17 listopada 2021 20:18
Grzegorz Głuch: Noether: The More Things Change, the More Stay the Same - śr. 24.11.2021, 14:15
Serdecznie zapraszamy na wykład Grzegorz Głucha - naszego absolwenta, który obecnie pracuje nad swoim doktoratem na EPFL i opowie o tym czym się tam zajmuje.
Wykład odbędzie się w środę 24.11.2021 w sali 119 II UWr. Ze względów covidowych prosimy o wcześniejszą rejestrację.
Noether: The More Things Change, the More Stay the Same
Symmetries have proven to be important ingredients in the analysis of neural networks. So far their use has mostly been implicit or seemingly coincidental. I will explain how to undertake a systematic study of the role that symmetry plays. In particular, how symmetry interacts with the learning algorithm. The key ingredient in the study is played by Noether’s celebrated theorem which, informally speaking, states that symmetry leads to conserved quantities (e.g., conservation of energy or conservation of momentum). In the realm of neural networks under gradient descent, model symmetries imply restrictions on the gradient path. E.g., I will show that symmetry of activation functions leads to boundedness of weight matrices, for the specific case of linear activations it leads to balance equations of consecutive layers, data augmentation leads to gradient paths that have “momentum”-type restrictions, and time symmetry leads to a version of the Neural Tangent Kernel.
Symmetry alone does not specify the optimization path, but the more symmetries are contained in the model the more restrictions are imposed on the path. Since symmetry also implies over-parametrization, this in effect implies that some part of this over-parametrization is cancelled out by the existence of the conserved quantities. Symmetry can therefore be thought of as one further important tool in understanding the performance of neural networks under gradient descent.