# An automatic differentiation system for the age of differential privacy

arXiv: https://arxiv.org/abs/2109.10573 · HTML: https://mlsanity.com/paper/2109.10573/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 20 of 20)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Adaptive Machine Unlearning](https://mlsanity.com/paper/2106.04378/) (2021)
- [Tempered Sigmoid Activations for Deep Learning with Differential Privacy](https://mlsanity.com/paper/2007.14191/) (2020)
- [Theano: A Python framework for fast computation of mathematical expressions](https://mlsanity.com/paper/1605.02688/) (2016)
- [Individual Privacy Accounting via a Renyi Filter](https://mlsanity.com/paper/2008.11193/) (2020)
- [Diffprivlib: The IBM Differential Privacy Library](https://mlsanity.com/paper/1907.02444/) (2019)
- [RecurJac: An Efficient Recursive Algorithm for Bounding Jacobian Matrix of Neural Networks and Its Applications](https://mlsanity.com/paper/1810.11783/) (2018)
- [LipBaB: Computing exact Lipschitz constant of ReLU networks](https://mlsanity.com/paper/2105.05495/) (2021)
- [Swift for TensorFlow: A portable, flexible platform for deep learning](https://mlsanity.com/paper/2102.13243/) (2021)
- [Sensitivity analysis in differentially private machine learning using hybrid automatic differentiation](https://mlsanity.com/paper/2107.04265/) (2021)
- [Syft 0.5: A Platform for Universally Deployable Structured Transparency](https://mlsanity.com/paper/2104.12385/) (2021)
- [DDUO: General-Purpose Dynamic Analysis for Differential Privacy](https://mlsanity.com/paper/2103.08805/) (2021)
- [From Identity to Difference: A Quantitative Interpretation of the Identity Type](https://mlsanity.com/paper/2107.06150/) (2021)

## Built on by (most cited first, 2 of 2)

- [DP-SGD Without Clipping: The Lipschitz Neural Network Way](https://mlsanity.com/paper/2305.16202/) (2023)
- [SoK: Differential Privacy on Graph-Structured Data](https://mlsanity.com/paper/2203.09205/) (2022)

## Abstract (arXiv)

We introduce Tritium, an automatic differentiation-based sensitivity analysis framework for differentially private (DP) machine learning (ML). Optimal noise calibration in this setting requires efficient Jacobian matrix computations and tight bounds on the L2-sensitivity. Our framework achieves these objectives by relying on a functional analysis-based method for sensitivity tracking, which we briefly outline. This approach interoperates naturally and seamlessly with static graph-based automatic differentiation, which enables order-of-magnitude improvements in compilation times compared to previous work. Moreover, we demonstrate that optimising the sensitivity of the entire computational graph at once yields substantially tighter estimates of the true sensitivity compared to interval bound propagation techniques. Our work naturally befits recent developments in DP such as individual privacy accounting, aiming to offer improved privacy-utility trade-offs, and represents a step towards the integration of accessible machine learning tooling with advanced privacy accounting systems.