Physical Society Colloquium

Unexpected lessons from neural networks built with symmetry

Tess Smidt

Department of Electrical Engineering and Computer Science
MIT

Physical data contains rich context that is difficult, awkward, or impossible to articulate using off-the-shelf machine learning methods. For example, geometry and geometric tensors used to describe physical systems are traditionally challenging data types to use for machine learning because coordinates and coordinate systems are sensitive to the symmetries of space. There are many ways to imbue machine learning models with this context (e.g. input representation, training schemes, constraining model structure); each vary in their flexibility and robustness. In this talk, I'll give examples of some surprising consequences of what happens when we build physical assumptions into the functional forms of our machine learning models, i.e. imposing physical constraints through the operations a model comprises.

Specifically, I'll discuss properties of Euclidean Neural Networks which are constructed to preserve 3D Euclidean symmetry: 3D rotations, translations, and inversion. Perhaps unsurprisingly, symmetry-preserving algorithms are extremely data-efficient; they are able to achieve better results with less training data. More unexpectedly, Euclidean Neural Networks also act as “symmetry-compilers”: they can only learn tasks that are symmetrically well-posed and they can also help uncover when there is symmetry implied missing information. I'll give examples of how these properties can help us ask scientific questions and illuminate the full implications of our assumptions. To conclude, I'll highlight some open questions in neural networks relevant to representing physical systems.