Hi everyone, we have a guest speaker **Nutan Chen** from ARGMAX.AI and you are all cordially invited to the AMLab Seminar on **Thursday 1st October at 16:00 CEST** on **Zoom**, where **Nutan** will give a talk titled ” **Distance in Latent Space** “.

**Title : Distance in Latent Space**

**Abstract :** Measuring the similarity between data points often requires domain knowledge. It can in parts be compensated by relying on unsupervised methods such as latent-variable models, where the similarity/distance is estimated in a more compact latent space. However, deep generative models such as vanilla VAEs are not distance-preserving. Therefore, this type of model is unreliable for tasks such as precise distance measurement or smooth interpolation directly from the latent space. To solve this problem, we proposed novel methods based VAEs to constrain or measure the distance in the latent space.

In the first section of this talk, I will explore a method that embeds dynamic movement primitives into the latent space of a time-dependent VAE framework (deep variational Bayes filters). Experimental results show that our framework generalizes well, e.g., switches between movements or changing goals. Additionally, the distance between two data points that are close in time is constrained, which results in influencing the data structure of the hidden space. In the second section, I will show how we transferred ideas from Riemannian geometry to deep generative models, letting the distance between two points be the shortest path on a Riemannian manifold induced by the transformation. The method yields a principled distance measure, provides a tool for visual inspection of deep generative models, and an alternative to linear interpolation in latent space. In the third section, I will propose an extension to the framework of VAEs that allows learning flat latent manifolds, where the Euclidean metric is a proxy for the similarity between data points. This is achieved by defining the latent space as a Riemannian manifold and by regularizing the metric tensor to be a scaled identity matrix. This results in a computational efficient distance metric which is practical for applications in real-time scenarios.

**Paper Link :** Learning flat manifold of VAEs. In *International Conference on Machine Learning (ICML)*. 2020.

To gain more deep insights into connections between VAEs and manifolds and see how these are applied to robotics, feel free to join and discuss it!