Can Large Language Models Reinvent Foundational Algorithms?

2026-04-07

AI Summary

This study investigates whether large language models (LLMs) can independently reinvent classical computer science algorithms, thereby assessing their foundational capacity for innovation. To this end, the authors propose a “forgetting–reinvention” framework: first, specific algorithmic knowledge is removed from the model using an online policy-based approach grounded in GRPO, and then the model’s ability to reinvent those algorithms is evaluated in a controlled setting. This work presents the first systematic assessment of LLMs’ algorithm reinvention capabilities, revealing the critical roles of high-level prompting and generative verifiers in sustaining coherent reasoning. Notably, test-time reinforcement learning enables the successful reinvention of Strassen’s algorithm. Experiments show that the Qwen3-4B-Thinking-2507 model can reinvent 50% of target algorithms without prompting, with success rates rising to as high as 90% when enhanced with tailored prompts.

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.

Problem

• Large Language Models
• foundational algorithms
• algorithm reinvention
• scientific discovery
• innovative thinking

Innovation

• Unlearn-and-Reinvent
• LLM unlearning
• foundational algorithm reinvention
• generative verifier
• test-time reinforcement learning