# Modulated Periodic Activations for Generalizable Local Functional Representations

**Authors:** Ishit Mehta, Michaël Gharbi, Connelly Barnes, Eli Shechtman, Ravi Ramamoorthi, Manmohan Chandraker  
**arXiv:** [2104.03960](https://arxiv.org/abs/2104.03960)  
**Date:** 2021-04-08  
**Summary page:** https://www.summarizepaper.com/en/paper/2104.03960v1/

## Key points

- The paper introduces a novel approach to improving functional representations in sampling and reconstruction problems involving low-dimensional signals like images, shapes, and light fields.
- The proposed method utilizes a dual-MLP architecture to encode signals and employs a synthesis network to create a functional mapping from low-dimensional inputs to the output domain.
- A modulation network maps a latent code corresponding to the target signal to parameters that modulate the periodic activations of the synthesis network, allowing for generalization across multiple instances.
- Introduction of a local-functional representation by partitioning the signal's domain into a regular grid enables capturing local features common across different instances while maintaining high-fidelity encoding during testing.
- The approach produces generalizable functional representations of images, videos, and shapes with superior reconstruction quality compared to previous methods optimized for single signals.

## Summary

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The paper "Modulated Periodic Activations for Generalizable Local Functional Representations" by Ishit Mehta, Michaël Gharbi, Connelly Barnes, Eli Shechtman, Ravi Ramamoorthi, and Manmohan Chandraker introduces a novel approach to improving the fidelity of functional representations in sampling and reconstruction problems involving low-dimensional signals like images, shapes, and light fields. Recent works have focused on enhancing high-frequency content representation through periodic activations or positional encodings. However, these methods often sacrifice generalization as they are optimized for a single signal. In contrast, the proposed method utilizes a dual-MLP architecture to encode signals and employs a synthesis network to create a functional mapping from low-dimensional inputs (such as pixel positions) to the output domain (e.g., RGB color). Additionally, a modulation network maps a latent code corresponding to the target signal to parameters that modulate the periodic activations of the synthesis network. This innovative approach allows for generalization across multiple instances and achieves state-of-the-art fidelity in reconstruction quality. One key aspect of this work is the introduction of a local-functional representation that enables enhanced generalization. By partitioning the signal's domain into a regular grid and assigning each tile a latent code, the method can effectively capture local features common across different instances while maintaining high-fidelity encoding during testing. The authors demonstrate through experiments that their approach produces generalizable functional representations of images, videos, and shapes with superior reconstruction quality compared to previous methods optimized for single signals. The strategy of exploiting locality in representing signals proves effective in capturing simple edges and textures that frequently reappear locally across distinct images at higher resolutions. This localized approach offers a cost-effective solution for representing high-resolution images with complex global structures by focusing on simpler local features. Overall, "Modulated Periodic Activations for Generalizable Local Functional Representations" presents an innovative framework for improving functional representations in various sampling and reconstruction tasks.