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We show that typical implicit regularization assumptions for deep neural networks (for regression) do not hold for coordinate-MLPs, a family of MLPs that are now ubiquitous in computer vision for representing high-frequency signals.
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Smoothing noisy data with spline functions
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The statistics of natural images
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A spectral analysis of function composition and its implications for sampling in direct volume visualization
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An analysis of single-layer networks in unsupervised feature learning
Coates, A., Ng, A., and Lee, H · 2011
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In search of the real inductive bias: On the role of implicit regularization in deep learning
Neyshabur, B., Tomioka, R., and Srebro, N · 2014
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Deep learning
Goodfellow, I., Bengio, Y., and Courville, A · 2016
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Neural networks and rational functions
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Understanding deep learning requires rethinking generalization (2016)
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Learning overparameterized neural networks via stochastic gradient descent on structured data
Li, Y. and Liang, Y · 2018
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Gradient descent quantizes relu network features
Maennel, H., Bousquet, O., and Gelly, S · 2018
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Theory iiib: Generalization in deep networks
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The implicit bias of gradient descent on separable data
Soudry, D., Hoffer, E., Nacson, M. S., Gunasekar, S., and Srebro, N · 2018
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Learning implicit fields for generative shape modeling
Chen, Z. and Zhang, H · 2019
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Implicit regularization of discrete gradient dynamics in linear neural networks
Gidel, G., Bach, F., and Lacoste-Julien, S · 2019
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How implicit regularization of neural networks affects the learned function–part i
Heiss, J., Teichmann, J., and Wutte, H · 2019
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Implicit regularization in over-parameterized neural networks
Kubo, M., Banno, R., Manabe, H., and Minoji, M · 2019
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Implicit neural representations with periodic activation functions
Sitzmann, V., Martel, J., Bergman, A., Lindell, D., and Wetzstein, G · 2020
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Fourier features let networks learn high frequency functions in low dimensional domains
Tancik, M., Srinivasan, P. P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J. T., and Ng, R · 2020
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Lightsal: Lightweight sign agnostic learning for implicit surface representation
Basher, A., Sarmad, M., and Boutellier, J · 2021
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Nerf in the wild: Neural radiance fields for unconstrained photo collections
Martin-Brualla, R., Radwan, N., Sajjadi, M. S., Barron, J. T., Dosovitskiy, A., and Duckworth, D · 2021
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A-sdf: Learning disentangled signed distance functions for articulated shape representation
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Texture fields: Learning texture representations in function space
Oechsle, M., Mescheder, L., Niemeyer, M., Strauss, T., and Geiger, A · 2019
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Deepsdf: Learning continuous signed distance functions for shape representation
Park, J. J., Florence, P., Straub, J., Newcombe, R., and Lovegrove, S · 2019
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Pifu: Pixel-aligned implicit function for high-resolution clothed human digitization
Saito, S., Huang, Z., Natsume, R., Morishima, S., Kanazawa, A., and Li, H · 2019
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How do infinite width bounded norm networks look in function space?
Savarese, P., Evron, I., Soudry, D., and Srebro, N · 2019
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Scene representation networks: Continuous 3d-structure-aware neural scene representations
Sitzmann, V., Zollhöfer, M., and Wetzstein, G · 2019
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On polynomial approximations for privacy-preserving and verifiable relu networks
Ali, R. E., So, J., and Avestimehr, A. S · 2020
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Nasa neural articulated shape approximation
Deng, B., Lewis, J. P., Jeruzalski, T., Pons-Moll, G., Hinton, G., Norouzi, M., and Tagliasacchi, A · 2020
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Mu, J., Qiu, W., Kortylewski, A., Yuille, A., Vasconcelos, N., and Wang, X · 2021
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Nerfies: Deformable neural radiance fields
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D-nerf: Neural radiance fields for dynamic scenes
Pumarola, A., Corona, E., Pons-Moll, G., and Moreno-Noguer, F · 2021
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Beyond periodicity: Towards a unifying framework for activations in coordinate-mlps
Ramasinghe, S. and Lucey, S · 2021
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Derf: Decomposed radiance fields
Rebain, D., Jiang, W., Yazdani, S., Li, K., Yi, K. M., and Tagliasacchi, A · 2021
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Neural-gif: Neural generalized implicit functions for animating people in clothing
Tiwari, G., Sarafianos, N., Tung, T., and Pons-Moll, G · 2021
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Nerf–: Neural radiance fields without known camera parameters
Wang, Z., Wu, S., Xie, W., Chen, M., and Prisacariu, V. A · 2021
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Neutex: Neural texture mapping for volumetric neural rendering
Xiang, F., Xu, Z., Hasan, M., Hold-Geoffroy, Y., Sunkavalli, K., and Su, H · 2021
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pixelnerf: Neural radiance fields from one or few images
Yu, A., Ye, V., Tancik, M., and Kanazawa, A · 2021
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Understanding deep learning (still) requires rethinking generalization
Zhang, C., Bengio, S., Hardt, M., Recht, B., and Vinyals, O · 2021
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Rethinking positional encoding
Zheng, J., Ramasinghe, S., and Lucey, S · 2021
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