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Do Language Models Exhibit the Same Cognitive Biases in Problem Solving as Human Learners?

Andreas Opedal, Alessandro Stolfo, Haruki Shirakami, Ying Jiao, Ryan Cotterell, Bernhard Schölkopf, Abulhair Saparov, Mrinmaya Sachan

TL;DR

This study investigates whether large language models (LLMs) mimic child-like cognitive biases in solving arithmetic word problems by modeling the solving process as four stages: text comprehension, mental modeling, solution planning, and solution execution. Using a neuro-symbolic, MathWorld-based generation pipeline, the authors create controlled word problems to isolate biases at each stage and evaluate multiple LLMs with direct and chain-of-thought prompting. They find that LLMs exhibit human-like consistency and transfer-vs-comparison biases during text comprehension and planning, but do not show a carry-bias during arithmetic execution. The results suggest that biases may stem from training data and reasoning strategies rather than fundamental arithmetic mechanisms, with important implications for cognitive modeling and educational applications of LLMs.

Abstract

There is increasing interest in employing large language models (LLMs) as cognitive models. For such purposes, it is central to understand which properties of human cognition are well-modeled by LLMs, and which are not. In this work, we study the biases of LLMs in relation to those known in children when solving arithmetic word problems. Surveying the learning science literature, we posit that the problem-solving process can be split into three distinct steps: text comprehension, solution planning and solution execution. We construct tests for each one in order to understand whether current LLMs display the same cognitive biases as children in these steps. We generate a novel set of word problems for each of these tests, using a neuro-symbolic approach that enables fine-grained control over the problem features. We find evidence that LLMs, with and without instruction-tuning, exhibit human-like biases in both the text-comprehension and the solution-planning steps of the solving process, but not in the final step, in which the arithmetic expressions are executed to obtain the answer.

Do Language Models Exhibit the Same Cognitive Biases in Problem Solving as Human Learners?

TL;DR

This study investigates whether large language models (LLMs) mimic child-like cognitive biases in solving arithmetic word problems by modeling the solving process as four stages: text comprehension, mental modeling, solution planning, and solution execution. Using a neuro-symbolic, MathWorld-based generation pipeline, the authors create controlled word problems to isolate biases at each stage and evaluate multiple LLMs with direct and chain-of-thought prompting. They find that LLMs exhibit human-like consistency and transfer-vs-comparison biases during text comprehension and planning, but do not show a carry-bias during arithmetic execution. The results suggest that biases may stem from training data and reasoning strategies rather than fundamental arithmetic mechanisms, with important implications for cognitive modeling and educational applications of LLMs.

Abstract

There is increasing interest in employing large language models (LLMs) as cognitive models. For such purposes, it is central to understand which properties of human cognition are well-modeled by LLMs, and which are not. In this work, we study the biases of LLMs in relation to those known in children when solving arithmetic word problems. Surveying the learning science literature, we posit that the problem-solving process can be split into three distinct steps: text comprehension, solution planning and solution execution. We construct tests for each one in order to understand whether current LLMs display the same cognitive biases as children in these steps. We generate a novel set of word problems for each of these tests, using a neuro-symbolic approach that enables fine-grained control over the problem features. We find evidence that LLMs, with and without instruction-tuning, exhibit human-like biases in both the text-comprehension and the solution-planning steps of the solving process, but not in the final step, in which the arithmetic expressions are executed to obtain the answer.
Paper Structure (43 sections, 5 equations, 4 figures, 5 tables)

This paper contains 43 sections, 5 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Cognitive Modeling of the Solving Process
  3. Our conceptualization.
  4. Background.
  5. Human Biases in Word Problems
  6. Problem text: Consistency bias.
  7. Mental model: Transfer vs comparison bias.
  8. Arithmetic expressions: The carry effect.
  9. Problem Generation Method
  10. Operationalizing \ref{['fig:solving-pyramid']}
  11. Plausibility of the mental model framework.
  12. Generation Pipeline
  13. (i) Problem structure generation.
  14. (ii) Problem structure instantiation.
  15. (iii) Template sampling.
  16. ...and 28 more sections

Figures (4)

  • Figure 1: A three-step model of the cognitive process involved in solving math word problems. We study whether LLMs exhibit similar biases as human children along each step of this process.
  • Figure 2: Overview of our generation pipeline with an example problem. (1) We start by generating the problem structure. The alignment between the graphical and sequential formats of the structure is illustrated by color coding, and the black containment boxes in the graph represent intermediate results. (2) The properties of those structures are then instantiated with values, resulting in a mental model. (3) Next, we sample a templated sentence for each of the logical forms in the mental model, and concatenate them in the ordering of the logical forms. (4) Finally, we correct errors and awkward phrasings by prompting an instruction-tuned LLM (the corrections are highlighted in blue). This particular example includes all predicate types that we use in \ref{['sec:experiments']}.
  • Figure 3: CATE for the consistency effect (\ref{['sec:consistency-hypothesis']}) in CoT-prompted models stratified by number of reasoning steps. 'Instruction-tuned' refers to the Chat and Instruct versions of LLaMA2 and Mistral/Mixtral, respectively.
  • Figure 4: CATE for transfer vs comparison (\ref{['sec:concept-test']}) in the CoT-prompted case stratified by number of reasoning steps. 'Instruction-tuned' refers to the Chat and Instruct versions of LLaMA2 and Mistral/Mixtral, respectively. Base and instruction-tuned models display opposite relationships between length and bias strength.