Anastasia Remizova

Rodrigo Veiga, Anastasia Remizova, Nicolas Macris

We investigate the test risk of continuous-time stochastic gradient flow dynamics in learning theory. Using a path integral formulation we provide, in the regime of a small learning rate, a general formula for computing the difference between test risk curves of pure gradient and stochastic gradient flows. We apply the general theory to a simple model of weak features, which displays the double descent phenomenon, and explicitly compute the corrections brought about by the added stochastic term in the dynamics, as a function of time and model parameters. The analytical results are compared to simulations of discrete-time stochastic gradient descent and show good agreement.

Andrey Davydov, Anastasia Remizova, Victor Constantin et al.

The Skinned Multi-Person Linear (SMPL) model can represent a human body by mapping pose and shape parameters to body meshes. This has been shown to facilitate inferring 3D human pose and shape from images via different learning models. However, not all pose and shape parameter values yield physically-plausible or even realistic body meshes. In other words, SMPL is under-constrained and may thus lead to invalid results when used to reconstruct humans from images, either by directly optimizing its parameters, or by learning a mapping from the image to these parameters. In this paper, we therefore learn a prior that restricts the SMPL parameters to values that produce realistic poses via adversarial training. We show that our learned prior covers the diversity of the real-data distribution, facilitates optimization for 3D reconstruction from 2D keypoints, and yields better pose estimates when used for regression from images. We found that the prior based on spherical distribution gets the best results. Furthermore, in all these tasks, it outperforms the state-of-the-art VAE-based approach to constraining the SMPL parameters.