# DP-SGD Without Clipping: The Lipschitz Neural Network Way

arXiv: https://arxiv.org/abs/2305.16202 · HTML: https://mlsanity.com/paper/2305.16202/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 93 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 30 of 62)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Large Language Models Can Be Strong Differentially Private Learners](https://mlsanity.com/paper/2110.05679/) (2021)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Systematic Evaluation of Privacy Risks of Machine Learning Models](https://mlsanity.com/paper/2003.10595/) (2020)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [Differentially Private Learning Needs Better Features (or Much More Data)](https://mlsanity.com/paper/2011.11660/) (2020)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [Differentially Private Learning with Adaptive Clipping](https://mlsanity.com/paper/1905.03871/) (2019)

## Built on by (most cited first, 11 of 11)

- [Training Transformers with Enforced Lipschitz Constants](https://mlsanity.com/paper/2507.13338/) (2025)
- [Convergent Privacy Loss of Noisy-SGD without Convexity and Smoothness](https://mlsanity.com/paper/2410.01068/) (2024)
- [An Adaptive Orthogonal Convolution Scheme for Efficient and Flexible CNN Architectures](https://mlsanity.com/paper/2501.07930/) (2025)
- [ATRI: Mitigating Multilingual Audio Text Retrieval Inconsistencies by Reducing Data Distribution Errors](https://mlsanity.com/paper/2502.14627/) (2025)
- [Characterizing the Training Dynamics of Private Fine-tuning with Langevin diffusion](https://mlsanity.com/paper/2402.18905/) (2024)
- [Slicing Mutual Information Generalization Bounds for Neural Networks](https://mlsanity.com/paper/2406.04047/) (2024)
- [Efficient Robust Conformal Prediction via Lipschitz-Bounded Networks](https://mlsanity.com/paper/2506.05434/) (2025)
- [Certification-Based Differentially Private Learning](https://mlsanity.com/paper/2609.39629/) (2026)
- [DNA: Differentially private Neural Augmentation for contact tracing](https://mlsanity.com/paper/2404.13381/) (2024)
- [Amplified Patch-Level Differential Privacy for Free via Random Cropping](https://mlsanity.com/paper/2603.24695/) (2026)
- [StraightDP: Geometry-Aware Differential Privacy for Rectified-Flow Transformers](https://mlsanity.com/paper/2607.29100/) (2026)

## Abstract (arXiv)

State-of-the-art approaches for training Differentially Private (DP) Deep Neural Networks (DNN) face difficulties to estimate tight bounds on the sensitivity of the network's layers, and instead rely on a process of per-sample gradient clipping. This clipping process not only biases the direction of gradients but also proves costly both in memory consumption and in computation. To provide sensitivity bounds and bypass the drawbacks of the clipping process, we propose to rely on Lipschitz constrained networks. Our theoretical analysis reveals an unexplored link between the Lipschitz constant with respect to their input and the one with respect to their parameters. By bounding the Lipschitz constant of each layer with respect to its parameters, we prove that we can train these networks with privacy guarantees. Our analysis not only allows the computation of the aforementioned sensitivities at scale, but also provides guidance on how to maximize the gradient-to-noise ratio for fixed privacy guarantees. The code has been released as a Python package available at https://github.com/Algue-Rythme/lip-dp