Can Large Language Models Reinvent Foundational Algorithms?

TL;DR

This paper investigates whether large language models can reinvent foundational algorithms by removing existing knowledge and testing their ability to generate these algorithms anew, revealing both potential and limitations.

Contribution

The study introduces an unlearning-and-reinvention pipeline and demonstrates that strong LLMs can successfully reinvent several foundational algorithms with minimal hints.

Findings

Qwen3-4B-Thinking-2507 reinvents 50-90% of algorithms depending on hints

High-level hints improve reinvention success, but complex algorithms often require more

Test-time reinforcement learning aids in reinvention of complex algorithms like Strassen

Abstract

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: can LLMs reinvent foundational algorithms in computer science? Our \textit{Unlearn-and-Reinvent} pipeline applies LLM unlearning to remove a specific foundational algorithm, such as Dijkstra's or Euclid's algorithm, from an LLM's pretrained knowledge, and then tests whether the model can reinvent it in a controlled environment. To enable effective unlearning, we adopt a GRPO-based, on-policy unlearning method. Across 10 target algorithms, 3 strong open-weight models, and 3 hint levels, our experiments demonstrate that (1) the strongest model Qwen3-4B-Thinking-2507 successfully reinvents 50% of the algorithms with no hint, 70% at hint level 1, and 90% at hint level 2; (2) a few high-level hints can enhance the reinvention success rate, but even step-by-step hints fail for those complicated algorithms; and (3) test-time reinforcement learning enables successful reinvention for the Strassen algorithm at hint level 2. Through analyses of output trajectories and ablation studies, we find that generative verifier in the reinvention phase plays a critical role in sustaining models' reasoning strength, helping to avoid the ``thought collapse'' phenomenon. These findings offer insights into both the potential and current limits of LLMs' innovative thinking.