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Geometric Sensitive Hashing functions, a family of Local Sensitive Hashingfunctions, are neural network models that learn class-specific manifoldgeometry in supervised learning. However, given a set of supervised learningtasks, understanding the manifold geometries that can represent each task andthe kinds of relationships between the tasks based on them has received littleattention. We explore a formalization of this question by considering agenerative process where each task is associated with a high-dimensionalmanifold, which can be done in brain-like models with neuromodulatory systems.Following this formulation, we define \emph{Task-specific Geometric SensitiveHashing~(T-GSH)} and show that a randomly weighted neural network with aneuromodulation system can realize this function.

Randomly Weighted Neuromodulation in Neural Networks Facilitates Learning of Manifolds Common Across Tasks