Following up on this, I also explored a more direct use of #WassersteinDistance in #WGANs: Instead of training a discriminator, the generator is optimized by explicitly computing the #OptimalTransport distance between real and generated samples. This turns the loss into the actual metric of interest and removes the adversarial setup, leading to a more direct and stable training signal. And we can generate cool animations, too ^_^
🌍 https://www.fabriziomusacchio.com/blog/2023-07-30-wgan_with_direct_wasserstein_distance/
I actually wrote a short introduction to #WassersteinDistance and #OptimalTransport some time ago, if you’re looking for a more intuitive entry point:
🌍 https://www.fabriziomusacchio.com/blog/2023-07-23-wasserstein_distance/
📐📚New study on #WassersteinDistance: Bonet et al. study #geodesic rays in #Wasserstein space and derive conditions for their existence. They show that #Busemann functions can be computed via #OT, with closed-form solutions for 1D and Gaussian cases. This enables efficient sliced distances for labeled datasets, closely matching classical metrics at lower cost and supporting dataset “flows” for #TransferLearning.
📐 New preprint by Gabriel Peyré: The paper introduces a new class of spectral #Wasserstein distances, linking #OptimalTransport with normalized #gradient methods. It shows that spectrally normalized #GradientDescent can be interpreted as a gradient flow in this spectral-W geometry, providing a principled bridge between #optimization dynamics and transport metrics:
Fabrizio Musacchio