$$ \newcommand{\bone}{\mathbf{1}} \newcommand{\bbeta}{\mathbf{\beta}} \newcommand{\bdelta}{\mathbf{\delta}} \newcommand{\bepsilon}{\mathbf{\epsilon}} \newcommand{\blambda}{\mathbf{\lambda}} \newcommand{\bomega}{\mathbf{\omega}} \newcommand{\bpi}{\mathbf{\pi}} \newcommand{\bphi}{\mathbf{\phi}} \newcommand{\bvphi}{\mathbf{\varphi}} \newcommand{\bpsi}{\mathbf{\psi}} \newcommand{\bsigma}{\mathbf{\sigma}} \newcommand{\btheta}{\mathbf{\theta}} \newcommand{\btau}{\mathbf{\tau}} \newcommand{\ba}{\mathbf{a}} \newcommand{\bb}{\mathbf{b}} \newcommand{\bc}{\mathbf{c}} \newcommand{\bd}{\mathbf{d}} \newcommand{\be}{\mathbf{e}} \newcommand{\boldf}{\mathbf{f}} \newcommand{\bg}{\mathbf{g}} \newcommand{\bh}{\mathbf{h}} \newcommand{\bi}{\mathbf{i}} \newcommand{\bj}{\mathbf{j}} \newcommand{\bk}{\mathbf{k}} \newcommand{\bell}{\mathbf{\ell}} \newcommand{\bm}{\mathbf{m}} \newcommand{\bn}{\mathbf{n}} \newcommand{\bo}{\mathbf{o}} \newcommand{\bp}{\mathbf{p}} \newcommand{\bq}{\mathbf{q}} 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2021

  1. Evaluating Large Language Models Trained on Code

    Mark Chen, Jerry Tworek, Heewoo Jun, and 55 more authors
    Jul 2021
    arXiv Bib PDF

    Paper Abstract

    We introduce Codex, a GPT language model fine-tuned on publicly available code from GitHub, and study its Python code-writing capabilities. A distinct production version of Codex powers GitHub Copilot. On HumanEval, a new evaluation set we release to measure functional correctness for synthesizing programs from docstrings, our model solves 28.8% of the problems, while GPT-3 solves 0% and GPT-J solves 11.4%. Furthermore, we find that repeated sampling from the model is a surprisingly effective strategy for producing working solutions to difficult prompts. Using this method, we solve 70.2% of our problems with 100 samples per problem. Careful investigation of our model reveals its limitations, including difficulty with docstrings describing long chains of operations and with binding operations to variables. Finally, we discuss the potential broader impacts of deploying powerful code generation technologies, covering safety, security, and economics.

Three Important Things

1. Codex

Codex is a model fine-tuned from GPT on code publicly available from Github. Given a docstring, it is capable of generating Python code that implements what is described in the docstring.

The authors use the pass@k metric to evaluate the functional correctness of the model on different problems. In the pass@k metric, the model generates \(k\) different code samples for a problem, and \(c\) is the number of outputs that passes all test cases for that problem. They then use the following estimator:

\[pass@k \coloneqq \mathbb{E}_{\text{Problems}} \left[ 1 - \frac{\binom{n-c}{k}}{\binom{n}{k}} \right].\]

They showed that Codex performed better than GPT on their own HumanEval dataset. The HumanEval dataset is their own newly-developed dataset of problems and solutions, to avoid testing on problems that the model may have already seen in training.

2. Codex-S

To further improve performance, they applied supervised fine-tuning on Codex to obtain Codex-S. The data used for fine-tuning came from two sources:

  1. Problems from competitive programming and interview preparation websites, complete with test cases
  2. Problems obtained from continuous integration setups in open-source projects. This is achieved by profiling the inputs and outputs of functions called during the integration tests, and collecting them.

3. Docstring Generation

The authors also consider the reverse problem of generating docstrings from a piece of code. This helps to improve the explainability of the code generated and helps with AI safety. This was trained by grading the sample docstrings manually by hand, and training was therefore limited in scale with only 10 samples per problem. This yielded a pass rate for docstring generation that was comparable to the pass rate for code generation by Codex-S.

The authors also experimented with choosing the code sample generated by Codex-S that maximizes the back-translation probability as evaluated by Codex-D, but this performed worse than just using the log-probabilities of Codex-S in the original setting.

Most Glaring Deficiency

Major limitations of Codex include remembering variable binding, and docstrings with long chains of operations. The former could possibly be rectified with a static analysis framework with feedback in a RLHF-manner, which helps to resolve many issues with code that almost compiles. However, approaches to resolve either of them were neither discussed nor attempted.

Conclusions for Future Work

Language models can also be successfully adapted to code generation. While the technology is nascent, it is very promising and there remains much future work to be done to improve on many of its most glaring limitations.

The many societal and economic considerations mentioned in the paper are also worth keeping in mind when making use of such technologies, such as the bias towards using popular libraries suggested by Codex, and its tendency to suggest weak security parameters and insecure code that exist in its training data.

Written 2023