Cumulative Reasoning with Large Language Models

Abstract: Recent advancements in LLMs have shown remarkable progress, yet their ability to solve complex problems remains limited. In this work, we introduce Cumulative Reasoning (CR), an approach that utilizes LLMs cumulatively and iteratively, mirroring human thought processes for problem-solving. CR decomposes tasks into smaller, manageable components and leverages previous propositions for effective composition, significantly enhancing problem-solving capabilities. We demonstrate CR's advantage through several complex reasoning tasks: it outperforms existing methods in logical inference tasks with up to a 9.3% improvement, achieving 98.04% accuracy on the curated FOLIO wiki dataset. In the Game of 24, it achieves 98% accuracy, marking a 24% improvement over the prior state-of-the-art. In solving MATH problems, CR achieves a 4.2% increase from previous methods and a 43% relative improvement in the most challenging level 5 problems. When incorporating a code environment with CR, we further harness LLMs' reasoning capabilities and outperform the Program of Thought (PoT) method by 38.8%. The code is available at https://github.com/iiis-ai/cumulative-reasoning.

• The paper introduces cumulative reasoning (CR), a novel framework that decomposes complex problems using Proposer, Verifier, and Reporter roles.
• The methodology achieves a 9.3% improvement in logical inference tasks and sets state-of-the-art results on the Game of 24 and MATH datasets.
• The approach bridges linear and hierarchical reasoning, potentially transforming fields like formal verification and theorem proving.

Essay on "Cumulative Reasoning with LLMs"

The paper "Cumulative Reasoning with LLMs" introduces Cumulative Reasoning (CR), a promising methodology to enhance the reasoning capabilities of LLMs. Addressing the challenges LLMs face with tasks requiring complex cognitive processing, the proposed CR approach efficiently decomposes such problems into smaller, manageable steps. This method is not limited to simple linear thought processes or hierarchical tree structures but instead posits a versatile framework incorporating a directed acyclic graph (DAG) to represent reasoning pathways.

Methodology

CR leverages three roles of LLMs—Proposer, Verifier, and Reporter—to simulate human-like thought processes. The Proposer suggests potential reasoning steps, which the Verifier assesses for accuracy, allowing only valid steps to populate the context. The Reporter concludes the reasoning process when sufficient evidence for an answer is gathered. This design promotes systemic exploration and validation of thought processes, which supports complex reasoning.

Numerical Results and Implications

Experimental results highlight CR’s superior performance over traditional reasoning methods such as Chain-of-Thought (CoT) and Tree-of-Thought (ToT). Notably, CR achieved a 9.3% improvement in logical inference tasks and established new state-of-the-art results in the Game of 24 and MATH dataset tasks. These substantial numerical gains underscore CR’s capacity to resolve high-order logic problems, converting exponential complexities into sequentially solvable components.

Bold Claims and Future Directions

The paper claims that CR generalizes over existing models by encompassing the benefits of both linear (CoT) and hierarchical (ToT) methodologies while advancing beyond their constraints. The integration of symbolic systems within the LLM environment without over-reliance on external aids, like retrieval or web browsing, is posited as a bold step towards autonomous reasoning systems.

Practical and Theoretical Implications

Practically, CR can potentially revolutionize fields reliant on intricate problem-solving, such as formal verification, complex mathematical theorem proving, and strategic game playing. Theoretically, CR emphasizes the limitations of both FOL and CoT approaches, showcasing a paradigm shift towards an integrated, verification-driven reasoning framework.

Future work could explore further enhancements to the Proposer through task-specific pre-training and the integration of more sophisticated external symbolic systems for verification. Additionally, the expansion of CR into other computational environments and its application to even broader domains presents exciting avenues for research and development.

Conclusion

In conclusion, "Cumulative Reasoning with LLMs" offers significant advancements in LLM reasoning approaches. By effectively emulating a holistic, incremental reasoning process, CR addresses key limitations in existing models and sets a new standard for complex problem-solving, marking a pivotal enhancement in AI’s reasoning capabilities.