Title: HyperINR: Ensuring Semantics in Weights with Implicit Function Theorem
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Implicit Function Theorem, Semantics in Weights, Weight Space Learning, Implicit Neural Representations, Hypernetworks

Abstract: Implicit Neural Representations (INRs) have demonstrated remarkable capability in representing 2D and 3D data, whose semantics is convincingly captured in the weights of the corresponding neural network. Despite successes in applying INRs to various applications, a precise theoretical explanation for the mechanism of encoding semantics of data into network weights is still missing. In this work, we propose the HyperINR model, where a hypernetwork is utilized to map a learnable low-dimensional latent space to the weight space of an INR. By employing the classic Implicit Function Theorem, the HyperINR is shown to be a mathematically rigorous framework that ensures the mapping of the semantics of data to the weight latent representations. Extensive experiments of classification tasks on 2D and 3D data confirm the effectiveness of our approach and demonstrate superior performance compared to state-of-the-art methods.