Learning Randomized Reductions and Program Properties

2024-12-24

arXiv.org

AI Summary

This work addresses the challenge of manually deriving Random Self-Reductions (RSRs) for ensuring correctness of numerical programs—a process that is labor-intensive and inherently unscalable. We propose the first automated method for learning RSRs, introducing polynomial-time linear regression as a novel technique for RSR inference. Our approach integrates symbolic analysis with machine learning to establish a theoretically grounded learning framework, and we release RSR-Bench—the first dedicated benchmark for RSR evaluation. The system supports C program analysis and provides both a Python package and a web interface. Experimental evaluation on benchmarks including NLA-DigBench demonstrates that our method significantly outperforms state-of-the-art tools in synthesizing nonlinear invariants. It achieves breakthroughs in scalability, robustness, and sample efficiency—enabling reliable RSR derivation from substantially fewer program executions.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The correctness of computations remains a significant challenge in computer science, with traditional approaches relying on automated testing or formal verification. Self-testing/correcting programs introduce an alternative paradigm, allowing a program to verify and correct its own outputs via randomized reductions, a concept that previously required manual derivation. In this paper, we present Bitween, a method and tool for automated learning of randomized (self)-reductions and program properties in numerical programs. Bitween combines symbolic analysis and machine learning, with a surprising finding: polynomial-time linear regression, a basic optimization method, is not only sufficient but also highly effective for deriving complex randomized self-reductions and program invariants, often outperforming sophisticated mixed-integer linear programming solvers. We establish a theoretical framework for learning these reductions and introduce RSR-Bench, a benchmark suite for evaluating Bitween's capabilities on scientific and machine learning functions. Our empirical results show that Bitween surpasses state-of-the-art tools in scalability, stability, and sample efficiency when evaluated on nonlinear invariant benchmarks like NLA-DigBench. Bitween is open-source as a Python package and accessible via a web interface that supports C language programs.

Problem

• Automating discovery of randomized self-reductions for mathematical functions
• Developing neuro-symbolic approach using LLMs for novel query functions
• Creating benchmark suite for evaluating self-reduction discovery methods

Innovation

• Automated learning of randomized self-reductions for mathematical functions
• Learning framework using linear regression outperforms existing symbolic methods
• Neuro-symbolic approach with LLMs dynamically discovers novel query functions