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Data-Centric Approach to Constrained Machine Learning: A Case Study on Conway's Game of Life

Anton Bibin, Anton Dereventsov

TL;DR

This work tackles learning the rules of Conway's Game of Life under tight architectural constraints by adopting a data-centric approach. It shows that a minimal two-layer CNN with 23 parameters can replicate the one-step transition, and that multi-step behavior can be studied via recursive or sequential network designs. By constructing two carefully designed datasets—a random, density-controlled board and a symmetry-enforced fixed board—the authors demonstrate that data design can vastly outperform random data in convergence speed and accuracy, even under limited model capacity. The study highlights the crucial role of domain expertise in data curation and suggests that data-centric strategies are especially valuable for constrained real-world applications with ethical, legal, or hardware limits.

Abstract

This paper focuses on a data-centric approach to machine learning applications in the context of Conway's Game of Life. Specifically, we consider the task of training a minimal architecture network to learn the transition rules of Game of Life for a given number of steps ahead, which is known to be challenging due to restrictions on the allowed number of trainable parameters. An extensive quantitative analysis showcases the benefits of utilizing a strategically designed training dataset, with its advantages persisting regardless of other parameters of the learning configuration, such as network initialization weights or optimization algorithm. Importantly, our findings highlight the integral role of domain expert insights in creating effective machine learning applications for constrained real-world scenarios.

Data-Centric Approach to Constrained Machine Learning: A Case Study on Conway's Game of Life

TL;DR

This work tackles learning the rules of Conway's Game of Life under tight architectural constraints by adopting a data-centric approach. It shows that a minimal two-layer CNN with 23 parameters can replicate the one-step transition, and that multi-step behavior can be studied via recursive or sequential network designs. By constructing two carefully designed datasets—a random, density-controlled board and a symmetry-enforced fixed board—the authors demonstrate that data design can vastly outperform random data in convergence speed and accuracy, even under limited model capacity. The study highlights the crucial role of domain expertise in data curation and suggests that data-centric strategies are especially valuable for constrained real-world applications with ethical, legal, or hardware limits.

Abstract

This paper focuses on a data-centric approach to machine learning applications in the context of Conway's Game of Life. Specifically, we consider the task of training a minimal architecture network to learn the transition rules of Game of Life for a given number of steps ahead, which is known to be challenging due to restrictions on the allowed number of trainable parameters. An extensive quantitative analysis showcases the benefits of utilizing a strategically designed training dataset, with its advantages persisting regardless of other parameters of the learning configuration, such as network initialization weights or optimization algorithm. Importantly, our findings highlight the integral role of domain expert insights in creating effective machine learning applications for constrained real-world scenarios.
Paper Structure (20 sections, 10 equations, 17 figures, 6 tables)

This paper contains 20 sections, 10 equations, 17 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Conway's Game of Life
  3. Constrained Machine Learning
  4. Data-Centric Machine Learning
  5. Related Work
  6. Game of Life as a Neural Network
  7. ReLU Activation
  8. Tanh Activation
  9. Multi-step Game of Life
  10. Training Data Design
  11. Random Dataset
  12. Fixed Dataset
  13. Numerical Experiments
  14. 1-step Game of Life.
  15. 2-step Game of Life with Recursive Networks.
  16. ...and 5 more sections

Figures (17)

  • Figure 1: An example of a state trajectory in the Game of Life. Alive cells are white and dead cells are black.
  • Figure 2: Minimal CNN architecture for the Game of Life network.
  • Figure 3: Minimal recursive CNN architecture for the multi-step Game of Life network.
  • Figure 4: Minimal sequential CNN architecture for the multi-step Game of Life network.
  • Figure 5: Average board density after multiple steps of the Game of Life.
  • ...and 12 more figures