# Emergence of Double-slit Interference by Representing Visual Space in Artificial Neural Networks

arXiv: https://arxiv.org/abs/2205.10081 · HTML: https://mlsanity.com/paper/2205.10081/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 15 of 15)

- [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)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [YOLOv4: Optimal Speed and Accuracy of Object Detection](https://mlsanity.com/paper/2004.10934/) (2020)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Simple Black-box Adversarial Attacks](https://mlsanity.com/paper/1905.07121/) (2019)
- [Emergence of grid-like representations by training recurrent neural networks to perform spatial localization](https://mlsanity.com/paper/1803.07770/) (2018)
- [Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motion](https://mlsanity.com/paper/1810.05597/) (2018)
- [DeepSkeleton: Learning Multi-task Scale-associated Deep Side Outputs for Object Skeleton Extraction in Natural Images](https://mlsanity.com/paper/1609.03659/) (2016)
- [SRN: Side-output Residual Network for Object Symmetry Detection in the Wild](https://mlsanity.com/paper/1703.02243/) (2017)
- [Ventral-Dorsal Neural Networks: Object Detection via Selective Attention](https://mlsanity.com/paper/2005.09727/) (2020)
- [ProMask: Probability Mask for Skeleton Detection](https://mlsanity.com/paper/2012.03003/) (2020)

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

- [Mode-locking Theory for Long-Range Interaction in Artificial Neural Networks](https://mlsanity.com/paper/2303.05695/) (2023)

## Abstract (arXiv)

Artificial neural networks have realized incredible successes at image recognition, but the underlying mechanism of visual space representation remains a huge mystery. Grid cells (2014 Nobel Prize) in the entorhinal cortex support a periodic representation as a metric for coding space. Here, we develop a self-supervised convolutional neural network to perform visual space location, leading to the emergence of single-slit diffraction and double-slit interference patterns of waves. Our discoveries reveal the nature of CNN encoding visual space to a certain extent. CNN is no longer a black box in terms of visual spatial encoding, it is interpretable. Our findings indicate that the periodicity property of waves provides a space metric, suggesting a general role of spatial coordinate frame in artificial neural networks.