%0 Generic %1 tancik2020fourier %A Tancik, Matthew %A Srinivasan, Pratul P. %A Mildenhall, Ben %A Fridovich-Keil, Sara %A Raghavan, Nithin %A Singhal, Utkarsh %A Ramamoorthi, Ravi %A Barron, Jonathan T. %A Ng, Ren %D 2020 %K nerf %T Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains %U http://arxiv.org/abs/2006.10739 %X We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem domains. These results shed light on recent advances in computer vision and graphics that achieve state-of-the-art results by using MLPs to represent complex 3D objects and scenes. Using tools from the neural tangent kernel (NTK) literature, we show that a standard MLP fails to learn high frequencies both in theory and in practice. To overcome this spectral bias, we use a Fourier feature mapping to transform the effective NTK into a stationary kernel with a tunable bandwidth. We suggest an approach for selecting problem-specific Fourier features that greatly improves the performance of MLPs for low-dimensional regression tasks relevant to the computer vision and graphics communities.

@misc{tancik2020fourier, abstract = {We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem domains. These results shed light on recent advances in computer vision and graphics that achieve state-of-the-art results by using MLPs to represent complex 3D objects and scenes. Using tools from the neural tangent kernel (NTK) literature, we show that a standard MLP fails to learn high frequencies both in theory and in practice. To overcome this spectral bias, we use a Fourier feature mapping to transform the effective NTK into a stationary kernel with a tunable bandwidth. We suggest an approach for selecting problem-specific Fourier features that greatly improves the performance of MLPs for low-dimensional regression tasks relevant to the computer vision and graphics communities.}, added-at = {2022-08-18T10:18:03.000+0200}, author = {Tancik, Matthew and Srinivasan, Pratul P. and Mildenhall, Ben and Fridovich-Keil, Sara and Raghavan, Nithin and Singhal, Utkarsh and Ramamoorthi, Ravi and Barron, Jonathan T. and Ng, Ren}, biburl = {https://www.bibsonomy.org/bibtex/28995d4ed9e9875d0a373a92c1905302d/m_gabriel}, description = {Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains}, interhash = {6fed9f77dea680e6ab7d7f159db8a3d3}, intrahash = {8995d4ed9e9875d0a373a92c1905302d}, keywords = {nerf}, note = {cite arxiv:2006.10739Comment: Project page: https://people.eecs.berkeley.edu/~bmild/fourfeat/}, timestamp = {2022-08-18T10:18:03.000+0200}, title = {Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains}, url = {http://arxiv.org/abs/2006.10739}, year = 2020 }