# Learning with Known Operators reduces Maximum Training Error Bounds

## TL;DR

This paper introduces a method to incorporate known operators into machine learning models, reducing maximum training error bounds and the number of free parameters, with applications in physics and imaging.

## Contribution

It presents a novel framework for embedding prior knowledge via known operators, leading to tighter error bounds and improved model efficiency.

## Key findings

- Inclusion of known operators reduces maximum training error bounds.
- Using known operators decreases the number of free parameters.
- The approach is effective across diverse applications like CT reconstruction and vessel segmentation.

## Abstract

We describe an approach for incorporating prior knowledge into machine learning algorithms. We aim at applications in physics and signal processing in which we know that certain operations must be embedded into the algorithm. Any operation that allows computation of a gradient or sub-gradient towards its inputs is suited for our framework. We derive a maximal error bound for deep nets that demonstrates that inclusion of prior knowledge results in its reduction. Furthermore, we also show experimentally that known operators reduce the number of free parameters. We apply this approach to various tasks ranging from CT image reconstruction over vessel segmentation to the derivation of previously unknown imaging algorithms. As such the concept is widely applicable for many researchers in physics, imaging, and signal processing. We assume that our analysis will support further investigation of known operators in other fields of physics, imaging, and signal processing.