# Descend or Rewind? Stochastic Gradient Descent Unlearning

arXiv: https://arxiv.org/abs/2511.15983 · HTML: https://mlsanity.com/paper/2511.15983/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 39 of its 51 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [When Machine Unlearning Jeopardizes Privacy](https://mlsanity.com/paper/2005.02205/) (2020)
- [Adaptive Machine Unlearning](https://mlsanity.com/paper/2106.04378/) (2021)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Better Theory for SGD in the Nonconvex World](https://mlsanity.com/paper/2002.03329/) (2020)
- [Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees](https://mlsanity.com/paper/2305.01588/) (2023)
- [SGD for Structured Nonconvex Functions: Learning Rates, Minibatching and Interpolation](https://mlsanity.com/paper/2006.10311/) (2020)
- [Efficient Private ERM for Smooth Objectives](https://mlsanity.com/paper/1703.09947/) (2017)
- [Forget Unlearning: Towards True Data-Deletion in Machine Learning](https://mlsanity.com/paper/2210.08911/) (2022)
- [Membership Inference Attacks Cannot Prove that a Model Was Trained On Your Data](https://mlsanity.com/paper/2409.19798/) (2024)
- [Langevin Unlearning: A New Perspective of Noisy Gradient Descent for Machine Unlearning](https://mlsanity.com/paper/2401.10371/) (2024)
- [Certified Graph Unlearning](https://mlsanity.com/paper/2206.09140/) (2022)
- [Algorithms that Approximate Data Removal: New Results and Limitations](https://mlsanity.com/paper/2209.12269/) (2022)
- [A Guide Through the Zoo of Biased SGD](https://mlsanity.com/paper/2305.16296/) (2023)
- [MAAD-Face: A Massively Annotated Attribute Dataset for Face Images](https://mlsanity.com/paper/2012.01030/) (2020)
- [Towards Certified Unlearning for Deep Neural Networks](https://mlsanity.com/paper/2408.00920/) (2024)
- [Certified Minimax Unlearning with Generalization Rates and Deletion Capacity](https://mlsanity.com/paper/2312.10336/) (2023)
- [Certified Unlearning for Neural Networks](https://mlsanity.com/paper/2506.06985/) (2025)
- [The Utility and Complexity of in- and out-of-Distribution Machine Unlearning](https://mlsanity.com/paper/2412.09119/) (2024)
- [Rewind-to-Delete: Certified Machine Unlearning for Nonconvex Functions](https://mlsanity.com/paper/2409.09778/) (2024)
- [SIFU: Sequential Informed Federated Unlearning for Efficient and Provable Client Unlearning in Federated Optimization](https://mlsanity.com/paper/2211.11656/) (2022)

## Abstract (arXiv)

Machine unlearning algorithms aim to remove the impact of selected training data from a model without the computational expenses of retraining from scratch. Two such algorithms are ``Descent-to-Delete" (D2D) and ``Rewind-to-Delete" (R2D), full-batch gradient descent algorithms that are easy to implement and satisfy provable unlearning guarantees. In particular, the stochastic version of D2D is widely implemented as the ``finetuning" unlearning baseline, despite lacking theoretical backing on nonconvex functions. In this work, we prove (varepsilon, δ) certified unlearning guarantees for stochastic R2D and D2D for strongly convex, convex, and nonconvex loss functions, by analyzing unlearning through the lens of disturbed or biased gradient systems, which may be contracting, semi-contracting, or expansive respectively. Our argument relies on optimally coupling the random behavior of the unlearning and retraining trajectories, resulting in a sensitivity bound that holds in expectation that yields (varepsilon, δ) unlearning. We determine that D2D can yield tighter guarantees for strongly convex functions, but R2D is more appropriate for convex and nonconvex functions. Finally, we compare the algorithms empirically, demonstrating the strengths and weaknesses of each approach.