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On the Thinking-Language Modeling Gap in Large Language Models

Chenxi Liu, Yongqiang Chen, Tongliang Liu, James Cheng, Bo Han, Kun Zhang

TL;DR

A new prompt technique termed Language-of-Thoughts (LoT) is proposed, which significantly reduces the language modeling biases in LLMs and improves the performance of LLMs across a variety of reasoning tasks.

Abstract

System 2 reasoning is one of the defining characteristics of intelligence, which requires slow and logical thinking. Human conducts System 2 reasoning via the language of thoughts that organizes the reasoning process as a causal sequence of mental language, or thoughts. Recently, it has been observed that System 2 reasoning can be elicited from Large Language Models (LLMs) pre-trained on large-scale natural languages. However, in this work, we show that there is a significant gap between the modeling of languages and thoughts. As language is primarily a tool for humans to share knowledge and thinking, modeling human language can easily absorb language biases into LLMs deviated from the chain of thoughts in minds. Furthermore, we show that the biases will mislead the eliciting of "thoughts" in LLMs to focus only on a biased part of the premise. To this end, we propose a new prompt technique termed Language-of-Thoughts (LoT) to demonstrate and alleviate this gap. Instead of directly eliciting the chain of thoughts from partial information, LoT instructs LLMs to adjust the order and token used for the expressions of all the relevant information. We show that the simple strategy significantly reduces the language modeling biases in LLMs and improves the performance of LLMs across a variety of reasoning tasks.

On the Thinking-Language Modeling Gap in Large Language Models

TL;DR

A new prompt technique termed Language-of-Thoughts (LoT) is proposed, which significantly reduces the language modeling biases in LLMs and improves the performance of LLMs across a variety of reasoning tasks.

Abstract

System 2 reasoning is one of the defining characteristics of intelligence, which requires slow and logical thinking. Human conducts System 2 reasoning via the language of thoughts that organizes the reasoning process as a causal sequence of mental language, or thoughts. Recently, it has been observed that System 2 reasoning can be elicited from Large Language Models (LLMs) pre-trained on large-scale natural languages. However, in this work, we show that there is a significant gap between the modeling of languages and thoughts. As language is primarily a tool for humans to share knowledge and thinking, modeling human language can easily absorb language biases into LLMs deviated from the chain of thoughts in minds. Furthermore, we show that the biases will mislead the eliciting of "thoughts" in LLMs to focus only on a biased part of the premise. To this end, we propose a new prompt technique termed Language-of-Thoughts (LoT) to demonstrate and alleviate this gap. Instead of directly eliciting the chain of thoughts from partial information, LoT instructs LLMs to adjust the order and token used for the expressions of all the relevant information. We show that the simple strategy significantly reduces the language modeling biases in LLMs and improves the performance of LLMs across a variety of reasoning tasks.
Paper Structure (54 sections, 4 theorems, 13 equations, 5 figures, 8 tables)

This paper contains 54 sections, 4 theorems, 13 equations, 5 figures, 8 tables.

Table of Contents

  1. Introduction
  2. The Language-Thought Gap in LLMs' Reasoning
  3. Formalization of the Data Generation Process
  4. Structural Causal Models
  5. Running example
  6. How the Language-Thought Gap Influence the Reasoning Process
  7. Training Phase
  8. Inference Phase
  9. Discussion and understanding
  10. Verification: Prompt Intervention with Controlled Implicitness
  11. The two types of implicitness
  12. The Control of Implicitness
  13. Control $L$-explicitness
  14. Control $q$-explicitness
  15. Prompt-level Intervention Scheme
  16. ...and 39 more sections

Key Result

Proposition 2.3

When encountering the natural language sentence in an anti-topological order, e.g., $(C_1, A, C_2)$, as shown in the right part of fig:thought-language-example, language modeling of $(C_1, A, C_2)$ with the next-token prediction objective, will yield an LLM to draw the conclusion with incomplete inf

Figures (5)

  • Figure 1: Different SCMs. Left: State conclusion at last; Right: State conclusion earlier.
  • Figure 2: Token cost analysis
  • Figure 3: The accuracy patterns on the combos from $L$- and $q$-implicitness.
  • Figure 4: Case study on BBQ example (the first) and the WinoBias example (the second). We post the responses from Echo, Expand, and Echo to understand the limitations of each component. The evaluation results are also annotated (N for no, Y for yes).
  • Figure 5: Comparison of LoT with Direct prompting and CoT across $8$ challenging reasoning benchmarks and $6$ LLMs. The results are present in terms of accuracy. A higher accuracy indicates a better reasoning ability. We skip the evaluation of Claude on Abductive and Deductive reasoning to align with Sprague2024ToCO. In most cases, LoT brings consistent and large improvements against CoT.

Theorems & Definitions (9)

  • Definition 2.1: Next-Token Predictor
  • Example 2.2: Two-premise QA
  • Proposition 2.3: Language-Modeling Bias
  • Theorem 2.4: Language-Thought Gap
  • Definition F.1: Markov Property elements_ci
  • Proposition F.2: Restatement of Proposition \ref{['prop:language-modeling-bias']}
  • proof : Proof for Proposition \ref{['prop:language-modeling-bias']}
  • Proposition F.3: Restatement of \ref{['prop:inference-gap']}
  • proof : Proof for \ref{['prop:inference-gap']}