Transformers are Efficient Compilers, Provably

• URL: http://arxiv.org/abs/2410.14706v1
• Date: Mon, 07 Oct 2024 20:31:13 GMT
• Title: Transformers are Efficient Compilers, Provably
• Authors: Xiyu Zhai, Runlong Zhou, Liao Zhang, Simon Shaolei Du,
• Abstract summary: Transformer-based large language models (LLMs) have demonstrated surprisingly robust performance across a wide range of language-related tasks. In this paper, we take the first steps towards a formal investigation of using transformers as compilers from an expressive power perspective. We introduce a representative programming language, Mini-Husky, which encapsulates key features of modern C-like languages.
• Score: 11.459397066286822
• License:
• 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.

Related papers

• Algorithmic Capabilities of Random Transformers [49.73113518329544]
  We investigate what functions can be learned by randomly transformers in which only the embedding layers are optimized. We find that these random transformers can perform a wide range of meaningful algorithmic tasks. Our results indicate that some algorithmic capabilities are present in transformers even before these models are trained.
  arXiv  Detail & Related papers  (2024-10-06T06:04:23Z)
• Separations in the Representational Capabilities of Transformers and Recurrent Architectures [27.783705012503237]
  We analyze the differences in the representational capabilities of Transformers and RNNs across several tasks of practical relevance. We show that a one-layer Transformer of logarithmic width can perform index lookup, whereas an RNN requires a hidden state of linear size. We also show that a log-size two-layer Transformer can implement the nearest neighbor algorithm in its forward pass.
  arXiv  Detail & Related papers  (2024-06-13T17:31:30Z)
• Transformers meet Neural Algorithmic Reasoners [16.5785372289558]
  We propose a novel approach that combines the Transformer's language understanding with the robustness of graph neural network (GNN)-based neural algorithmic reasoners (NARs) We evaluate our resulting TransNAR model on CLRS-Text, the text-based version of the CLRS-30 benchmark, and demonstrate significant gains over Transformer-only models for algorithmic reasoning.
  arXiv  Detail & Related papers  (2024-06-13T16:42:06Z)
• The Expressive Power of Transformers with Chain of Thought [29.839710738657203]
  In practice, transformers can be improved by allowing them to use a "chain of thought" or "scratchpad" We show that the answer is yes, but the amount of increase depends crucially on the amount of intermediate generation. Our results also imply that linear steps keep transformer decoders within context-sensitive languages.
  arXiv  Detail & Related papers  (2023-10-11T22:35:18Z)
• Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection [88.23337313766353]
  This work first provides a comprehensive statistical theory for transformers to perform ICL. We show that transformers can implement a broad class of standard machine learning algorithms in context. A emphsingle transformer can adaptively select different base ICL algorithms.
  arXiv  Detail & Related papers  (2023-06-07T17:59:31Z)
• Learning Transformer Programs [78.9509560355733]
  We introduce a procedure for training Transformers that are mechanistically interpretable by design. Instead of compiling human-written programs into Transformers, we design a modified Transformer that can be trained using gradient-based optimization. The Transformer Programs can automatically find reasonable solutions, performing on par with standard Transformers of comparable size.
  arXiv  Detail & Related papers  (2023-06-01T20:27:01Z)
• Error Correction Code Transformer [92.10654749898927]
  We propose to extend for the first time the Transformer architecture to the soft decoding of linear codes at arbitrary block lengths. We encode each channel's output dimension to high dimension for better representation of the bits information to be processed separately. The proposed approach demonstrates the extreme power and flexibility of Transformers and outperforms existing state-of-the-art neural decoders by large margins at a fraction of their time complexity.
  arXiv  Detail & Related papers  (2022-03-27T15:25:58Z)
• Causal Transformers Perform Below Chance on Recursive Nested Constructions, Unlike Humans [7.897143833642971]
  We test four different Transformer LMs on two different types of nested constructions. We find that Transformers achieve near-perfect performance on short-range embedded dependencies. On long-range embedded dependencies, Transformers' performance sharply drops below chance level.
  arXiv  Detail & Related papers  (2021-10-14T09:22:17Z)
• Thinking Like Transformers [64.96770952820691]
  We propose a computational model for the transformer-encoder in the form of a programming language. We show how RASP can be used to program solutions to tasks that could conceivably be learned by a Transformer. We provide RASP programs for histograms, sorting, and Dyck-languages.
  arXiv  Detail & Related papers  (2021-06-13T13:04:46Z)
• Addressing Some Limitations of Transformers with Feedback Memory [51.94640029417114]
  Transformers have been successfully applied to sequential, auto-regressive tasks despite being feedforward networks. We propose the Feedback Transformer architecture that exposes all previous representations to all future representations. We demonstrate on a variety of benchmarks in language modeling, machine translation, and reinforcement learning that the increased representation capacity can create small, shallow models with much stronger performance than comparable Transformers.
  arXiv  Detail & Related papers  (2020-02-21T16:37:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.