Learning Randomized Reductions (arxiv.org)

A significant advancement in the field of machine learning has been made with the introduction of Bitween, a novel method for automating the learning of randomized self-reductions (RSRs). RSRs are crucial for developing self-correctors that ensure a function approximates accuracy across all inputs by leveraging correlated random samples. Traditionally, discovering these reductions required intricate manual derivation, but Bitween utilizes a linear regression framework that surpasses established methods like genetic algorithms and mixed-integer programming. This breakthrough not only streamlines the process but enhances the effectiveness of building self-correcting functions. Moreover, the release of Agentic Bitween showcases a neuro-symbolic approach where large language models dynamically identify new query functions for discovering RSR properties, in contrast to the limited fixed query functions used previously. Through testing on the RSR-Bench, which encompasses a diverse suite of 80 scientific and machine learning functions, both Bitween and Agentic Bitween demonstrated superior performance compared to traditional symbolic methods, heralding a new era in automating mathematical function analysis and yielding implications in complexity theory and cryptography. This sets the stage for further exploration and automation in both theoretical and applied AI domains.