Variational Neural Belief

VNB represents uncertainty over object pose and contact parameters with a Gaussian mixture model. The belief parameterization uses mixture logits, component means, and log standard deviations. VNB uses Gumbel-Softmax and location-scale reparameterization to make samples differentiable. The article argues that differentiable Gaussian-mixture samples allow CVaR gradients to flow through belief parameters into action optimization. VNB may need many mixture components for highly multimodal or complex contact posteriors.