Operator-theoretic Implicit Neural Representation

Sourav Pal, Harshavardhan Adepu, Clinton Wang, Polina Golland, Vikas Singh

Keywords: implicit neural representation, operator

Abstract: The idea of representing a signal as the weights of a neural network, called Implicit Neural Representations (INR), has led to exciting implications for compression, view synthesis and 3D volumetric data understanding. An emergent problem setting here pertains to the use of INR for downstream processing tasks. Despite a few conceptual results, this remains extremely challenging because the INR for a given signal often exists in isolation. What does the local region in the neighborhood around a given INR even correspond to? Based on this inspiration, we offer an operator theoretic reformulation of the INR model, which we call Operator INR (or O-INR). At a high level, instead of mapping positional encodings to a signal, O-INR maps function spaces to function spaces. A practical form of this general casting of the problem is obtained by appealing to Integral Transform. The resultant model can mostly do away with Multi-layer Perceptrons (MLPs) that dominate nearly all existing INR models -- we show that convolutions are sufficient and offer numerous benefits in training including numerically stable behavior. We show that O-INR can easily handle most problem settings in the literature, where it meets or exceeds the performance profile of baselines. These benefits come with minimal, if any, compromise.

Primary Area: representation learning for computer vision, audio, language, and other modalities

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Submission Number: 2967