# On the Universal Statistical Consistency of Expansive Hyperbolic Deep Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2411.10128 · HTML: https://mlsanity.com/paper/2411.10128/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 46 references that are in the map.
- First posted on arXiv 15 Nov 2024.

## Builds on (most cited first, 6 of 6)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [Contrastive Multi-view Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2205.02618/) (2022)
- [Autoencoding Hyperbolic Representation for Adversarial Generation](https://mlsanity.com/paper/2201.12825/) (2022)
- [Hyperbolic Neural Networks++](https://mlsanity.com/paper/2006.08210/) (2020)

## Built on by (most cited first, 2 of 2)

- [Cartan Networks: Group theoretical Hyperbolic Deep Learning](https://mlsanity.com/paper/2505.24353/) (2025)
- [Transformers Are Universally Consistent](https://mlsanity.com/paper/2505.24531/) (2025)

## Abstract (arXiv)

The emergence of Deep Convolutional Neural Networks (DCNNs) has been a pervasive tool for accomplishing widespread applications in computer vision. Despite its potential capability to capture intricate patterns inside the data, the underlying embedding space remains Euclidean and primarily pursues contractive convolution. Several instances can serve as a precedent for the exacerbating performance of DCNNs. The recent advancement of neural networks in the hyperbolic spaces gained traction, incentivizing the development of convolutional deep neural networks in the hyperbolic space. In this work, we propose Hyperbolic DCNN based on the Poincar'e Disc. The work predominantly revolves around analyzing the nature of expansive convolution in the context of the non-Euclidean domain. We further offer extensive theoretical insights pertaining to the universal consistency of the expansive convolution in the hyperbolic space. Several simulations were performed not only on the synthetic datasets but also on some real-world datasets. The experimental results reveal that the hyperbolic convolutional architecture outperforms the Euclidean ones by a commendable margin.