# Parametric machines: a fresh approach to architecture search

arXiv: https://arxiv.org/abs/2007.02777 · HTML: https://mlsanity.com/paper/2007.02777/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2020.

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

- [Machines of finite depth: towards a formalization of neural networks](https://mlsanity.com/paper/2204.12786/) (2022)
- [Neural network layers as parametric spans](https://mlsanity.com/paper/2208.00809/) (2022)

## Abstract (arXiv)

Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how simple machines can be combined into more complex ones. We explore finite- and infinite-depth machines, which generalize neural networks and neural ordinary differential equations. Borrowing ideas from functional analysis and kernel methods, we build complete, normed, infinite-dimensional spaces of machines, and we discuss how to find optimal architectures and parameters -- within those spaces -- to solve a given computational problem. In our numerical experiments, these kernel-inspired networks can outperform classical neural networks when the training dataset is small.