arXiv:2606.16575v1 Announce Type: new Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors. In this study, we investigate this limitation by examining the failure of shallow ReLU neural networks in fitting high-frequency functions. This observation identifies two important factors in resolving rapid oscillations: the initial slope scale and the distribution of partition points induced by the networks. Motivated by this analysis, we propose RepNet, a reparameteri
The paper addresses a known limitation (spectral bias) in DNNs, particularly relevant as AI systems are pushed into more complex scientific and real-world applications requiring high-fidelity function approximation.
Improving the ability of DNNs to handle oscillatory and multiscale data directly enhances their utility in scientific computing, potentially unlocking new applications and improving existing AI performance.
The proposed RepNet offers a method to mitigate spectral bias, suggesting a pathway for more robust and accurate deep learning models, especially for high-frequency data challenges.
- · AI/ML researchers
- · Scientific computing sector
- · Deep learning practitioners
- · High-performance computing (HPC)
- · AI models suffering from spectral bias
- · Traditional numerical methods (in some cases)
- · Developers unaware of advanced mitigation techniques
Deep neural networks become more effective at modeling complex physical phenomena and high-frequency signals.
This improved capability could accelerate scientific discovery and engineering design processes relying on AI simulations.
Enhanced DNN performance might reduce the need for certain domain-specific traditional solvers, expanding AI's footprint in specialized fields.
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Read at arXiv cs.LG