Discovering Algorithms with Computational Language Processing

2025-07-03

AI Summary

This work addresses fundamental combinatorial optimization problems—particularly strongly NP-hard instances—and core quantum algorithms (e.g., Grover’s search and QAOA), targeting *instance-specific* algorithm discovery and customization. We propose a novel paradigm termed *computational tokenization*, which models algorithms as syntax-constrained sequences of elementary computational operations, generated directly at the computational (rather than source-code) level. To efficiently explore high-performing algorithmic structures, we integrate Monte Carlo tree search guided by reinforcement learning. Our approach transcends conventional general-purpose algorithm design, enabling fine-grained, instance-level performance optimization. Empirically, we successfully reconstruct and enhance both Grover’s algorithm and QAOA, achieving substantial improvements over state-of-the-art classical heuristics and quantum algorithms across multiple strongly NP-hard benchmarks.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a grammar, enabling the formation of increasingly sophisticated procedures. Our ensemble Monte Carlo tree search (MCTS) guided by reinforcement learning (RL) explores token chaining and drives the creation of new tokens. This methodology rediscovers, improves, and generates new algorithms that substantially outperform existing methods for strongly NP-hard combinatorial optimization problems and foundational quantum computing approaches such as Grover's and Quantum Approximate Optimization Algorithm. Operating at the computational rather than code-generation level, our framework produces algorithms that can be tailored specifically to problem instances, not merely classes.

Problem

• Automating algorithm discovery via token sequences
• Enhancing NP-hard and quantum computing algorithms
• Generating instance-specific algorithms, not just class-wide

Innovation

• Automating algorithm discovery via token sequences
• MCTS and RL guide token chaining exploration
• Generates instance-specific algorithms, not just classes