Combinatorial Reasoning: Selecting Reasons in Generative AI Pipelines via Combinatorial Optimization
(2407.00071)Abstract
Recent LLMs have demonstrated impressive capabilities at tasks that require human intelligence and are a significant step towards human-like AI. Yet the performance of LLMs at reasoning tasks have been subpar and the reasoning capability of LLMs is a matter of significant debate. While it has been shown that the choice of the prompting technique to the LLM can alter its performance on a multitude of tasks, including reasoning, the best performing techniques require human-made prompts with the knowledge of the tasks at hand. We introduce a framework for what we call Combinatorial Reasoning (CR), a fully-automated prompting method, where reasons are sampled from an LLM pipeline and mapped into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The framework investigates whether QUBO solutions can be profitably used to select a useful subset of the reasons to construct a Chain-of-Thought style prompt. We explore the acceleration of CR with specialized solvers. We also investigate the performance of simpler zero-shot strategies such as linear majority rule or random selection of reasons. Our preliminary study indicates that coupling a combinatorial solver to generative AI pipelines is an interesting avenue for AI reasoning and elucidates design principles for future CR methods.
Overview
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The paper presents Combinatorial Reasoning (CR), a novel framework that leverages combinatorial optimization for automated prompt engineering to enhance the reasoning capabilities of LLMs.
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CR operates by generating and refining reasons using techniques like Sentence Transformers and Quadratic Unconstrained Binary Optimization (QUBO) to create superior prompts for zero-shot settings.
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Empirical validation on the BIG-bench Hard (BBH) suite shows that CR outperforms existing methods, achieving up to 59.88% accuracy, and opens avenues for further research in semantic matching, QUBO mapping, and advanced solvers.
Combinatorial Reasoning in Generative AI: A Novel Framework for Automated Prompt Engineering
The paper "Combinatorial Reasoning: Selecting Reasons in Generative AI Pipelines via Combinatorial Optimization" presents a sophisticated approach to enhancing the reasoning capabilities of LLMs through automated prompt engineering. This framework, named Combinatorial Reasoning (CR), introduces a fully-automated, zero-shot prompting technique that leverages combinatorial optimization to improve the reasoning performance of LLMs without human intervention.
Core Problem and Background
LLMs such as those built upon auto-regressive architectures have demonstrated considerable prowess in generating human-like text for a variety of tasks. However, their inherent lack of mechanisms for deep reasoning and strategic planning remains a significant bottleneck, especially in applications requiring high-level cognitive functions. Traditional methods like Chain-of-Thought (CoT) and Self-Consistency have posed some solutions, but they heavily rely on human-crafted exemplars and annotations, which do not generalize well across different tasks.
Combinatorial Reasoning Framework
CR aims to transcend these limitations by integrating an external reasoning engine within existing LLM pipelines. This engine does not modify the foundational architecture of LLMs but augments their reasoning capabilities through automated prompt engineering. The CR pipeline comprises several stages:
Sampling of Reasons:
- Given a question, an LLM is queried multiple times to generate a set of reasons. These reasons are filtered for semantic redundancy using a Sentence Transformer, resulting in a collection of distinct reasons with associated embeddings.
QUBO Mapping:
- The distinct reasons are mapped into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The objective function, inspired by portfolio optimization, selects reasons based on their frequency and pairwise correlations, aiming to maximize reasoning quality.
Combinatorial Optimization Solver:
- An Ising machine, employing simulated annealing or more sophisticated methods like Adaptive Parallel Tempering (APT), solves the QUBO problem to identify a subset of reasons. These selected reasons are weighted and used to construct an enhanced prompt.
Final Prompt Creation:
- The selected reasons, each associated with a weight indicating their relative importance, are concatenated to form a final prompt. This prompt is used to query the LLM in a zero-shot setting to provide the final answer.
Empirical Validation
The effectiveness of CR is demonstrated using the BIG-bench Hard (BBH) suite, a collection of reasoning-oriented tasks proven challenging for LLMs. The paper reports that CR performs favorably compared to existing methods, such as zero-shot prompting and Universal Self-Adaptive Prompting (USP). Specifically, CR achieves an average accuracy of 59.88% across BBH tasks, outperforming zero-shot methods and USP by 12.20% and 4.0%, respectively. Notably, CR exhibits the potential to perform at a human level on certain reasoning tasks.
Implications and Future Directions
The implications of this research are profound. Practically, CR offers a scalable solution for enhancing the reasoning capabilities of LLMs, potentially transforming their application in tasks requiring strategic thought and deep reasoning. Theoretically, this framework presents a novel intersection between generative AI and probabilistic combinatorial optimization, opening avenues for further exploration.
Future Prospects
The paper suggests several avenues for future research:
- Enhanced Semantic Matching: Improving the semantic similarity measures to better capture the relationships between reasons, potentially incorporating more sophisticated natural language processing techniques or additional LLM queries for disambiguation.
- Refined QUBO Mappings: Investigating alternate QUBO formulations, including those incorporating budget constraints and higher-order correlations, to better capture the complexity of reasoning tasks.
- Advanced Optimization Solvers: Experimenting with different combinatorial optimization solvers, particularly quantum-inspired or hardware-accelerated solvers, to further reduce runtime and improve solution accuracy.
- Integration with Deterministic Solvers: Combining probabilistic methods with deterministic theorem provers to handle tasks with conflicting reasons, thereby enhancing the robustness of the CR framework.
- Expansion to Knowledge-Intensive Tasks: Extending CR to tasks that require knowledge retrieval by integrating Retrieval Augmented Generation (RAG) methods, thereby leveraging large context windows of modern LLMs.
In conclusion, the paper presents a robust and innovative approach to automated prompt engineering, significantly enhancing the reasoning capabilities of LLMs. By bridging generative AI with combinatorial optimization, CR paves the way for future advancements in AI reasoning and strategic planning.
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