Spectral Bias

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Spectral bias describes how neural networks often fit smooth, low-frequency structure before fine detail, which can limit performance on oscillatory signals, sharp boundaries, and complex physical fields. Researchers study this behavior in implicit neural representations, physics-informed neural networks, neural operators, and other models, using tools such as Fourier analysis and neural tangent kernels. Mitigation methods include Fourier and wavelet features, SIREN-style periodic activations, frequency-aware losses, local or multibranch architectures, and changes to initialization or optimization. A central open question is when these interventions genuinely improve high-frequency fidelity and generalization, since benefits vary across tasks and added frequency capacity can also complicate training or distort important structure.

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37 papers6 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

PILIR: Physics-Informed Local Implicit Representation
May 1, 2026Jianfeng Li, Feng Wang, Ke TangNeural PDE Solvers Implicit Neural Representations
School of Computer Science, Wuhan University · School of Computer Science and Technology, Southern University of Science and Technology
Implicit Neural Representations: A Signal Processing Perspective
Apr 16, 2026Dhananjaya Jayasundara, Vishal M. PatelImplicit Neural Representations Spectral Bias
Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD 21218 USA
Mathematical analysis of one-layer neural network with fixed biases, a new activation function and other observations
Apr 9, 2026Fabricio Macià, Shu NakamuraShallow Neural Networks Neural Network Training Dynamics
M2ASAI, Universidad Politécnica de Madrid. ETSI Navales. Avda. de la Memoria, 4. 28040 Madrid, Spain. · Department of Mathematics, Faculty of Sciences, Gakushuin University, 1-5-1, Mejiro, Toshima, Tokyo, 171-8588 Japan
(Sparse) Attention to the Details: Preserving Spectral Fidelity in ML-based Weather Forecasting Models
Apr 6, 2026Maksim Zhdanov, Ana Lucic, Max Welling +1Weather Forecasting Probabilistic Forecasting
AMLab · University of Amsterdam · CuspAI
Coordinate Encoding on Linear Grids for Physics-Informed Neural Networks
Mar 24, 2026Tetsuro Tsuchino, Motoki ShigaNeural PDE Solvers Physics-Informed ML
Graduate School of Engineering, Gifu University, Japan · International Center for Synchrotron Radiation Innovation Smart, Tohoku University, Japan · Unprecedented-scale Data Analytics Center, Tohoku University, Japan +3
Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines
Feb 22, 2026Siavash Khodakarami, Vivek Oommen, Nazanin Ahmadi Daryakenari +2Spectral Bias Physics-Informed ML
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA · School of Engineering, Brown University, Providence, RI 02912, USA
Pseudo-differential-enhanced physics-informed neural networks
Feb 16, 2026Andrew GracykPDE Solving Spectral Bias
Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States

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PILIR: Physics-Informed Local Implicit Representation

Jianfeng Li, Feng Wang, Ke Tang

School of Computer Science, Wuhan University · School of Computer Science and Technology, Southern University of Science and Technology

Neural PDE Solvers Implicit Neural Representations Spectral Bias PDE Operator Learning Physics-Informed ML Physics-Informed Neural Operators

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Physics-Informed Neural Networks have become a powerful mesh-free method for solving partial differential equations, but their performance is often limited by spectral bias. Specifically, in standard MLPs used in PINNs, the global parameter coupling causes the model to prioritize learning low-frequency components, resulting in slow convergence for high-frequency details. To overcome this limitation, we introduce the Physics-Informed Local Implicit Representation (PILIR). Our approach separates the global physical domain into a discrete latent feature space and a continuous generative decoder. By using a learnable grid to encode explicit spatial locality, PILIR can capture high-frequency details locally, preventing dilution by global patterns. A generative neural operator then synthesizes these local latent features into continuous physical fields, allowing accurate reconstruction of fine-scale structures. Experiments on a range of challenging PDEs show that PILIR effectively mitigates spectral bias, thereby boosting the convergence of high-frequency details and achieving superior accuracy compared to state-of-the-art methods.