Selected work

Representative Papers

Towards chemistries in dynamical systems

Jul 21, 2026

This work proposes a modeling framework that maps arbitrary dynamical systems onto chemical-reaction-like processes by defining “positions,” “species existence,” and “reaction rules” between states, thereby describing system evolution as updates to chemical equations constrained by a “minimal unique reaction path.” This approach constitutes the first systematic formalization of general dynamical systems using chemical language, ensuring that each state transition is driven by the smallest possible set of reactions that is also uniquely determined. Applied to the glider in Conway’s Game of Life, the framework successfully reproduces its dynamic behavior and demonstrates the feasibility of the proposed constraint, while simultaneously highlighting inherent limitations of the current methodology.

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It's Much Easier for Neural Networks to learn Game of Life Dynamics with the Right Activation Function: Polynomial Kolmogorov-Arnold Networks

Jun 22, 2026

This work addresses the challenge that neural networks typically require large architectures and specialized initialization to learn the rules of Conway’s Game of Life, often failing to converge reliably in small models. The authors propose incorporating task-specific inductive biases to transform this difficult search problem into a tractable learning task. Their key innovation is a compact network architecture based on the Kolmogorov–Arnold representation theorem, employing a second-order polynomial activation function. Experimental results demonstrate that this design consistently reproduces the dynamics of the Game of Life—both with and without weight training—and substantially outperforms standard activation functions such as ReLU. These findings challenge the prevailing paradigm that model scale is the primary determinant of performance in such rule-learning tasks.

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Recent publications

Latest Papers

Towards chemistries in dynamical systems

Jul 21, 2026

This work proposes a modeling framework that maps arbitrary dynamical systems onto chemical-reaction-like processes by defining “positions,” “species existence,” and “reaction rules” between states, thereby describing system evolution as updates to chemical equations constrained by a “minimal unique reaction path.” This approach constitutes the first systematic formalization of general dynamical systems using chemical language, ensuring that each state transition is driven by the smallest possible set of reactions that is also uniquely determined. Applied to the glider in Conway’s Game of Life, the framework successfully reproduces its dynamic behavior and demonstrates the feasibility of the proposed constraint, while simultaneously highlighting inherent limitations of the current methodology.

0 citationsRead paper

It's Much Easier for Neural Networks to learn Game of Life Dynamics with the Right Activation Function: Polynomial Kolmogorov-Arnold Networks

Jun 22, 2026

This work addresses the challenge that neural networks typically require large architectures and specialized initialization to learn the rules of Conway’s Game of Life, often failing to converge reliably in small models. The authors propose incorporating task-specific inductive biases to transform this difficult search problem into a tractable learning task. Their key innovation is a compact network architecture based on the Kolmogorov–Arnold representation theorem, employing a second-order polynomial activation function. Experimental results demonstrate that this design consistently reproduces the dynamics of the Game of Life—both with and without weight training—and substantially outperforms standard activation functions such as ReLU. These findings challenge the prevailing paradigm that model scale is the primary determinant of performance in such rule-learning tasks.

0 citationsRead paper