---
title: "SOUL — paper by Jia et al. (2024) — summary and ideas"
description: "From this link they build SOUL, which turns that one-step update into an iterative fine-tuning procedure. 86 references, cited by 30 papers here."
authors: ["Jinghan Jia", "Yihua Zhang", "Yimeng Zhang", "Jiancheng Liu", "Bharat Runwal", "James Diffenderfer", "Bhavya Kailkhura", "Sijia Liu"]
year: 2024
venue: "Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing"
source: "https://aclanthology.org/2024.emnlp-main.245/"
doi: "10.18653/v1/2024.emnlp-main.245"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/jia-2024-soul-unlocking-power-second-order/"
---
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# SOUL: Unlocking the Power of Second-Order Optimization for LLM Unlearning

**Authors:** [Jinghan Jia](https://md.research.elamur.ai/free/en/authors/jinghan-jia/), [Yihua Zhang](https://md.research.elamur.ai/free/en/authors/yihua-zhang/), [Yimeng Zhang](https://md.research.elamur.ai/free/en/authors/yimeng-zhang/), Jiancheng Liu, Bharat Runwal, James Diffenderfer, Bhavya Kailkhura and [Sijia Liu](https://md.research.elamur.ai/free/en/authors/sijia-liu/) · **Year:** 2024 · **Venue:** [Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing](https://md.research.elamur.ai/free/en/venues/emnlp/) ([EMNLP 2024](https://md.research.elamur.ai/free/en/venues/emnlp/2024/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2024.emnlp-main.245/) · [PDF](https://aclanthology.org/2024.emnlp-main.245.pdf) · [DOI 10.18653/v1/2024.emnlp-main.245](https://doi.org/10.18653/v1/2024.emnlp-main.245) · [OpenAlex](https://openalex.org/W4404782927)

**Citations:** 16 citations (OpenAlex, 2026-10-14) · [30](https://md.research.elamur.ai/free/en/papers/jia-2024-soul-unlocking-power-second-order/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
The paper addresses LLM unlearning: removing the effect of unwanted data, such as private, copyrighted or toxic content, without full retraining and without harming general utility. Previous work mostly changed the unlearning loss, for example GradDiff, PO or NPO, and kept first-order optimizers. The authors are the first to study optimizer choice for this task. They show that second-order optimization is closely related to influence unlearning, a classical one-step method based on influence functions. From this link they build SOUL, which turns that one-step update into an iterative fine-tuning procedure. SOUL is based on the Sophia optimizer and works with any unlearning loss. It was tested on fictitious-author unlearning (TOFU) and on model detoxification, using OPT and LLaMA2 models. Compared with first-order versions of the same objectives, SOUL usually forgets more effectively while keeping utility similar or better. Its running time and memory use stay close to Adam. The results suggest that optimizer design is an overlooked and useful way to improve unlearning.

## Key points
- SOUL estimates the diagonal Hessian from squared gradients, as Sophia does. It can be paired with GradDiff, PO and NPO objectives. Code is at github.com/OPTML-Group/SOUL.
- The benchmarks are TOFU for fictitious unlearning and a detoxification task. Detoxification is scored with Real Toxicity Prompts and PKU-SafeRLHF toxicity, plus PPL, zero-shot accuracy and TruthfulQA. The models are OPT-350M, OPT-1.3B and LLaMA2-7B.
- In detoxification on LLaMA2-7B, SO-PO reduced the PKU-SafeRLHF toxic score to 0.0443, compared with 0.0790 for FO-PO. On OPT-1.3B, SO-PO raised zero-shot accuracy to 48.60%, compared with 46.25% for FO-PO.
- The overhead on TOFU is small. NPO took 35 minutes with SOUL versus 32 minutes with the first-order version, and memory differences were under 0.1%.
- SOUL outperforms static influence unlearning and resists jailbreak prompts better than first-order methods. The authors note it has not been tested on very large models or under thorough adversarial evaluation.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Massachusetts Institute of Technology](https://md.research.elamur.ai/free/en/universities/massachusetts-institute-of-technology/) — University, Cambridge, United States · 243 works · 76,506 citations
- [IBM](https://md.research.elamur.ai/free/en/companies/ibm/) — Company, Armonk, United States · 154 works · 72,606 citations
- [Michigan State University](https://md.research.elamur.ai/free/en/universities/michigan-state-university/) — University, East Lansing, United States · 30 works · 1,375 citations
- [Lawrence Livermore National Laboratory](https://md.research.elamur.ai/free/en/labs/lawrence-livermore-national-laboratory/) — Research institute, Livermore, United States · 6 works · 2,127 citations

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🧭 Topics (1): [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · 3,894 works

## Cite

Cite as: Jinghan Jia, Yihua Zhang, Yimeng Zhang, Jiancheng Liu, Bharat Runwal, James Diffenderfer, Bhavya Kailkhura and Sijia Liu. 2024. SOUL: Unlocking the Power of Second-Order Optimization for LLM Unlearning. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{jia2024soul,
  title = {{SOUL: Unlocking the Power of Second-Order Optimization for LLM Unlearning}},
  author = {Jinghan Jia, Yihua Zhang, Yimeng Zhang, Jiancheng Liu, Bharat Runwal, James Diffenderfer, Bhavya Kailkhura and Sijia Liu},
  booktitle = {Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing},
  year = {2024},
  doi = {10.18653/v1/2024.emnlp-main.245},
  url = {https://doi.org/10.18653/v1/2024.emnlp-main.245}
}
```

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86. Guanhua Zhang, Yihua Zhang, Yang Zhang, Wenqi Fan, Qing Li, Sijia Liu, and Shiyu Chang. 2022a. Fairness reprogramming. Advances in Neural Information Processing Systems, 35:34347–34362. [find](https://scholar.google.com/scholar?q=Guanhua+Zhang%2C+Yihua+Zhang%2C+Yang+Zhang%2C+Wenqi+Fan%2C+Qing+Li%2C+Sijia+Liu%2C+and+Shiyu+Chang%2E+2022a%2E+Fairness+reprogramming%2E+Advances+in+Neural+Information+Processing+Systems%2C+35%3A34347%E2%80%9334362%2E)

*Updated 2 November 2026*