Einblick - Algorithmic reasoning - # Improving algorithmic reasoning in language models

Language Models as Compilers: Simulating Pseudocode Execution Improves Algorithmic Reasoning in Language Models

Q: How can the THINK-AND-EXECUTE framework be extended to other reasoning tasks beyond algorithmic reasoning, such as multi-hop reasoning or symbolic reasoning

The THINK-AND-EXECUTE framework can be extended to other reasoning tasks beyond algorithmic reasoning by adapting the approach to suit the specific requirements of the new tasks. For tasks like multi-hop reasoning, where multiple steps are involved in deriving a conclusion, the framework can be modified to generate pseudocode that captures the sequential logic of the reasoning process. This pseudocode can outline the steps involved in connecting different pieces of information or making inferences across multiple sources. Similarly, for tasks involving symbolic reasoning, where abstract symbols or concepts need to be manipulated according to certain rules, the framework can generate pseudocode that represents the symbolic operations and transformations required to arrive at the solution. By providing task-level pseudocode that encapsulates the core logic of the reasoning process, the framework can guide the language model in performing complex reasoning tasks effectively. Adapting the THINK-AND-EXECUTE framework to these tasks would involve designing meta prompts that capture the essence of the reasoning process, generating pseudocode prompts that reflect the specific logic of each task, and simulating the execution of the pseudocode to guide the language model in reasoning through the task steps.

Q: What are the limitations of using pseudocode compared to natural language or programming languages, and how can these limitations be addressed

Using pseudocode in the THINK-AND-EXECUTE framework has certain limitations compared to natural language or programming languages. One limitation is the potential lack of expressiveness in pseudocode, as it may not capture all the nuances and intricacies of a complex reasoning process as effectively as natural language. Pseudocode may also lack the specificity and precision of programming languages, which could lead to ambiguity or misinterpretation of the logic by the language model. To address these limitations, one approach could be to incorporate a more structured and formalized pseudocode format that includes specific syntax and conventions for representing different types of reasoning processes. This could help in standardizing the pseudocode prompts and making them more interpretable for the language model. Additionally, providing clear and detailed comments within the pseudocode prompts can help in explaining the rationale behind each step and guiding the language model in understanding the logic more accurately. Including annotations or annotations in the pseudocode can also enhance the clarity and comprehensibility of the logic represented in the prompts.

Q: How can the task-level logic discovered by the Instructor LM be further refined or validated to ensure its correctness and generalizability across a wider range of instances

To refine and validate the task-level logic discovered by the Instructor LM in the THINK-AND-EXECUTE framework, several strategies can be employed: Cross-validation: The discovered logic can be tested on a separate validation set of instances to ensure its generalizability across a wider range of examples. By evaluating the performance of the pseudocode prompts on unseen instances, the robustness and effectiveness of the logic can be assessed. Expert Review: Subject matter experts can review the task-level logic generated by the Instructor LM to validate its correctness and relevance to the task. Expert feedback can help in refining the logic and ensuring that it aligns with the expected reasoning process for the given task. Iterative Refinement: The task-level logic can be iteratively refined based on feedback from the Reasoner LM's performance on different instances. By analyzing the reasoning steps generated by the Reasoner LM and comparing them to the expected logic, adjustments can be made to improve the accuracy and consistency of the task-level pseudocode prompts. By incorporating these validation and refinement strategies, the THINK-AND-EXECUTE framework can enhance the quality and reliability of the task-level logic discovered by the Instructor LM, leading to improved reasoning performance across a variety of instances.

Kernkonzepte

Decomposing the reasoning process of language models into two steps - THINK to discover task-level logic expressed in pseudocode, and EXECUTE to tailor the pseudocode and simulate its execution - can significantly improve their performance on various algorithmic reasoning tasks.

Zusammenfassung

The paper introduces THINK-AND-EXECUTE, a novel framework for improving the algorithmic reasoning capabilities of large language models (LLMs).

THINK phase:

The Instructor LM analyzes a few example instances of a given task and generates a pseudocode prompt that captures the underlying logic required to solve the task.
The pseudocode prompt is designed to be task-level, meaning it can be applied to solve any instance of the task, rather than being instance-specific.

EXECUTE phase:

The Reasoner LM takes the generated pseudocode prompt and the input instance, and simulates the execution of the pseudocode step-by-step.
The Reasoner LM outputs the intermediate reasoning steps as a chain-of-thought, and the final answer.

The authors demonstrate that THINK-AND-EXECUTE outperforms strong baselines like Chain-of-Thought and Program-of-Thought prompting across various algorithmic reasoning tasks from the Big-Bench Hard benchmark. They also show that the pseudocode prompt generated by an LLM can be effectively transferred to smaller language models, improving their reasoning abilities.

The key insights are:

Discovering task-level logic and expressing it in pseudocode is more effective than generating instance-specific code.
Simulating the execution of pseudocode helps guide the reasoning of LLMs better than natural language plans.
LLMs pre-trained on code corpora can better understand and apply the task-level pseudocode prompt.

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arxiv.org

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"Algorithmic reasoning has long been a formidable challenge for LLMs, as it requires to scrutinize a complicated reasoning pattern and to translate it into a long sequence of reasoning steps."
"We demonstrate that THINK-AND-EXECUTE achieves notable improvements over strong baselines, including Chain-of-Thought and Program-of-Thought prompting, across various algorithmic tasks in Big-Bench Hard."
"We empirically show that the pseudocode prompt discovered by an LLM can be applied to small LMs (SLMs), such as CodeLlama-7B, to boost their reasoning ability."

Zitate

"To improve the reasoning capabilities of LLMs, prior works have primarily pursued two directions. The first direction includes enhancing the reasoning execution step by generating a rationale in natural language (e.g., Chain-of-Thought (Wei et al., 2022; Kojima et al., 2022)) or a piece of code (e.g., Program-of-Thought (Chen et al., 2023), Program-Aided LMs (Gao et al., 2023))."
"The second direction involves explicitly generating a plan described in natural language with LLMs. The plan describes the logic of the task and the LLM would subsequently concretize it into a sequence of reasoning steps (e.g., Least-to-Most (Zhou et al., 2022b), Plan-and-Solve (Wang et al., 2023))."

Wichtige Erkenntnisse aus

Language Models as Compilers

by Hyungjoo Cha... um arxiv.org 04-04-2024

https://arxiv.org/pdf/2404.02575.pdf

Tiefere Fragen

How can the THINK-AND-EXECUTE framework be extended to other reasoning tasks beyond algorithmic reasoning, such as multi-hop reasoning or symbolic reasoning

The THINK-AND-EXECUTE framework can be extended to other reasoning tasks beyond algorithmic reasoning by adapting the approach to suit the specific requirements of the new tasks. For tasks like multi-hop reasoning, where multiple steps are involved in deriving a conclusion, the framework can be modified to generate pseudocode that captures the sequential logic of the reasoning process. This pseudocode can outline the steps involved in connecting different pieces of information or making inferences across multiple sources.
Similarly, for tasks involving symbolic reasoning, where abstract symbols or concepts need to be manipulated according to certain rules, the framework can generate pseudocode that represents the symbolic operations and transformations required to arrive at the solution. By providing task-level pseudocode that encapsulates the core logic of the reasoning process, the framework can guide the language model in performing complex reasoning tasks effectively.
Adapting the THINK-AND-EXECUTE framework to these tasks would involve designing meta prompts that capture the essence of the reasoning process, generating pseudocode prompts that reflect the specific logic of each task, and simulating the execution of the pseudocode to guide the language model in reasoning through the task steps.

What are the limitations of using pseudocode compared to natural language or programming languages, and how can these limitations be addressed

Using pseudocode in the THINK-AND-EXECUTE framework has certain limitations compared to natural language or programming languages. One limitation is the potential lack of expressiveness in pseudocode, as it may not capture all the nuances and intricacies of a complex reasoning process as effectively as natural language. Pseudocode may also lack the specificity and precision of programming languages, which could lead to ambiguity or misinterpretation of the logic by the language model.
To address these limitations, one approach could be to incorporate a more structured and formalized pseudocode format that includes specific syntax and conventions for representing different types of reasoning processes. This could help in standardizing the pseudocode prompts and making them more interpretable for the language model.
Additionally, providing clear and detailed comments within the pseudocode prompts can help in explaining the rationale behind each step and guiding the language model in understanding the logic more accurately. Including annotations or annotations in the pseudocode can also enhance the clarity and comprehensibility of the logic represented in the prompts.

How can the task-level logic discovered by the Instructor LM be further refined or validated to ensure its correctness and generalizability across a wider range of instances

To refine and validate the task-level logic discovered by the Instructor LM in the THINK-AND-EXECUTE framework, several strategies can be employed:

Cross-validation: The discovered logic can be tested on a separate validation set of instances to ensure its generalizability across a wider range of examples. By evaluating the performance of the pseudocode prompts on unseen instances, the robustness and effectiveness of the logic can be assessed.

Expert Review: Subject matter experts can review the task-level logic generated by the Instructor LM to validate its correctness and relevance to the task. Expert feedback can help in refining the logic and ensuring that it aligns with the expected reasoning process for the given task.

Iterative Refinement: The task-level logic can be iteratively refined based on feedback from the Reasoner LM's performance on different instances. By analyzing the reasoning steps generated by the Reasoner LM and comparing them to the expected logic, adjustments can be made to improve the accuracy and consistency of the task-level pseudocode prompts.

By incorporating these validation and refinement strategies, the THINK-AND-EXECUTE framework can enhance the quality and reliability of the task-level logic discovered by the Instructor LM, leading to improved reasoning performance across a variety of instances.