titled On the Lipschitz Continuity of Set Aggregation Functions and Neural Networks for Sets, by Giannis Nikolentzos and 1 other authors View PDF HTML (experimental) Abstract:The Lipschitz constant of a neural network is connected to several important prop- erties of the network such as its robustness and generalization. It is thus useful in many settings to estimate the Lipschitz constant of a model. Prior work has fo- cused mainly on estimating the Lipschitz constant of multi-layer perceptrons and convolutional neural networks. Here we focus on data modeled as sets or multi- sets of vectors and on neural networks that can handle such data. These models typically apply some permutation invariant aggregation function, such as the sum, mean or max operator, to the input multisets to produce a single vector for each input sample. In this paper, we investigate whether these aggregation functions, along with an attention-based aggregation function, are Lipschitz continuous with respect to three distance functions for unordered multisets, and we compute their Lipschitz constants. In the general case, we find that each aggregation function is Lipschitz continuous with respect to only...
