Blog

2023 CMS Winter Meeting: Final thoughts and congrats to Marco!

Co-organizing the 2023 CMS Winter Meeting together with Alina Stancu and François Bergeron, the scientific organizing committee and the CMS staff has been a real blast. The success of this meeting makes me proud to be part of the Canadian mathematical community: we are so vibrant, diverse, and friendly! I am also grateful to all the Department members and colleagues from other institutions (faculty, postdocs, and students) who enthusiastically participated in this meeting by co-organizing sessions, offering minicourses, delivering talks, and presenting posters, hence showcasing our excellent work at the national level, and contributing to making this event the success that it was. I would also like to thank the Faculty of Arts and Science and our Department for financially supporting the event and our students.

And congratulations to Marco Mignacca, a former undergraduate student from Concordia University (now a grad student at McGill) who received the CMS Student Committee Award for the best poster in the AARMS/CMS Poster competition! Marco was awarded a prestigious NSERC undergraduate student summer fellowship to collaborate with Jason Bramburger and me on the award-winning research poster in the summer of 2023.

For more info, see our Departmental Notice (by Christopher Plenzich):

https://www.concordia.ca/cunews/artsci/math-stats/2023/12/08/successful-2023-canadian-mathematical-society-winter-meeting-led.html?c=/artsci/math-stats 

Model-adapted Fourier sampling for generative compressed sensing 

A new paper in collaboration with A. Berk, Y. Plan, M. Scott, X. Sheng and O. Yilmaz has just been accepted to the NeurIPS 2023 workshop "Deep Learning and Inverse Problems"! 

https://arxiv.org/abs/2310.04984 

In this work, we provide new recovery guarantees for compressed sensing with deep generative priors and Fourier-type measurements, motivated by applications in computational imaging. Our new theoretical results show that adapting the sampling scheme to the generative model yields substantially improved sample complexity than random uniform sampling. Our theory is validated by numerical experiments on the CelebA dataset.

Generalization Limits of Graph Neural Networks in Identity Effects Learning

A new preprint in collaboration with Giuseppe Alessio D'Inverno and Mirco Ravanelli is on the arXiv!

https://arxiv.org/abs/2307.00134 

We establish new theorems about fundamental generalization limits of Graph Neural Networks (GNNs) for the problem of identity effect learning (i.e., classifying whether two objects are identical or not). In the paper, we prove impossibility theorems for GNNs when the identity effect information is encoded at the node feature level. Conversely, we show that GNNs are able to learn identity effects based on graph topological information using an approach based on the Weisfeiler-Lehman coloring test. The theory is validated and complemented by extensive numerical illustrations.

A GitHub repository with code needed to reproduce our numerical results, curated by G.A. D'Inverno, can be found at the following link:

https://github.com/AleDinve/gnn_identity_effects 

The Square Root LASSO and the "tuning trade off"

Aaron Berk, Tim Hoheisel and I have recently submitted a new paper on the Square Root LASSO, available on the arXiv at 

https://arxiv.org/abs/2303.15588

Building on our recent work LASSO Reloaded, we propose a variational analysis of the Square Root LASSO, showing regularity results for the solution map and studying tuning parameter sensitivity. More specifically, we identify assumptions that guarantee well-posedness and Lipschitz stability, with explicit upper bounds. Our investigation reveals the presence of a "tuning trade off" and suggests that the robustness of the Square Root LASSO's optimal tuning to measurement noise comes at the price of increased sensitivity of the solution map to the tuning parameter itself.