Can Large Language Models Invent Algorithms to Improve Themselves?: Algorithm Discovery for Recursive Self-Improvement through Reinforcement Learning

Abstract: LLMs have achieved remarkable capabilities, yet their improvement methods remain fundamentally constrained by human design. We present Self-Developing, a framework that enables LLMs to autonomously discover, implement, and refine their own improvement algorithms. Our approach employs an iterative cycle where a seed model generates algorithmic candidates as executable code, evaluates their effectiveness, and uses Direct Preference Optimization to recursively improve increasingly sophisticated improvement strategies. We demonstrate this framework through model merging, a practical technique for combining specialized models. Self-Developing successfully discovered novel merging algorithms that outperform existing human-designed algorithms. On mathematical reasoning benchmarks, the autonomously discovered algorithms improve the seed model's GSM8k performance by 6\% and exceed human-designed approaches like Task Arithmetic by 4.3\%. Remarkably, these algorithms exhibit strong generalization, achieving 7.4\% gains on out-of-domain models without re-optimization. Our findings demonstrate that LLMs can transcend their training to invent genuinely novel optimization techniques. This capability represents a crucial step toward a new era where LLMs not only solve problems but autonomously develop the methodologies for their own advancement.

• The paper introduces the Self-Developing framework, demonstrating that Large Language Models (LLMs) can autonomously generate algorithms that outperform human-designed methods for self-improvement.
• LLM-discovered algorithms achieved a 6% performance increase over the seed model on mathematical reasoning tasks like GSM8k and showed strong transferability to new models.
• This research paves the way for self-improving AI systems that require less human intervention in algorithm design, potentially leading to more efficient and scalable AI development.

Autonomous Algorithm Generation in LLMs

The paper "Can LLMs Invent Algorithms to Improve Themselves?" presents an innovative exploration into the autonomous self-improvement of LLMs. The authors propose the Self-Developing framework, a paradigm designed to enable LLMs to generate and refine model-improving algorithms without human intervention. This research aims to transcend the limitations of human-designed algorithms by harnessing the intrinsic capabilities of LLMs to discover novel, high-performance strategies, potentially extending the frontier of artificial intelligence beyond known methodologies.

The paper is driven by a key inquiry: can LLMs improve their performance through self-generated algorithms? To address this, the authors introduce a cyclical framework involving iterative improvements of a seed model via an algorithm factory. The algorithm factory, initialized with the seed model, autonomously generates candidate algorithms expressed as executable code, particularly in Python. These algorithms are applied to produce new models, evaluated for task performance, and refined through Direct Preference Optimization (DPO), iteratively enhancing both the LLM-generated algorithms and the performance of the improved models.

Key Contributions and Findings

The Self-Developing framework is evaluated across mathematical reasoning tasks using datasets like GSM8k and MATH. The results reveal impressive improvements. Notably, LLM-generated algorithms exceed the performance of established human-designed methods such as Task Arithmetic and TIES merging.

1. Performance Outcomes: The LLM-discovered algorithms effect a performance increase over the seed model by 6% on GSM8k tasks, with a remarkable improvement of 4.3% over human-designed algorithm performance. The strongest LLM-discovered models achieved a 76.1% accuracy on GSM8k, a notable leap from the seed model’s 70.1%.
2. Transferability: Support for the strong transferability of LLM-discovered algorithms to out-of-domain models is evidenced, with these algorithms outperforming Task Arithmetic optimized for new model sets by 7.4% on GSM8k. This indicates robustness in the autonomously generated algorithms, evidencing adaptability across various model architectures.
3. Iterative Enhancement: The iterative refinement of the algorithm factory establishes an effective feedback loop, yielding increasingly superior algorithms. The gradual improvement from iteration to iteration illustrates the potential of continuous self-improvement within LLM frameworks.

Implications and Future Directions

The implications of this research are profound, offering a blueprint for building self-improving AI systems that minimize human involvement. In practice, the Self-Developing framework reduces the necessity for extensive human-derived algorithm designs, shifting towards a model where LLMs can iteratively enhance capabilities through self-derived insights. This shift promises more flexible, scalable, and efficient AI development processes.

Theoretically, this research underscores the potential of LLMs beyond static performance benchmarks, suggesting a pathway to AI systems capable of evolving their algorithmic strategies dynamically. Future explorations might extend this framework to more diverse model architectures and broader domains, assessing the generalizability and effectiveness of autonomous self-optimization.

Conclusion

In summary, the paper presents a compelling model of self-improving LLMs that can independently generate high-performance algorithms, establishing a significant stride towards autonomous AI development. This work not only introduces a novel methodology for enhancing LLM capabilities but also provides critical insights into the potential for AI systems to transcend the bounds of human-derived problem-solving frameworks. As this line of inquiry evolves, we may observe even greater steps toward truly autonomous, intelligent systems capable of continuous learning and self-enhancement.