# Empirical Evidence for Simply Connected Decision Regions in Image Classifiers

Source: [Empirical Evidence for Simply Connected Decision Regions in Image Classifiers](<https://www.sota2.com/research/paper/69fd6e585497b3b670c896ca>)

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

Data updated: 2026-05-14T06:00:04.528Z

Authors: Arjhun Swaminathan, Mete Akg\\"un

Published: 2026-05-07T14:59:17.000Z

## Abstract

Understanding the topology of decision regions is central to explaining the inner workings of deep neural networks. Prior empirical work has provided evidence that these regions are path connected. We study a stronger topological question: whether closed loops inside a decision region can be contracted without leaving that region. To this end, we propose an iterative quad-mesh filling procedure that constructs a finite-resolution label-preserving surface bounded by a given loop and lying entirely within the same decision region. We further connect this construction to natural Coons patches in order to quantify its deviation from a canonical geometric interpolation of the loop. By evaluating our method across several modern image-classification models, we provide empirical evidence supporting the hypothesis that decision regions in deep neural networks are not only path connected, but also simply connected.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2605.06380>)

[PDF](<https://arxiv.org/pdf/2605.06380.pdf>)

[Implementation](<https://github.com/mdppml/contractible-class-regions>)