Vertical Summarization of Ground-Truth Expression for Symbolic Regression

In this article, we explore the concept of dual cognition in machine learning, specifically in the context of symbolic regression. Our approach leverages both fast and slow thinking to achieve better outcomes. Fast thinking refers to the use of brute force methods like big data and heavy computation, while slow thinking involves careful meta-reasoning on strategies to determine ground-truth equations. We argue that by combining these two cognitive styles, we can improve upon traditional machine learning approaches that rely solely on fast thinking.
To illustrate our approach, we present seven experiments demonstrating the superiority of VSR-MCTS (a general outline of which is given in Algorithm 3) over multiple baselines. VSR-MCTS combines symbolic regression using mathematical operators (Op) with MCTS (Monte Carlo Tree Search), a popular algorithm for solving decision-making problems.
In essence, our approach works by starting with the current best symbolic expression ϕinit, a data Oracle under control variable setup, and a library of mathematical operators Op as input. We then repeat four basic operations of MCTS – selection, expansion, simulation, and backpropagation for a fixed number of episodes.
The key insight is that by incorporating slow thinking into the machine learning process, we can create a more robust model that better captures the underlying causal relationships between variables. By using control variable experiments to accelerate symbolic regression, we can identify correlations instead of causal relationships. However, by carefully meta-reasoning on these correlations, we can determine the ground-truth equations that lead to better outcomes.
In summary, our dual cognition approach represents a new way of thinking about machine learning that combines the strengths of both fast and slow thinking. By leveraging the power of brute force methods while also incorporating careful meta-reasoning, we can create more robust and accurate models that lead to better outcomes in the field of symbolic regression.