Learning Randomized Reductions

2024-11-12 · Source: cs.SE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Software Development & Engineering, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

Bitween, a method and tool developed in 2018, automates the learning of randomized (self)-reductions and program properties in numerical programs. It combines symbolic analysis with machine learning, notably demonstrating that polynomial-time linear regression is highly effective for deriving complex randomized self-reductions and program invariants, often surpassing sophisticated mixed-integer linear programming solvers. Bitween establishes a theoretical framework for these reductions and introduces RSR-Bench, a benchmark suite. Empirical results show Bitween outperforms state-of-the-art tools like Dig and SymInfer in scalability, stability, and sample efficiency, particularly on nonlinear invariant benchmarks such as NLA-DigBench. The tool is open-source as a Python package and offers a web interface supporting C language programs.

Key takeaway

For Research Scientists or Machine Learning Engineers focused on program correctness and verification, Bitween offers a powerful, automated approach to discovering randomized self-reductions and program invariants. You should explore its linear regression-based methodology, as it demonstrates superior scalability and efficiency compared to traditional solvers. Consider integrating Bitween into your verification workflows or leveraging its principles to enhance the robustness and self-correction capabilities of your numerical programs.

Key insights

Simple linear regression can effectively automate the discovery of complex randomized self-reductions and program invariants.

Principles

• Randomized self-reductions enable programs to verify and correct their own outputs.
• Polynomial-time linear regression can outperform complex MILP solvers for reduction learning.
• Loop invariants are crucial for formal program verification tools.

Method

Bitween collects samples, constructs linear models by treating nonlinear terms as constants, iteratively refines models by eliminating irrelevant targets, and refines coefficients using best rational approximation before validation.

In practice

• Automate generation of self-reductions for numerical programs.
• Infer loop invariants and post-conditions for program verification.
• Reduce computation costs for functions like sigmoid in weak devices.

Topics

• Randomized Self-Reductions
• Program Verification
• Linear Regression
• Loop Invariants
• Numerical Programs
• Automated Learning

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.SE updates on arXiv.org.