mlsanityData to 7 Oct 2026

Learning Smooth Neural Functions via Lipschitz Regularization

arXiv 2202.08345 ↗First posted 16 Feb 2022cs.CV cs.GRcited by 86

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Abstract (arXiv)

Neural implicit fields have recently emerged as a useful representation for 3D shapes. These fields are commonly represented as neural networks which map latent descriptors and 3D coordinates to implicit function values. The latent descriptor of a neural field acts as a deformation handle for the 3D shape it represents. Thus, smoothness with respect to this descriptor is paramount for performing shape-editing operations. In this work, we introduce a novel regularization designed to encourage smooth latent spaces in neural fields by penalizing the upper bound on the field's Lipschitz constant. Compared with prior Lipschitz regularized networks, ours is computationally fast, can be implemented in four lines of code, and requires minimal hyperparameter tuning for geometric applications. We demonstrate the effectiveness of our approach on shape interpolation and extrapolation as well as partial shape reconstruction from 3D point clouds, showing both qualitative and quantitative improvements over existing state-of-the-art and non-regularized baselines.

Key facts. Cited by 86 papers in the map (data through 7 Oct 2026). Builds on 43 of its 60 references that are in the map. First posted on arXiv 16 Feb 2022.

Builds on

43 of 60 references.

References · 43

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  3. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  4. 2013Intriguing properties of neural networkscited by 5,114
  5. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  6. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  7. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  8. 2017Improved Training of Wasserstein GANscited by 2,223
  9. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,037
  10. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  11. 2017Deep Image Priorcited by 1,097
  12. 2020Implicit Geometric Regularization for Learning Shapescited by 707
31 more
  1. 2018Pixel2Mesh: Generating 3D Mesh Models from Single RGB Imagescited by 649
  2. 2016Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networkscited by 541
  3. 2021Neural Fields in Visual Computing and Beyondcited by 539
  4. 2017Neural 3D Mesh Renderercited by 437
  5. 2019Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoningcited by 420
  6. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  7. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 311
  8. 2017Parseval Networks: Improving Robustness to Adversarial Examplescited by 288
  9. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  10. 2019Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderercited by 221
  11. 2018Sorting out Lipschitz function approximationcited by 211
  12. 2017Spectral Norm Regularization for Improving the Generalizability of Deep Learningcited by 178
  13. 2018Robustness via curvature regularization, and vice versacited by 174
  14. 2019Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networkscited by 162
  15. 2019Robust Learning with Jacobian Regularizationcited by 127
  16. 2018Deep Geometric Prior for Surface Reconstructioncited by 110
  17. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
  18. 2017Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networkscited by 92
  19. 2018Improving DNN Robustness to Adversarial Attacks using Jacobian Regularizationcited by 88
  20. 2019Preventing Gradient Attenuation in Lipschitz Constrained Convolutional Networkscited by 86
  21. 2020Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networkscited by 52
  22. 2020Deep Geometric Texture Synthesiscited by 51
  23. 2020A case for new neural network smoothness constraintscited by 43
  24. 2019Adversarial Lipschitz Regularizationcited by 29
  25. 2017Gradient Regularization Improves Accuracy of Discriminative Modelscited by 26
  26. 2014Analyzing noise in autoencoders and deep networkscited by 25
  27. 2018Lipschitz regularized Deep Neural Networks generalize and are adversarially robustcited by 19
  28. 2021Mending Neural Implicit Modeling for 3D Vehicle Reconstruction in the Wildcited by 19
  29. 2018High Fidelity Semantic Shape Completion for Point Clouds using Latent Optimizationcited by 9
  30. 2020Intrinsic Point Cloud Interpolation via Dual Latent Space Navigationcited by 8
  31. 2021Intuitive Shape Editing in Latent Spacecited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 9; 2023: 18; 2024: 30; 2025: 14; 2026: 15.

86 papers.

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  1. 2023MeshDiffusion: Score-based Generative 3D Mesh Modelingcited by 198
  2. 2023Input Perturbation Reduces Exposure Bias in Diffusion Modelscited by 88
  3. 2022E-NeRV: Expedite Neural Video Representation with Disentangled Spatial-Temporal Contextcited by 76
  4. 2022PermutoSDF: Fast Multi-View Reconstruction with Implicit Surfaces using Permutohedral Latticescited by 72
  5. 2023Deep Learning on Implicit Neural Representations of Shapescited by 62
  6. 2024SpotlessSplats: Ignoring Distractors in 3D Gaussian Splattingcited by 61
  7. 2022A Policy-Guided Imitation Approach for Offline Reinforcement Learningcited by 58
  8. 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representationscited by 56
  9. 2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 49
  10. 2022A Level Set Theory for Neural Implicit Evolution under Explicit Flowscited by 42
  11. 2022On the Effectiveness of Lipschitz-Driven Rehearsal in Continual Learningcited by 39
  12. 2024Weight Clipping for Deep Continual and Reinforcement Learningcited by 29
38 more
  1. 2023IntrinsicAvatar: Physically Based Inverse Rendering of Dynamic Humans from Monocular Videos via Explicit Ray Tracingcited by 20
  2. 2024RoMo: Robust Motion Segmentation Improves Structure from Motioncited by 20
  3. 2024DecisionNCE: Embodied Multimodal Representations via Implicit Preference Learningcited by 19
  4. 2023Advancing Bayesian Optimization via Learning Correlated Latent Spacecited by 18
  5. 2023SDF4CHD: Generative Modeling of Cardiac Anatomies with Congenital Heart Defectscited by 17
  6. 2024Neuroplastic Expansion in Deep Reinforcement Learningcited by 17
  7. 2024Unsupervised Occupancy Learning from Sparse Point Cloudcited by 15
  8. 2023Transforming Radiance Field with Lipschitz Network for Photorealistic 3D Scene Stylizationcited by 14
  9. 2023FaceCLIPNeRF: Text-driven 3D Face Manipulation using Deformable Neural Radiance Fieldscited by 12
  10. 2023Mixing-Denoising Generalizable Occupancy Networkscited by 12
  11. 2024Geometry-Informed Neural Networkscited by 12
  12. 20243D Reconstruction with Fast Dipole Sumscited by 12
  13. 2025Action Tokenizer Matters in In-Context Imitation Learningcited by 12
  14. 2022Deep Deformable 3D Caricatures with Learned Shape Controlcited by 10
  15. 2023Explicit Neural Surfaces: Learning Continuous Geometry With Deformation Fieldscited by 10
  16. 2023Shape of my heart: Cardiac models through learned signed distance functionscited by 10
  17. 2023Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Modelcited by 10
  18. 2023Neural Implicit Morphing of Face Imagescited by 9
  19. 2024Rethinking Robustness Assessment: Adversarial Attacks on Learning-based Quadrupedal Locomotion Controllerscited by 9
  20. 20241-Lipschitz Neural Distance Fieldscited by 8
  21. 20254Deform: Neural Surface Deformation for Robust Shape Interpolationcited by 7
  22. 2025Optimizing Rank for High-Fidelity Implicit Neural Representationscited by 7
  23. 2022ROAD: Learning an Implicit Recursive Octree Auto-Decoder to Efficiently Encode 3D Shapescited by 6
  24. 2024Learning a Generalized Physical Face Model From Datacited by 6
  25. 2024Neural Gaussian Scale-Space Fieldscited by 6
  26. 2024CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequencescited by 6
  27. 2023Deep Learning on Object-centric 3D Neural Fieldscited by 5
  28. 2024Understanding What Affects the Generalization Gap in Visual Reinforcement Learning: Theory and Empirical Evidencecited by 5
  29. 2024Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamicscited by 5
  30. 2024Few-Shot Unsupervised Implicit Neural Shape Representation Learning with Spatial Adversariescited by 5
  31. 2024Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimizationcited by 5
  32. 2024Benchmarking Smoothness and Reducing High-Frequency Oscillations in Continuous Control Policiescited by 5
  33. 2026Structure-Preserving Learning Improves Geometry Generalization in Neural PDEscited by 5
  34. 2023TEGLO: High Fidelity Canonical Texture Mapping from Single-View Imagescited by 4
  35. 2024CombiNeRF: A Combination of Regularization Techniques for Few-Shot Neural Radiance Field View Synthesiscited by 4
  36. 2024Dual-Camera Smooth Zoom on Mobile Phonescited by 4
  37. 2023Text-guided Image-and-Shape Editing and Generation: A Short Surveycited by 3
  38. 2024An Implicit Physical Face Model Driven by Expression and Stylecited by 3

50 most cited of 86 All 86 (JSON)