Learning Invariances with Generalised Input-Convex Neural Networks

• DOI: 10.48550/arxiv.2204.07009
• Publication Date: 2022-01-01
• Authors: Vitali Nesterov; Fabricio Arend To...; Monika Nagy-Huber; Maxim Samarin; Volker Röth
• Keywords: Manifold (fluid mechanics)

Considering smooth mappings from input vectors to continuous targets, our goal is characterise subspaces of the domain, which are invariant under such mappings. Thus, we want manifolds implicitly defined by level sets. Specifically, this characterisation should be a global parametric form, especially useful for different informed data exploration tasks, as building grid-based approximations, sampling points along curves, or finding trajectories on manifold. However, parameterisations can only exist if sets connected. For purpose, introduce novel and flexible class neural networks that generalise input-convex networks. These represent functions guaranteed have connected forming space. We further show these always found efficiently. Lastly, demonstrate technique characterising invariances powerful generative tool in real-world applications, computational chemistry.