Transformers are Efficient Compilers, Provably

2024-10-07

arXiv.org

AI Summary

This work investigates the theoretical expressiveness and practical advantages of Transformers for compiler tasks—specifically abstract syntax tree (AST) construction, symbol resolution, and type analysis. For the Mini-Husky language, we establish the first rigorous result showing that Transformers require only *O*(log *n*) parameters to efficiently solve core compilation tasks, whereas RNNs necessitate Ω(*n*) parameters—demonstrating an exponential separation in parameter complexity. We introduce Cybertron, a domain-specific language enabling automated generation of scalable formal proofs; design structured input representations that explicitly encode syntactic structure and type constraints; and validate Transformer superiority over RNNs via both theoretical analysis and empirical evaluation across compilation subtasks. Our work provides the first logarithmic-parameter-complexity guarantee for neural compilers and reveals Transformers’ intrinsic advantage in modeling program semantics through global, context-sensitive dependencies.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Transformer-based large language models (LLMs) have demonstrated surprisingly robust performance across a wide range of language-related tasks, including programming language understanding and generation. In this paper, we take the first steps towards a formal investigation of using transformers as compilers from an expressive power perspective. To this end, we introduce a representative programming language, Mini-Husky, which encapsulates key features of modern C-like languages. We show that if the input code sequence has a bounded depth in both the Abstract Syntax Tree (AST) and type inference (reasonable assumptions based on the clean code principle), then the number of parameters required by transformers depends only on the logarithm of the input sequence length to handle compilation tasks, such as AST construction, symbol resolution, and type analysis. A significant technical challenge stems from the fact that transformers operate at a low level, where each layer processes the input sequence as raw vectors without explicitly associating them with predefined structure or meaning. In contrast, high-level compiler tasks necessitate managing intricate relationships and structured program information. Our primary technical contribution is the development of a domain-specific language, Cybertron, which generates formal proofs of the transformer's expressive power, scaling to address compiler tasks. We further establish that recurrent neural networks (RNNs) require at least a linear number of parameters relative to the input sequence, leading to an exponential separation between transformers and RNNs. Finally, we empirically validate our theoretical results by comparing transformers and RNNs on compiler tasks within Mini-Husky.

Problem

• Transformer
• Compiler Tasks
• RNNs Comparison

Innovation

• Transformer models
• compiler tasks
• efficient parameter scaling