Explore an innovative approach to unsupervised learning of geometrically meaningful representations through equivariant variational autoencoders (VAEs) with hyperspherical latent representations in this 20-minute conference talk. Discover how the equivariant encoder/decoder ensures geometrically meaningful latents grounded in the input space, and learn about mapping these latents to hyperspheres for interpretation as points in a Kendall shape space. Examine the extension of the Kendall-shape VAE paradigm, providing a general definition of Kendall shapes in terms of group representations for more flexible KS-VAE modeling. Gain insights into how learning with generalized Kendall shapes, as opposed to landmark-based shapes, enhances representation capacity in this cutting-edge presentation from the Conference GSI.