Theory and Practice of Un-trained Neural Networks

• Applicant: Professor Dr. Reinhard Heckel
• Subject Area: Communication Technology and Networks, High-Frequency Technology and Photonic Systems, Signal Processing and Machine Learning for Information Technology
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 456465471

Deep neural networks have emerged as highly successful tools for signal and image recovery and restoration. This success is often attributed to large amounts of training data. However, recent findings challenge this view and instead suggest that a major contributing factor to this success is that the architecture of the network imposes strong prior assumptions---so strong that it enables image recovery without any training data. For example, our promising preliminary results show that it is possible i) to remove noise and corruptions from an image by fitting a convolutional network to the corrupted image, without ever having trained the network, and to ii) achieve state-of-the-art performance for accelerated magnetic resonance imaging, an important medical imaging technique, again without using any training data.However, it is widely open why un-trained networks work so well for signal recovery problems, how their high computational cost can be reduced, and whether this technique is applicable to a much broader set of problems, beyond image reconstruction problems. Motivated by the recent success of un-trained neural networks, the goal of this project is to i) understand theoretically why un-trained neural networks work so well for imaging problems, ii) evaluate and guarantee robustness of un-trained neural networks,iii) develop fast algorithms for signal recovery with un-trained methods, andiv) to build new algorithms based on un-trained neural networks for applications beyond imaging, in particular for unsupervised learning.

• DFG Programme: Research Grants