Diverse Inference and Verification for Advanced Reasoning (2502.09955v1)

Abstract: Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions. We use a diverse inference approach that combines multiple models and methods at test time. We find that verifying mathematics and code problems, and rejection sampling on other problems is simple and effective. We automatically verify correctness of solutions to IMO problems by Lean, and ARC puzzles by code, and find that best-of-N effectively answers HLE questions. Our approach increases answer accuracy on IMO combinatorics problems from 33.3% to 77.8%, accuracy on HLE questions from 8% to 37%, and solves 80% of ARC puzzles that 948 humans could not and 26.5% of ARC puzzles that o3 high compute does not. Test-time simulations, reinforcement learning, and meta-learning with inference feedback improve generalization by adapting agent graph representations and varying prompts, code, and datasets. Our approach is reliable, robust, and scalable, and in the spirit of reproducible research, we will make it publicly available upon publication.

• The paper proposes a diverse inference mechanism combining multiple models and verification techniques to significantly improve accuracy on complex reasoning tasks.
• It employs test-time simulations and reinforcement learning to generate additional data and enhance solutions for challenging combinatorial and logical problems.
• The study introduces empirical scaling laws and meta-learning of agent graphs, offering promising insights for future AI reasoning and verification research.

Critical Review of "Diverse Inference and Verification for Advanced Reasoning"

The paper, "Diverse Inference and Verification for Advanced Reasoning," addresses the performance limitations of reasoning LLMs in tackling challenging mathematical and reasoning tasks, such as those found in the International Mathematical Olympiad (IMO) combinatorics problems, the Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions. The researchers propose an approach that combines diverse models and methods during inference. This paper claims several significant outcomes: notably, increasing the accuracy of solving IMO combinatorics problems from 33.3% to 77.8%, and improving accuracy on HLE questions from 8% to 37%.

The key contributions can be highlighted as follows:

• Diverse Inference Mechanism: The use of multiple models or methods at test time instead of relying on a single approach enables leveraging the strengths of different methods. For instance, in the IMO dataset, using methods like LEAP, Z3, and others, varying approaches are used for verification and synthesis of answers. The diverse models automatically verify correctness using best-of-N sampling, Lean verification, or synthesized code execution, thereby contributing to a substantial increase in accuracy. This principle reflects the value of leveraging multiple logical perspectives and computational processes to cross-check and validate results in reasoning tasks.
• Test-time Simulations and Reinforcement Learning: The researchers adopt reinforcement learning to refine problem-specific data at inference time. For example, combinatorial search and deep reinforcement learning are utilized to maneuver mathematical challenges by simulating interactive game environments. This method is adept at generating additional data and providing proofs or solutions for challenging tasks, such as complex combinatorial problems, which historically have been difficult for machine learning models.
• Empirical Scaling Laws: The authors suggest a third empirical scaling law—supplementing the existing model size versus data size laws—concerning the performance on verifiable problems as a function of the number of diverse models and methods utilized. This insight could illuminate future research on scaling models and leveraging diversity in solving new classes of reasoning problems.
• Meta-learning of Agent Graphs: Expanding on the AI decision-making pipeline, the usage of agent graphs that adapt through meta-learning to optimize hyperparameters, prompts, and graph configurations shows promise for enhancing the adaptability and precision of AI systems in reasoning tasks.

Numerical Results and Impact: The researchers report demonstrable improvements across benchmarks, notably solving 80% of ARC puzzles that humans collectively failed on and 26.5% that another major platform, o3 high compute, could not solve. The paper refrains from being sensational and acknowledges the boundaries of its approach, indicating areas of potential improvement and ongoing experimentation.

Implications and Future Prospects: The implications of this research thread through the potential generalization of diverse inference methods for broader reasoning tasks and optimized meta-learning techniques for improved problem-solving. Future investigations could explore refining the balance between the depth and breadth of diverse inference, addressing computational efficiency, and exploring alternative forms of reasoning tasks beyond combinatorics and logic puzzles. These strides contribute not only theoretically but bear promising applications in educational technology and AI-assisted tutoring systems, embodying robust explanations and correctness in educational mathematics.

In conclusion, while the paper firmly advances AI’s capacity to tackle higher-complexity reasoning tasks through diversity in inference and strong verification frameworks, further empirical testing and theoretical exploration are warranted to bridge these methods to additional domains and insights.