Generative artificial intelligence (AI) has opened the possibility of automated content production, including coding in software development, which can significantly influence the participation and performance of software developers. To explore this impact, we investigate the role of GitHub Copilot, a generative AI pair programmer, on software development in open-source community, where multiple developers voluntarily collaborate on software projects. Using GitHub's dataset for open-source repositories and a generalized synthetic control method, we find that Copilot significantly enhances project-level productivity by 6.5%. Delving deeper, we dissect the key mechanisms driving this improvement. Our findings reveal a 5.5% increase in individual productivity and a 5.4% increase in participation. However, this is accompanied with a 41.6% increase in integration time, potentially due to higher coordination costs. Interestingly, we also observe the differential effects among developers. We discover that core developers achieve greater project-level productivity gains from using Copilot, benefiting more in terms of individual productivity and participation compared to peripheral developers, plausibly due to their deeper familiarity with software projects. We also find that the increase in project-level productivity is accompanied with no change in code quality. We conclude that AI pair programmers bring benefits to developers to automate and augment their code, but human developers' knowledge of software projects can enhance the benefits. In summary, our research underscores the role of AI pair programmers in impacting project-level productivity within the open-source community and suggests potential implications for the structure of open-source software projects.

We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, they can be a powerful tool for unsupervised representation learning from video or pairs of data. We derive a training algorithm for Spectral Inference Networks that addresses the bias in the gradients due to finite batch size and allows for online learning of multiple eigenfunctions. We show results of training Spectral Inference Networks on problems in quantum mechanics and feature learning for videos on synthetic datasets as well as the Arcade Learning Environment. Our results demonstrate that Spectral Inference Networks accurately recover eigenfunctions of linear operators, can discover interpretable representations from video and find meaningful subgoals in reinforcement learning environments.