# Learning Fourier shapes to probe the geometric world of deep neural networks

arXiv: https://arxiv.org/abs/2511.04970 · HTML: https://mlsanity.com/paper/2511.04970/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 47 references that are in the map.
- First posted on arXiv 7 Nov 2025.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Adversarial Patch](https://mlsanity.com/paper/1712.09665/) (2017)
- [Fooling automated surveillance cameras: adversarial patches to attack person detection](https://mlsanity.com/paper/1904.08653/) (2019)
- [Physically Realizable Adversarial Examples for LiDAR Object Detection](https://mlsanity.com/paper/2004.00543/) (2020)
- [Exploring the Adversarial Vulnerabilities of Vision-Language-Action Models in Robotics](https://mlsanity.com/paper/2411.13587/) (2024)
- [Physical Attack on Monocular Depth Estimation with Optimal Adversarial Patches](https://mlsanity.com/paper/2207.04718/) (2022)
- [Fooling thermal infrared pedestrian detectors in real world using small bulbs](https://mlsanity.com/paper/2101.08154/) (2021)
- [Infrared Invisible Clothing:Hiding from Infrared Detectors at Multiple Angles in Real World](https://mlsanity.com/paper/2205.05909/) (2022)
- [DAP: A Dynamic Adversarial Patch for Evading Person Detectors](https://mlsanity.com/paper/2305.11618/) (2023)
- [One Perturbation is Enough: On Generating Universal Adversarial Perturbations against Vision-Language Pre-training Models](https://mlsanity.com/paper/2406.05491/) (2024)
- [Physically Adversarial Infrared Patches with Learnable Shapes and Locations](https://mlsanity.com/paper/2303.13868/) (2023)
- [Unified Adversarial Patch for Cross-modal Attacks in the Physical World](https://mlsanity.com/paper/2307.07859/) (2023)
- [Hide in Thicket: Generating Imperceptible and Rational Adversarial Perturbations on 3D Point Clouds](https://mlsanity.com/paper/2403.05247/) (2024)
- [Dimensions underlying the representational alignment of deep neural networks with humans](https://mlsanity.com/paper/2406.19087/) (2024)
- [Benchmarking Adversarial Patch Against Aerial Detection](https://mlsanity.com/paper/2210.16765/) (2022)

## Built on by (most cited first, 1 of 1)

- [Unleashing the Representational Power of Fourier Shapes for Attacking Infrared Object Detection](https://mlsanity.com/paper/2605.17822/) (2026)

## Abstract (arXiv)

While both shape and texture are fundamental to visual recognition, research on deep neural networks (DNNs) has predominantly focused on the latter, leaving their geometric understanding poorly probed. Here, we show: first, that optimized shapes can act as potent semantic carriers, generating high-confidence classifications from inputs defined purely by their geometry; second, that they are high-fidelity interpretability tools that precisely isolate a model's salient regions; and third, that they constitute a new, generalizable adversarial paradigm capable of deceiving downstream visual tasks. This is achieved through an end-to-end differentiable framework that unifies a powerful Fourier series to parameterize arbitrary shapes, a winding number-based mapping to translate them into the pixel grid required by DNNs, and signal energy constraints that enhance optimization efficiency while ensuring physically plausible shapes. Our work provides a versatile framework for probing the geometric world of DNNs and opens new frontiers for challenging and understanding machine perception.