# Fiber Bundle Networks: A Geometric Machine Learning Paradigm

arXiv: https://arxiv.org/abs/2512.01151 · HTML: https://mlsanity.com/paper/2512.01151/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 7 of 7)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [PANNs: Large-Scale Pretrained Audio Neural Networks for Audio Pattern Recognition](https://mlsanity.com/paper/1912.10211/) (2019)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Riemannian Metric Learning via Optimal Transport](https://mlsanity.com/paper/2205.09244/) (2022)
- [End-to-End Environmental Sound Classification using a 1D Convolutional Neural Network](https://mlsanity.com/paper/1904.08990/) (2019)
- [Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps](https://mlsanity.com/paper/2110.06983/) (2021)
- [FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles](https://mlsanity.com/paper/2206.06513/) (2022)

## Abstract (arXiv)

We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate classification as interpretable geometric optimization on fiber bundles, where categories form the base space and wavelet-transformed features lie in the fibers above each category. We introduce two innovations: (1) learnable Riemannian metrics identifying important frequency feature components, (2) variational prototype optimization through energy function minimization. Classification is performed via Voronoi tessellation under the learned Riemannian metric, where each prototype defines a decision region and test samples are assigned to the nearest prototype, providing clear geometric interpretability. This work demonstrates that the integration of fiber bundle with machine learning provides interpretability and efficiency, which are difficult to obtain simultaneously in conventional deep learning.