LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models

Scientific equation discovery is a fundamental task in the history of scientific progress, enabling the derivation of laws governing natural phenomena. Recently, Large Language Models (LLMs) have gained interest for this task due to their potential to leverage embedded scientific knowledge for hypothesis generation. However, evaluating the true discovery capabilities of these methods remains challenging, as existing benchmarks often rely on common equations that are susceptible to memorization by LLMs, leading to inflated performance metrics that do not reflect discovery. In this paper, we introduce LLM-SRBench, a comprehensive benchmark with 239 challenging problems across four scientific domains specifically designed to evaluate LLM-based scientific equation discovery methods while preventing trivial memorization. Our benchmark comprises two main categories: LSR-Transform, which transforms common physical models into less common mathematical representations to test reasoning beyond memorized forms, and LSR-Synth, which introduces synthetic, discovery-driven problems requiring data-driven reasoning. Through extensive evaluation of several state-of-the-art methods, using both open and closed LLMs, we find that the best-performing system so far achieves only 31.5% symbolic accuracy. These findings highlight the challenges of scientific equation discovery, positioning LLM-SRBench as a valuable resource for future research.

Towards Efficient Communication Federated Recommendation System via Low-rank Training

In Federated Recommendation (FedRec) systems, communication costs are a critical bottleneck that arises from the need to transmit neural network models between user devices and a central server. Prior approaches to these challenges often lead to issues such as computational overheads, model specificity constraints, and compatibility issues with secure aggregation protocols. In response, we propose a novel framework, called Correlated Low-rank Structure (CoLR), which leverages the concept of adjusting lightweight trainable parameters while keeping most parameters frozen. Our approach substantially reduces communication overheads without introducing additional computational burdens. Critically, our framework remains fully compatible with secure aggregation protocols, including the robust use of Homomorphic Encryption. Our approach resulted in a reduction of up to 93.75% in payload size, with only an approximate 8% decrease in recommendation performance across datasets. Code for reproducing our experiments can be found at https://github.com/NNHieu/CoLR-FedRec.