# Mathematical Foundation of Interpretable Equivariant Surrogate Models

Source: [Mathematical Foundation of Interpretable Equivariant Surrogate Models](<https://www.sota2.com/research/paper/68fa773b1e209131cea71d99>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T04:12:54.213Z

Authors: Jacopo Joy Colombini, Filippo Bonchi, Francesco Giannini, Fosca Giannotti, Roberto Pellungrini, Patrizio Frosini

Published: 2025-03-03T15:06:43.000Z

## Abstract

This paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant Operators (GEOs) based on Group Equivariant Non-Expansive Operators (GENEOs) transformations. The central concept involves quantifying the distance between GEOs by measuring the non-commutativity of specific diagrams. Additionally, the paper proposes a definition of interpretability of GEOs according to a complexity measure that can be defined according to each user preferences. Moreover, we explore the formal properties of this framework and show how it can be applied in classical machine learning scenarios, like image classification with convolutional neural networks.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2503.01942>)

[PDF](<https://arxiv.org/pdf/2503.01942.pdf>)