# Can Large Language Models Reinvent Foundational Algorithms?

arXiv: https://arxiv.org/abs/2604.05716 · HTML: https://mlsanity.com/paper/2604.05716/

## 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 24 of its 44 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [Can LLMs Generate Novel Research Ideas? A Large-Scale Human Study with 100+ NLP Researchers](https://mlsanity.com/paper/2409.04109/) (2024)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning](https://mlsanity.com/paper/2410.07163/) (2024)
- [Machine Unlearning of Pre-trained Large Language Models](https://mlsanity.com/paper/2402.15159/) (2024)
- [Learning to Discover at Test Time](https://mlsanity.com/paper/2601.16175/) (2026)
- [RULE: Reinforcement UnLEarning Achieves Forget-Retain Pareto Optimality](https://mlsanity.com/paper/2506.07171/) (2025)
- [Unlearning vs. Obfuscation: Are We Truly Removing Knowledge?](https://mlsanity.com/paper/2505.02884/) (2025)
- [Improving LLM Unlearning Robustness via Random Perturbations](https://mlsanity.com/paper/2501.19202/) (2025)
- [Wisdom is Knowing What not to Say: Hallucination-Free LLMs Unlearning via Attention Shifting](https://mlsanity.com/paper/2510.17210/) (2025)
- [Understanding the Dilemma of Unlearning for Large Language Models](https://mlsanity.com/paper/2509.24675/) (2025)
- [Reinforcement Unlearning via Group Relative Policy Optimization](https://mlsanity.com/paper/2601.20568/) (2026)
- [Unlearning as Ablation: Toward a Falsifiable Benchmark for Generative Scientific Discovery](https://mlsanity.com/paper/2508.17681/) (2025)

## Abstract (arXiv)

LLMs have shown strong potential to advance scientific discovery. Whether they possess the capacity for foundational innovation, however, remains an open question. In this work, we focus on a prerequisite for foundational innovation: textitcan LLMs reinvent foundational algorithms in computer science? We use LLM unlearning methods to suppress direct recall of the target algorithm and let the model reason with the remaining knowledge to recover it. Although unlearning does not guarantee full knowledge removal, LLMs fail to recover nearly half of the target algorithms. Notably, even suppressing the mention of the algorithm's name during decoding without unlearning makes the models' recovery rate drop dramatically (19--39%), suggesting their overreliance on memorized knowledge. We observe that recoverable algorithms tend to be simple in structure or core ideas, whereas the others are less straightforward. We also introduce a generative verifier that sustains models' reasoning strength, helping to avoid the ``thought collapse'' phenomenon. Taken together, by treating the unlearned model's recovery rate as an approximate upper bound, our empirical results suggest that current LLM systems still have limited ability to make foundational algorithm innovation. Our code is available at https://github.com/Algo-Reinvention/algo-reinvention.