Tao Wu

Pierre Bréchet, Tao Wu, Thomas Möllenhoff et al.

We tackle the challenge of disentangled representation learning in generative adversarial networks (GANs) from the perspective of regularized optimal transport (OT). Specifically, a smoothed OT loss gives rise to an implicit transportation plan between the latent space and the data space. Based on this theoretical observation, we exploit a structured regularization on the transportation plan to encourage a prescribed latent subspace to be informative. This yields the formulation of a novel informative OT-based GAN. By convex duality, we obtain the equivalent view that this leads to perturbed ground costs favoring sparsity in the informative latent dimensions. Practically, we devise a stable training algorithm for the proposed informative GAN. Our experiments support the hypothesis that such regularizations effectively yield the discovery of disentangled and interpretable latent representations. Our work showcases potential power of a regularized OT framework in the context of generative modeling through its access to the transport plan. Further challenges are addressed in this line.

Emanuel Laude, Tao Wu, Daniel Cremers

In this work, we consider nonconvex composite problems that involve inf-convolution with a Legendre function, which gives rise to an anisotropic generalization of the proximal mapping and Moreau-envelope. In a convex setting such problems can be solved via alternating minimization of a splitting formulation, where the consensus constraint is penalized with a Legendre function. In contrast, for nonconvex models it is in general unclear that this approach yields stationary points to the infimal convolution problem. To this end we analytically investigate local regularity properties of the Moreau-envelope function under prox-regularity, which allows us to establish the equivalence between stationary points of the splitting model and the original inf-convolution model. We apply our theory to characterize stationary points of the penalty objective, which is minimized by the elastic averaging SGD (EASGD) method for distributed training. Numerically, we demonstrate the practical relevance of the proposed approach on the important task of distributed training of deep neural networks.

Yvain Quéau, Bastien Durix, Tao Wu et al.

We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve in practice. Rather, we use light-emitting diodes (LEDs) to illuminate the scene to reconstruct. Such point light sources are very convenient to use, yet they yield a more complex photometric stereo model which is arduous to solve. We first derive in a physically sound manner this model, and show how to calibrate its parameters. Then, we discuss two state-of-the-art numerical solutions. The first one alternatingly estimates the albedo and the normals, and then integrates the normals into a depth map. It is shown empirically to be independent from the initialization, but convergence of this sequential approach is not established. The second one directly recovers the depth, by formulating photometric stereo as a system of PDEs which are partially linearized using image ratios. Although the sequential approach is avoided, initialization matters a lot and convergence is not established either. Therefore, we introduce a provably convergent alternating reweighted least-squares scheme for solving the original system of PDEs, without resorting to image ratios for linearization. Finally, we extend this study to the case of RGB images.