CogSimulator: A Model for Simulating User Cognition & Behavior with Minimal Data for Tailored Cognitive Enhancement

TL;DR

CogSimulator addresses the challenge of modeling user cognition for tailored educational games using minimal data. It combines a sampling-based simulator with Markov-Chain–Monte-Carlo–style parameter fitting, optimized by Coordinate Search and assessed via the Wasserstein-1 distance $W_1$, to predict word difficulty and generates distributions of user guesses. Empirical results on Wordle using a Wordle Stats 2022 dataset and a Google Books Ngram-based word dictionary show CogSimulator achieving higher accuracy and lower mean squared error than several baselines, demonstrating data-efficient prediction of cognitive difficulty and trial distributions. The work offers a practical, generalizable tool for adaptive game design in niche or new educational games, with future potential to incorporate player profiling and dynamic reward mechanisms to further enhance cognitive training outcomes.

Abstract

The interplay between cognition and gaming, notably through educational games enhancing cognitive skills, has garnered significant attention in recent years. This research introduces the CogSimulator, a novel algorithm for simulating user cognition in small-group settings with minimal data, as the educational game Wordle exemplifies. The CogSimulator employs Wasserstein-1 distance and coordinates search optimization for hyperparameter tuning, enabling precise few-shot predictions in new game scenarios. Comparative experiments with the Wordle dataset illustrate that our model surpasses most conventional machine learning models in mean Wasserstein-1 distance, mean squared error, and mean accuracy, showcasing its efficacy in cognitive enhancement through tailored game design.

Figures (3)

• Figure 1: An overview of the CogSimulator model. It starts by aggregating Wordle data from Twitter and using it to form a true trial distribution for training. The simulator, via Markov Chain Monte Carlo, adjusts hyperparameters to match this distribution. Parameter optimization is performed with a Coordinate Search Method Algorithm, and model accuracy is ensured using the Wasserstein-1 metric to compare simulated outputs to actual trials. Functional PCA relates simulated and true word difficulties, enabling precise predictions for new word trials based on players' cognitive patterns.
• Figure 2: Distribution of word difficulties in the Wordle game. The x-axis represents the number of attempts, and the y-axis represents the frequency of each attempt number.
• Figure 3: We obtain 200 simulated trial distributions of the word eerie. Displayed at the top, the visualization method projects these results into a 2-dimensional functional space. At the bottom, the predicted mean is highlighted with a green line, and a $95\%$ empirical confidence interval is constructed around it.