Exponential Family Attention

The self-attention mechanism is the backbone of the transformer neural network underlying most large language models. It can capture complex word patterns and long-range dependencies in natural language. This paper introduces exponential family attention (EFA), a probabilistic generative model that extends self-attention to handle high-dimensional sequence, spatial, or spatial-temporal data of mixed data types, including both discrete and continuous observations. The key idea of EFA is to model each observation conditional on all other existing observations, called the context, whose relevance is learned in a data-driven way via an attention-based latent factor model. In particular, unlike static latent embeddings, EFA uses the self-attention mechanism to capture dynamic interactions in the context, where the relevance of each context observations depends on other observations. We establish an identifiability result and provide a generalization guarantee on excess loss for EFA. Across real-world and synthetic data sets -- including U.S. city temperatures, Instacart shopping baskets, and MovieLens ratings -- we find that EFA consistently outperforms existing models in capturing complex latent structures and reconstructing held-out data.