We propose an Optimal Transport (OT)-based generative model from the Wasserstein Autoencoder (WAE) family of models, with the following innovative property: the optimization of the latent point positions takes place over the full training dataset rather than over a minibatch. Our contributions are the following: We define a new class of global Wasserstein Autoencoder models, and implement an Optimal Transport-based incarnation we call the Global Sinkhorn Autoencoder. We implement several metrics for evaluating such models, both in the unsupervised setting, and in a semi-supervised setting, which are the following: the global OT loss, which measures the OT loss on the full test dataset; the reconstruction error on the full test dataset; a so-called covered area which measures how well the latent points are matched; and two types of clustering measures.

I will introduce some theoretical results related to the convergence and generalization capabilities of neural networks, in light of articles published at the NeurIPS 2023 conference in December. The first part of the presentation will summarize some important, earlier results, and then it will cover numerous articles based on these, which were presented at NeurIPS. The aim of the presentation is to provide a comprehensive overview of the current state of the field and the currently popular research directions.

I will overview some applications of supervised and reinforcement learning methods to knot theory that might be useful in other areas of mathematics.

We explore element-wise convex combinations of two permutation-aligned neural network parameter vectors $\Theta_A$ and $\Theta_B$ of size $d$. We conduct extensive experiments by examining various distributions of such model combinations parametrized by elements of the hypercube and its vicinity. Our findings reveal that broad regions of the hypercube form surfaces of low loss values, indicating that the notion of linear mode connectivity extends to a more general phenomenon which we call mode combinability.