Monday, November 14, 2022
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All day |
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3pm |
11/14/2022 - 3:00pm Abstract: Consider the problem to infer the input data X given outcome labels Y, where both X and Y are defined on each node on a graph. The problem can be viewed as reversing the node prediction problem on a graph, and since the mapping from Y to X is one-to-many, it can be formulated as a conditional generative task. We propose a model of invertible graph neural networks to address the problem, where an invertible normalizing flow network is used to construct a one-to-one mapping from X to an intermediate feature H, and then a classification network is used to map H to Y. The expressiveness of graph convolution layers is analyzed in the context of the problem and supported by experiments. In computation, we introduce Wasserstein-2 regularization in the training of the flow network. We will also discuss new designs of the invertible flow network based on Wasserstein gradient flow. Joint work with Chen Xu and Yao Xie. Location:
AKW 200
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4pm |
11/14/2022 - 4:30pm We will discuss the general notion of symplectic duality between symplectic resolutions of singularities and give examples. Equivariant Hikita-Nakajima conjecture is a general conjecture about the relation between the geometry of symplectically dual varieties. We will consider the example of the Hilbert scheme of points on the affine plane and discuss the proof of the equivariant Hikita-Nakajima conjecture in this particular case. We will also briefly discuss the generalization of this proof to the case of ADHM spaces (moduli spaces of instantons on R^4). Time permitting, we will say about the possible approach towards the proof of Hikita-Nakajima conjecture for other symplectically dual pairs (such as Higgs and Coulomb branches of quiver gauge theories). The talk is based on the joint work with Pavel Shlykov arXiv:2202.09934. Location:
LOM214
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