Shashank Gupta

Parshin Shojaee, Kazem Meidani, Shashank Gupta et al.

Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the necessity of navigating extremely large combinatorial hypothesis spaces. Current methods of equation discovery, commonly known as symbolic regression techniques, largely focus on extracting equations from data alone, often neglecting the domain-specific prior knowledge that scientists typically depend on. They also employ limited representations such as expression trees, constraining the search space and expressiveness of equations. To bridge this gap, we introduce LLM-SR, a novel approach that leverages the extensive scientific knowledge and robust code generation capabilities of Large Language Models (LLMs) to discover scientific equations from data. Specifically, LLM-SR treats equations as programs with mathematical operators and combines LLMs' scientific priors with evolutionary search over equation programs. The LLM iteratively proposes new equation skeleton hypotheses, drawing from its domain knowledge, which are then optimized against data to estimate parameters. We evaluate LLM-SR on four benchmark problems across diverse scientific domains (e.g., physics, biology), which we carefully designed to simulate the discovery process and prevent LLM recitation. Our results demonstrate that LLM-SR discovers physically accurate equations that significantly outperform state-of-the-art symbolic regression baselines, particularly in out-of-domain test settings. We also show that LLM-SR's incorporation of scientific priors enables more efficient equation space exploration than the baselines. Code and data are available: https://github.com/deep-symbolic-mathematics/LLM-SR

Shashank Gupta, Olivier Jeunen, Harrie Oosterhuis et al.

The off-policy learning paradigm allows for recommender systems and general ranking applications to be framed as decision-making problems, where we aim to learn decision policies that optimize an unbiased offline estimate of an online reward metric. With unbiasedness comes potentially high variance, and prevalent methods exist to reduce estimation variance. These methods typically make use of control variates, either additive (i.e., baseline corrections or doubly robust methods) or multiplicative (i.e., self-normalisation). Our work unifies these approaches by proposing a single framework built on their equivalence in learning scenarios. The foundation of our framework is the derivation of an equivalent baseline correction for all of the existing control variates. Consequently, our framework enables us to characterize the variance-optimal unbiased estimator and provide a closed-form solution for it. This optimal estimator brings significantly improved performance in both evaluation and learning, and minimizes data requirements. Empirical observations corroborate our theoretical findings.