Generative modeling of symmetric densities has a range of applications in AI for science, from drug discovery to physics simulations. The existing generative modeling paradigm for invariant densities combines an invariant prior with an equivariant generative process. However, we observe that this technique is not necessary and has several drawbacks resulting from the limitations of equivariant networks. Instead, we propose to model a learned slice of the density so that only one representative element per orbit is learned. To accomplish this, we learn a group-equivariant canonicalization network that maps training samples to a canonical pose and train a non-equivariant generative model over these canonicalized samples. We implement this idea in the context of diffusion models. Our preliminary experimental results on molecular modeling are promising, demonstrating improved sample quality and faster inference time.

Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not always obvious. Here, we analyze a key limitation that arises in equivariant functions: their incapacity to break symmetry at the level of individual data samples. In response, we introduce a novel notion of 'relaxed equivariance' that circumvents this limitation. We further demonstrate how to incorporate this relaxation into equivariant multilayer perceptrons (E-MLPs), offering an alternative to the noise-injection method. The relevance of symmetry breaking is then discussed in various application domains: physics, graph representation learning, combinatorial optimization and equivariant decoding.

Computing science researcher Siamak Ravanbakhsh (middle), with his co-supervisors Russell Greiner (left) and David Wishart. Ravanbakhsh has developed a computer system called Bayesil that could dramatically improve diagnosis and treatment of a wide spectrum of diseases. Siamak Ravanbakhsh, who recently completed his PhD in computing science at the University of Alberta and whose research was recently published in the scientific journal PLOS ONE, said Bayesil, the computer application resulting from this breakthrough, is pretty easy to explain in basic terms. "There is this technology called NMR spectrometry, which uses some of the same physical principles as MRI. This technology is very cool, because it can determine the concentration of certain compounds in your body," he said.