A Notion of Complexity for Theory of Mind via Discrete World Models

TL;DR

This work proposes a framework inspired by cognitive load theory to measure the complexity of ToM tasks, and designs a prompting technique that augments the information available to a model with a description of how the environment changes with the agents' interactions.

Abstract

Theory of Mind (ToM) can be used to assess the capabilities of Large Language Models (LLMs) in complex scenarios where social reasoning is required. While the research community has proposed many ToM benchmarks, their hardness varies greatly, and their complexity is not well defined. This work proposes a framework inspired by cognitive load theory to measure the complexity of ToM tasks. We quantify a problem's complexity as the number of states necessary to solve it correctly. Our complexity measure also accounts for spurious states of a ToM problem designed to make it apparently harder. We use our method to assess the complexity of five widely adopted ToM benchmarks. On top of this framework, we design a prompting technique that augments the information available to a model with a description of how the environment changes with the agents' interactions. We name this technique Discrete World Models (DWM) and show how it elicits superior performance on ToM tasks.

Figures (13)

• Figure 1: Example of the DWM prompting technique on a classical Sally-Anne QA task baron-cohenDoesAutisticChild1985. Inspired by our complexity framework (Section \ref{['sec:complexity']}), DWM takes the original task and splits it into sequences, the state events (see Def. \ref{['def:state-event']}), and prompts the LLMs to describe the states. We show that, in most cases, this aids the LLM in providing correct answers.
• Figure 2: How statefulness and statelessness (Def. \ref{['def:partition']}) are computed for the motivating example in Fig. \ref{['fig:example']}. For ${obj_1}$, an optimal split to track the apple merges the first two states and chunks of the input prompt. For ${obj_2}$, which involves the $1^{\text{st}}$-order belief of Bob, the statefulness is higher, with $e_2$ that cannot be merged with $e_3$ as it introduces partial observability. The complexity of the task (bottom) is computed as per Eq. \ref{['def:tom-complexity']}, where the complexity of objects that are not directly relevant to the question/answer is discounted.
• Figure 3: Left: illustration of DWM prompting as per the example in Figure \ref{['fig:example']}. We interactively prompt an LLM with a ToM problem, asking to provide a succinct representation of each agent's beliefs. Right: schematic presentation of the DWM method. We first break the input string into $T$state descriptions. Then, for each part, we ask the LLM to provide the state event of the environment and how it changes. In the last step, every part of the input and description is fed to the LLM with another prompt to get the answer for the task.
• Figure 4: Benchmarks of GPT-3.5-Turbo (top) and Mixtral 8x7B (bottom) models on different ToM tasks for DWM (one to five splits), CoT, ToT and structured prompts (JSON and Yaml).
• Figure 5: Example of a real ToMi example where GPT-4 fails when prompted with CoT, yet succeeds with DWM. CoT elicits an untruthful reasoning process (in red), while DWM correctly informs the model with the implicit information about Benjamin's first-order belief (in green). More examples are reported in the Appendix, Section \ref{['a:dwm-vs-cot']}.

Theorems & Definitions (2)

• Definition 3.1: State event
• Definition 3.2: Partitions