The Fibonacci Network: A Simple Alternative for Positional Encoding

TL;DR

The paper introduces Fibonacci Networks, a simple architecture that enables MLPs to reconstruct high-frequency signals without positional encoding, by training blocks on specific frequency components.

Contribution

It proposes a novel Fibonacci Network architecture that reconstructs high frequencies without positional encoding, reducing artifacts and hyperparameters.

Findings

Fibonacci Networks can output high frequencies from low-frequency inputs.

Training each block on specific frequencies enables high-frequency reconstruction.

The approach reduces artifacts compared to traditional positional encoding.

Abstract

Coordinate-based Multi-Layer Perceptrons (MLPs) are known to have difficulty reconstructing high frequencies of the training data. A common solution to this problem is Positional Encoding (PE), which has become quite popular. However, PE has drawbacks. It has high-frequency artifacts and adds another hyper-hyperparameter, just like batch normalization and dropout do. We believe that under certain circumstances PE is not necessary, and a smarter construction of the network architecture together with a smart training method is sufficient to achieve similar results. In this paper, we show that very simple MLPs can quite easily output a frequency when given input of the half-frequency and quarter-frequency. Using this, we design a network architecture in blocks, where the input to each block is the output of the two previous blocks along with the original input. We call this a {\it Fibonacci Network}. By training each block on the corresponding frequencies of the signal, we show that Fibonacci Networks can reconstruct arbitrarily high frequencies.