AutoSR: Automatic Symbolic Regression by Searching Research States

Imagine you're a scientist trying to derive equations that explain complex phenomena from experimental data. Traditionally, you might use symbolic regression to find a mathematical expression that fits your data, but this often leads to equations that work well only within the specific range of your data. This is problematic because the resulting equations can behave unpredictably outside that range, and the process usually discards valuable insights about why certain equations were considered in the first place. This is what's called a lack of scientific credibility in the results. Existing methods focus on refining equations but often overlook the broader context of the research, including motivations and the reasoning behind each candidate equation.

The approach introduced in this paper, Automatic Symbolic Regression (AutoSR), addresses these issues by coupling each candidate equation with a comprehensive record of the research process, including the reasoning and evidence that led to its development. By using a method called progressive-widening Monte Carlo tree search (PW-MCTS), AutoSR explores multiple scientific investigations simultaneously, ensuring that the accumulated knowledge informs future searches. This means that instead of just getting a final equation, you also receive a detailed report explaining how that equation was derived and why it was chosen. Compared to previous work, AutoSR not only finds mathematically valid expressions but also preserves the scientific narrative that guides the exploration, making it a more robust tool for scientific inquiry.

AutoSR introduces a novel approach to symbolic regression by integrating a research record with equation search.

The evaluation across multiple benchmark challenges demonstrates solid performance, though details on baselines could be clearer.