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

arXiv: https://arxiv.org/abs/2605.12709 · HTML: https://mlsanity.com/paper/2605.12709/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [The Convergence Rate of Neural Networks for Learned Functions of Different Frequencies](https://mlsanity.com/paper/1906.00425/) (2019)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Understanding training and generalization in deep learning by Fourier analysis](https://mlsanity.com/paper/1808.04295/) (2018)
- [A Comprehensive Benchmark for Single Image Compression Artifacts Reduction](https://mlsanity.com/paper/1909.03647/) (2019)
- [ResFields: Residual Neural Fields for Spatiotemporal Signals](https://mlsanity.com/paper/2309.03160/) (2023)
- [An Analytical Theory of Spectral Bias in the Learning Dynamics of Diffusion Models](https://mlsanity.com/paper/2503.03206/) (2025)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [FreSh: Frequency Shifting for Accelerated Neural Representation Learning](https://mlsanity.com/paper/2410.05050/) (2024)
- [A Scalable Walsh-Hadamard Regularizer to Overcome the Low-degree Spectral Bias of Neural Networks](https://mlsanity.com/paper/2305.09779/) (2023)
- [TabINR: An Implicit Neural Representation Framework for Tabular Data Imputation](https://mlsanity.com/paper/2510.01136/) (2025)

## Abstract (arXiv)

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.