Learning with Known Operators reduces Maximum Training Error Bounds.

Area of Science:

• Machine Learning
• Physics
• Signal Processing
• Image Reconstruction

Background:

• Machine learning algorithms often lack embedded prior knowledge crucial for specific scientific domains.
• Incorporating domain-specific operations into algorithms is challenging but essential for accuracy.

Purpose of the Study:

• To present a novel framework for integrating prior knowledge into machine learning algorithms.
• To demonstrate the benefits of incorporating known operators in terms of error reduction and parameter efficiency.

Main Methods:

• Developed a framework accepting operations with computable gradients or sub-gradients.
• Derived a maximal error bound for deep neural networks incorporating prior knowledge.
• Conducted experiments on tasks like CT image reconstruction and vessel segmentation.

Main Results:

• Inclusion of prior knowledge demonstrably reduces the maximal error bound in deep networks.
• Experimental results show that known operators decrease the number of free parameters.
• Successfully applied the approach to diverse tasks including CT reconstruction and vessel segmentation.

Conclusions:

• The proposed framework is widely applicable across physics, imaging, and signal processing.
• Embedding prior knowledge enhances machine learning model performance and efficiency.
• This work encourages further investigation of known operators in scientific machine learning.