arXiv:2606.29331v1 Announce Type: new Abstract: Scientific discovery via symbolic regression is often viewed as statistically and computationally intractable because the hypothesis space of expressions grows combinatorially with depth. This paper revisits the statistical side through the lens of PAC learning, focusing on compositional function trees built from a finite vocabulary of smooth operators (e.g., $\{+,\times,\sin,\exp\}$ and affine maps). We prove that the relevant generalization quantity, Rademacher complexity, hence the excess risk, does not necessarily blow up exponentially with t
The paper provides a theoretical breakthrough in understanding the statistical complexity of symbolic regression at a time when AI systems are increasingly tasked with scientific discovery.
This research suggests that automatically discovering scientific laws may be more tractable than previously assumed, potentially accelerating AI-driven scientific breakthroughs across various disciplines.
The perceived statistical intractability of symbolic regression for compositional function trees is being challenged, shifting expectations for AI's capacity in complex scientific discovery.
- · AI researchers in symbolic regression
- · Pharmaceuticals sector
- · Materials science sector
- · AI/ML software developers
- · Traditional empirical scientific methods
- · Research areas reliant on purely human-driven hypothesis generation
Accelerated development of AI systems capable of discovering complex scientific laws from data.
Increased efficiency and speed in R&D across scientific and engineering fields, leading to faster innovation cycles.
Potentially, a paradigm shift in scientific methodology where AI becomes a primary generator of fundamental theories and models.
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Read at arXiv cs.LG