# Mathematics of Deep Learning

arXiv: https://arxiv.org/abs/1712.04741 · HTML: https://mlsanity.com/paper/1712.04741/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2017.

## Built on by (most cited first, 11 of 11)

- [Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscape](https://mlsanity.com/paper/2201.08025/) (2022)
- [A Falsificationist Account of Artificial Neural Networks](https://mlsanity.com/paper/2205.01421/) (2022)
- [Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learning](https://mlsanity.com/paper/2107.01081/) (2021)
- [Combining Image Features and Patient Metadata to Enhance Transfer Learning](https://mlsanity.com/paper/2110.05239/) (2021)
- [A Reflection on Learning from Data: Epistemology Issues and Limitations](https://mlsanity.com/paper/2107.13270/) (2021)
- [Deep Neural Networks and PIDE discretizations](https://mlsanity.com/paper/2108.02430/) (2021)
- [Enhanced Transfer Learning Through Medical Imaging and Patient Demographic Data Fusion](https://mlsanity.com/paper/2111.14388/) (2021)
- [Towards the One Learning Algorithm Hypothesis: A System-theoretic Approach](https://mlsanity.com/paper/2112.02256/) (2021)
- [Scoliosis Detection using Deep Neural Network](https://mlsanity.com/paper/2210.17269/) (2022)
- [On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon](https://mlsanity.com/paper/2308.10720/) (2023)
- [On the Expressive Power of Graph Neural Networks](https://mlsanity.com/paper/2401.01626/) (2024)

## Abstract (arXiv)

Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain elusive. This tutorial will review recent work that aims to provide a mathematical justification for several properties of deep networks, such as global optimality, geometric stability, and invariance of the learned representations.