Spectral Energy Centroid: a Metric for Improving Performance and Analyzing Spectral Bias in Implicit Neural Representations

TL;DR

This paper introduces the Spectral Energy Centroid (SEC) metric to analyze and improve implicit neural representations by quantifying spectral bias, aiding hyperparameter tuning, and understanding model performance.

Contribution

It presents SEC as a versatile tool for analyzing spectral bias, optimizing hyperparameters, and aligning spectral properties across INR architectures.

Findings

SEC outperforms existing heuristics in hyperparameter selection.

SEC reliably proxies signal complexity.

SEC effectively aligns spectral biases across models.

Abstract

Implicit Neural Representations (INRs) model continuous signals using multilayer perceptrons (MLPs), enabling compact, differentiable, and high-fidelity representations of data across diverse domains. However, due to the low-frequency bias of MLPs that prevents effective learning of small details, the model's frequency must be carefully tuned through the embedding layer. Prior work established that this tuning can be performed before training based on the target signal, but it did not account for the significant effect of model depth, indicating that our understanding of the relationship between frequency and INR performance remains limited. To gain insights into this relationship, we utilize the Spectral Energy Centroid (SEC) metric that quantifies the frequency of target images and the spectral bias of INR models. We show that SEC is a versatile tool for INR analysis, demonstrating its utility across three tasks: (1) a data-driven strategy (SEC-Conf) for hyperparameter selection that outperforms existing heuristics and is robust to model depth, (2) a reliable proxy for signal complexity, and (3) effective alignment of spectral biases across diverse INR architectures.