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Toward the Spectral Bias Alleviation by Normalizations in Coordinate Networks
IEEE Transactions on Pattern Analysis and Machine Intelligence
|February 23, 2026
Summary
Normalization techniques improve coordinate networks by addressing spectral bias, enhancing their ability to learn high-frequency signals in inverse problems. This overcomes limitations in tasks like image reconstruction and signal processing.
Area of Science:
- Scientific computing
- Inverse problems
- Machine learning
Background:
- Coordinate networks are prevalent in inverse problems for signal representation.
- A significant challenge is spectral bias, hindering the learning of high-frequency components.
- This bias stems from the pathological eigenvalue distribution of the neural tangent kernel (NTK).
Purpose of the Study:
- To investigate the impact of classical normalization techniques on the spectral bias of coordinate networks.
- To propose novel normalization methods for improving coordinate network performance.
- To demonstrate the effectiveness of normalization in enhancing high-frequency signal learning.
Main Methods:
- Analyzing the eigenvalue distribution of the NTK in coordinate networks.
- Applying batch normalization and layer normalization to coordinate networks.
- Developing and testing two new hybrid normalization techniques.
Main Results:
- Normalization techniques were shown to reduce the maximum and variance of NTK eigenvalues.
- This reduction shifts the eigenvalue distribution, effectively alleviating spectral bias.
- The proposed normalization methods achieved state-of-the-art results across various scientific computing tasks.
Conclusions:
- Classical and novel normalization techniques can significantly mitigate spectral bias in coordinate networks.
- These improvements enable coordinate networks to better capture high-frequency signal components.
- Normalization-based coordinate networks offer enhanced performance in diverse applications like image compression and medical imaging reconstruction.
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