Evaluating Reasoning Capabilities of Language Models through Symbolic Verification

Core Concepts

Language models can be prompted with logical demonstrations to generate plausible explanations for reasoning tasks over knowledge bases, and constraining outputs and ensuring intermediate reasoning correctness are important for improving reasoning performance.

Abstract

This paper investigates the reasoning capabilities of language models (LMs) from a symbolic perspective. The authors curate synthetic datasets containing equivalent natural language and symbolic data pairs, where the symbolic part contains first-order logic rules and predicates from non-parametric knowledge bases (KBs). This allows for automated verification of the intermediate reasoning results.
The authors propose a method called Language Models as Logic Programmers (LMLP), which learns from demonstrations containing logic rules and corresponding examples to iteratively reason over KBs. LMLP recovers Prolog's backward chaining algorithm and supports automated verification of LMs' outputs.
The authors conduct comprehensive experiments to systematically compare LMLP with Chain-of-Thought (CoT) prompting in deductive reasoning settings. The results show that LMLP enjoys more than 25% higher accuracy than CoT on length generalization benchmarks, even with smaller model sizes.
The authors also analyze the LMLP method in depth, finding that:

Prompting with multiple examples and prompt ensembling can further boost the reasoning capability of LMLP.
LMLP can be robust to large search spaces, maintaining a success rate of over 38% even when the majority of facts in the KB are noisy.
Larger language models generally lead to better performance for LMLP.

The paper provides insights into the role of symbolic representations in improving the reasoning capabilities of language models through in-context learning.

Stats

LMLP can achieve more than 25% higher accuracy than CoT on length generalization benchmarks.
LMLP maintains a success rate of over 38% even when the majority of facts in the KB are noisy.

Quotes

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Key Insights Distilled From

Evaluating Step-by-Step Reasoning through Symbolic Verification

by Yi-Fan Zhang... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2212.08686.pdf

Deeper Inquiries

How can the LMLP approach be extended to handle more complex reasoning tasks beyond relational reasoning, such as causal reasoning or commonsense reasoning

The LMLP approach can be extended to handle more complex reasoning tasks beyond relational reasoning by incorporating additional symbolic representations and rules for different types of reasoning. For causal reasoning, the LMLP model can be trained on datasets that contain causal relationships between entities or events. By providing examples and logic rules that capture causal dependencies, the model can learn to reason causally.
For commonsense reasoning, the LMLP can be trained on datasets that require understanding of everyday knowledge and reasoning about implicit information. This can involve prompts that require the model to make logical inferences based on common knowledge or societal norms. By providing diverse examples and rules that cover a wide range of commonsense scenarios, the model can learn to reason in a more nuanced and contextually appropriate manner.

What are the potential limitations of the symbolic verification approach used in LMLP, and how could it be further improved to handle more ambiguous or open-ended reasoning scenarios

The symbolic verification approach used in LMLP may have limitations when handling more ambiguous or open-ended reasoning scenarios. One potential limitation is the reliance on predefined logic rules and predicates, which may not cover all possible reasoning paths or interpretations in complex scenarios. To improve this, the symbolic verification process could be enhanced by incorporating probabilistic reasoning or fuzzy logic to handle uncertainty and ambiguity in reasoning tasks.
Additionally, the verification process could be further improved by integrating feedback mechanisms that allow for iterative refinement of reasoning paths based on human feedback. This would enable the model to learn from its mistakes and adjust its reasoning strategies over time. Furthermore, incorporating contextual information and domain-specific knowledge bases could help the model make more informed and contextually relevant reasoning decisions in open-ended scenarios.

Given the importance of prompt engineering highlighted in this work, how can the process of designing effective prompts for in-context learning be automated or made more systematic

The process of designing effective prompts for in-context learning can be automated or made more systematic by leveraging techniques from natural language processing and machine learning. One approach is to use reinforcement learning to automatically generate prompts that lead to successful reasoning outcomes. By training a reinforcement learning agent to generate prompts that result in correct reasoning paths, the model can learn to optimize the prompt design process over time.
Another approach is to use neural architecture search techniques to automatically discover effective prompt structures for different types of reasoning tasks. By defining a search space of possible prompt structures and training a search algorithm to find the most effective prompts for a given task, the model can adapt to different reasoning requirements and optimize prompt design for improved performance.
Additionally, leveraging pre-trained language models to generate prompts based on input data and task requirements can streamline the prompt design process and ensure that prompts are tailored to the specific context of the reasoning task. This can help reduce the manual effort required for prompt engineering and improve the efficiency of in-context learning systems.