Computational Model of Hypothesis Formation, Experimentation, and Belief Revision for Discovering Hidden Rules

Core Concepts

Humans actively infer hidden rules by constructing a small set of fuzzy probabilistic hypotheses, updating these hypotheses online based on new experiments, and designing informative experiments to efficiently discover the underlying rule.

Abstract

The paper presents a computational model that aims to explain how humans actively infer hidden rules through experimentation and belief revision. The key components of the model are: Probabilistic Model: Hypotheses are represented as natural language rules with associated fuzzy probabilities. The model maintains a joint probability distribution over hypotheses, experiments, and feedback. The likelihood function assumes the true rule is deterministic but the learner represents it probabilistically, allowing for some noise in the feedback. Online Inference: The model uses a Sequential Monte Carlo (SMC) algorithm to track a small set of evolving hypotheses. After each experiment, the hypotheses are reweighted based on the new feedback, revised using a language model to better explain the latest data, and then resampled to focus on high-probability hypotheses. Active Learning: The model proposes new experiments by generating a diverse set of candidate structures using a language model. It then selects the most informative experiment by maximizing the expected change in the posterior distribution of hypotheses. The model is evaluated on the Zendo game, where humans try to infer a hidden rule by building structures and receiving feedback on whether they follow the rule. The results show that the full model, with all its components, can accurately predict human performance, while ablated versions fail to capture key patterns in the data. This suggests that humans may employ a similar strategy of constructing and revising fuzzy hypotheses, and designing informative experiments, when functioning as "intuitive experimentalists".

Stats

"Even if the rule is deterministic, the learner considers a broader space of fuzzy probabilistic rules, which it represents in natural language." "We find that the combination of these three principles—explicit hypotheses, probabilistic rules, and online updates—can explain human performance on a Zendo-style task, and that removing any of these components leaves the model unable to account for the data."

Quotes

"Actual learners are bounded, and can only consider a small number of hypotheses at a time." "Our model uses two tricks, both of which we believe have analogues in human thinking." "Recent work has found that LLM-generated natural language hypotheses can predict certain judgments of human learners, particularly when embedded in a Bayesian framework."

Key Insights Distilled From

Doing Experiments and Revising Rules with Natural Language and Probabilistic Reasoning

by Wasu Top Pir... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2402.06025.pdf

Deeper Inquiries

How might the model be extended to handle more complex, compositional rules that go beyond simple attribute-based descriptions?

To extend the model to handle more complex, compositional rules, we can introduce a hierarchical structure to the hypotheses. Instead of focusing solely on individual attributes like color, size, or orientation, the model can incorporate relationships between these attributes. For example, instead of just stating "there is a blue block," the model could generate rules like "if there is a blue block, then there must also be a small block." This hierarchical approach allows for the creation of more intricate rules that involve combinations of attributes and their interactions. Additionally, the model can utilize recursive reasoning to build up complex rules from simpler components. By recursively combining basic rules, the model can generate more sophisticated hypotheses that capture the interplay between different attributes in a scene. This recursive process mirrors how humans often break down complex concepts into simpler parts to understand them better. Furthermore, incorporating neural-symbolic integration techniques can enhance the model's ability to handle compositional rules. By integrating neural networks with symbolic reasoning, the model can leverage the strengths of both approaches to represent and manipulate complex rules effectively. This integration allows for the seamless transition between symbolic rule-based reasoning and neural network-based pattern recognition, enabling the model to handle a wider range of compositional rules.

How could the model be adapted to study the development of inductive reasoning skills from childhood to adulthood?

To adapt the model to study the development of inductive reasoning skills across different age groups, we can introduce age-specific cognitive biases and heuristics into the hypothesis generation and experiment design processes. For children, who may exhibit more concrete thinking and rely heavily on perceptual features, the model can incorporate biases such as confirmation bias, where they tend to seek out information that confirms their existing beliefs. The model can also simulate children's preference for simple, intuitive explanations by generating hypotheses that prioritize straightforward rules based on visible attributes. In contrast, for adults who may have more abstract thinking and higher cognitive abilities, the model can incorporate biases like anchoring and adjustment, where initial hypotheses heavily influence subsequent thinking. By adjusting the hypothesis generation process to reflect these biases, the model can simulate how adults may approach inductive reasoning tasks differently from children. Moreover, the model can simulate the developmental trajectory of inductive reasoning skills by gradually increasing the complexity of rules and experiments as the simulated participants age. By introducing more challenging tasks and rules over time, the model can capture the progression from simpler, perceptually-driven reasoning to more abstract, conceptually-based reasoning seen in adult cognitive development. By incorporating age-specific biases, heuristics, and developmental trajectories into the model, researchers can gain insights into how inductive reasoning skills evolve from childhood to adulthood and how cognitive processes change across different stages of development.