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

2026-05-12

AI Summary

Implicit Neural Representations (INRs) are inherently biased toward low-frequency components due to the spectral preferences of multilayer perceptrons, hindering effective reconstruction of high-frequency details. Moreover, existing frequency-tuning approaches overlook the influence of model depth. To address these limitations, this work introduces the Spectral Energy Centroid (SEC) as a universal metric to quantify the spectral discrepancy between target signals and INRs. Based on SEC, we develop SEC-Conf, a depth-agnostic hyperparameter configuration strategy that accurately assesses signal complexity, guides embedding layer tuning, and aligns spectral behaviors across diverse architectures. Experiments demonstrate that SEC-Conf consistently outperforms existing heuristic methods across multiple tasks, exhibits strong robustness to varying network depths, and reveals a reliable correlation between signal complexity and INR performance.

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.

Problem

• Implicit Neural Representations
• spectral bias
• frequency learning
• model depth
• Spectral Energy Centroid

Innovation

• Spectral Energy Centroid
• Implicit Neural Representations
• spectral bias
• hyperparameter selection
• frequency analysis