Boualem Djehiche: On the asymptotic outcomes of generative AI

Abstract

Starting from a simple deterministic model, we show that the asymptotic outcomes of both shallow and deep neural networks such as those used in BloombergGPT to generate economic time series are exactly the Nash equilibria of a non-potential game. We then analyze deep neural network algorithms that converge to these equilibria. The approach is easily extended to federated deep neural networks between clusters of regional servers and on-device clients. Finally, the variational inequalities behind large language models including encoder-decoder related transformers are established.