Plan of Thoughts: Heuristic-Guided Problem Solving with Large Language Models
(2404.19055)Abstract
While language models (LMs) offer significant capability in zero-shot reasoning tasks across a wide range of domains, they do not perform satisfactorily in problems which requires multi-step reasoning. Previous approaches to mitigate this involves breaking a larger, multi-step task into sub-tasks and asking the language model to generate proposals ("thoughts") for each sub-task and using exhaustive planning approaches such as DFS to compose a solution. In this work, we leverage this idea to introduce two new contributions: first, we formalize a planning-based approach to perform multi-step problem solving with LMs via Partially Observable Markov Decision Processes (POMDPs), with the LM's own reflections about the value of a state used as a search heuristic; second, leveraging the online POMDP solver POMCP, we demonstrate a superior success rate of 89.4% on the Game of 24 task as compared to existing approaches while also offering better anytime performance characteristics than fixed tree-search which is used previously. Taken together, these contributions allow modern LMs to decompose and solve larger-scale reasoning tasks more effectively.
Overview
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The paper discusses enhancing multi-step reasoning in LLMs (LMs) like GPT-3, which struggle with complex reasoning tasks, through the introduction of Partially Observable Markov Decision Processes (POMDP).
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It introduces a new model called 'Plan of Thoughts' (PoT), which builds on the 'Tree of Thoughts' (ToT) and other models to generate and assess thoughts, leading more effectively toward solutions using a structured decision-making process underlined by POMDP.
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The proposed method significantly outperforms previous models in a benchmark problem-solving task and hints at future applications in more complex scenarios, emphasizing the potential for scalability and efficiency improvements in AI-driven complex decision-making.
Enhancing Multi-Step Reasoning in Language Models Using POMDP
Introduction to Multi-Step Reasoning Challenges
Language models (LMs) like GPT-3 have shown remarkable adeptness in handling a wide variety of reasoning tasks through advancements such as few-shot or zero-shot learning. However, they falter when faced with complex multi-step reasoning tasks, which are essential for applications that require depth and comprehensive understanding, like advanced problem-solving or complex decision-making scenarios.
Previous methods such as the Chain of Thought approach have attempted to mediate this issue by internally verbalizing the reasoning process of the LM, but they fall short when backtracking is necessary because the approach straightforwardly extends predictions without revisiting previous states. This approach often results in repetitive loops or ‘de-generation’, where the likelihood of a certain phrase being predicted increases unjustly, reducing the effectiveness of the model in providing meaningful solutions to complex problems.
Leveraging POMDP in Language Models
The introduction of Partially Observable Markov Decision Processes (POMDP) within this context aims to formalize a method that allows LMs to tackle such multi-step reasoning more effectively. The core concept behind using POMDP involves treating the problem-solving process as a series of decisions made under uncertainty, with each decision (or action) influenced by the current state as "observed" through the LM's response or "thought".
POMDPs are not wholly new in computational fields, but their application in moderating the decision-making of LMs is innovative because it presupposes that the LM can not only generate potential solutions (thoughts) but also evaluate the likelihood of these solutions leading to a correct final answer.
Implementation Using Plan of Thoughts (PoT)
Building on prior established methods like the Tree of Thoughts (ToT), this paper proposes a model dubbed "Plan of Thoughts" (PoT). PoT orchestrates thought generation and reasoning, using a hierarchy of actions to optimally progress toward a solution. The observations in this POMDP setup are generated by the LM's evaluations of each thought, guiding the subsequent actions more informatively.
Performance Evaluation and Results: Using a benchmark problem, the Game of 24, where the objective is to manipulate four numbers through basic arithmetic to result in the number 24, the PoT approach substantially outperformed previous models. It achieved a success rate of 89.4%, which is notably higher than the previous approaches (ToT and CoT), illustrating the practical effectiveness of incorporating POMDP into LM-based problem-solving.
Speculative Future Developments
The successful integration of POMDP with LMs through PoT hints at several promising directions:
- Scalability: There is potential for scaling this method to more complex reasoning tasks beyond arithmetic, such as symbolic mathematics, complex scheduling, or even strategic game playing.
- Model Adaptability: Fine-tuning the model to adapt the heuristic evaluations based on specific problem characteristics could yield even more effective problem-solving strategies.
- Efficiency Improvements: Future work could also explore ways to reduce the computational demand of this method, making it more feasible for real-time applications.
Concluding Moments
The success of PoT in facilitating better multi-step reasoning demonstrates a significant stride toward utilizing advanced AI techniques in practical, complex decision-making scenarios. By dissecting the thought process into a series of observable decision points guided by evaluations, PoT marks a method that could broadly enhance the capacity of LMs in advanced reasoning tasks.
In conclusion, while existing single-pass, generative models like CoT offer simplicity, the depth and adaptive reasoning made possible through PoT advocate for its application where complexity and thoroughness are paramount. Moving forward, this approach could be refined and potentially integrated with other AI systems to provide even richer decision-making capabilities.