FRIA Doctoral Project

Bessel CNNs

For much longer than Machine Learning has existed, Physics has tried to model processes from observations. In the past, multiple theoretical and experimental tools were developed by physicists to carry out this task. As the objectives of Physics and Machine Learning are quite similar, several works have shown that Machine Learning can sometimes benefit from work initially done in Physics. This project follows this line of work by taking advantage of the well-known Bessel functions used in Physics in image analysis. For a number of applications in image analysis, learning models already prepared to handle rotation-invariance may be desirable as it might require less data for training and result in models with fewer parameters and better performance. The goal of this research project is to develop a new kind of layer in convolutional neural networks in order to achieve rotation-invariance for multichannel image analysis with the use of Bessel functions. Bessel functions will allow us to obtain a new representation of the image, more suitable to developing a rotation-invariant operation between filters and images. Another important part of the project will be to consider using (bi-)quaternions or other Clifford algebras in order to manage multiple channels of the image. Recent studies have already shown that these algebras are promising for several applications, and it will be interesting to consider them in our developments.



Advances in Neural Information Processing Systems