# Mathematical Perspective of Machine Learning

arXiv: https://arxiv.org/abs/2007.01503 · HTML: https://mlsanity.com/paper/2007.01503/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2020.

## Built on by (most cited first, 5 of 5)

- [An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning](https://mlsanity.com/paper/2408.13222/) (2024)
- [Convergence for adaptive resampling of random Fourier features](https://mlsanity.com/paper/2509.03151/) (2025)
- [Non-asymptotic estimates of the minimal risk in statistical learning](https://mlsanity.com/paper/2606.23295/) (2026)
- [Finite Samples for Shallow Neural Networks](https://mlsanity.com/paper/2503.12744/) (2025)
- [Cluster-Based Generalized Additive Models Informed by Random Fourier Features](https://mlsanity.com/paper/2512.19373/) (2025)

## Abstract (arXiv)

We take a closer look at some theoretical challenges of Machine Learning as a function approximation, gradient descent as the default optimization algorithm, limitations of fixed length and width networks and a different approach to RNNs from a mathematical perspective.