A Theoretical Study of (Hyper) Self-Attention through the Lens of Interactions: Representation, Training, Generalization

Self-attention has emerged as a core component of modern neural architectures, yet its theoretical underpinnings remain elusive. In this paper, we study self-attention through the lens of interacting entities, ranging from agents in multi-agent reinforcement learning to alleles in genetic sequences, and show that a single layer linear self-attention can efficiently represent, learn, and generalize functions capturing pairwise interactions, including out-of-distribution scenarios. Our analysis reveals that self-attention acts as a mutual interaction learner under minimal assumptions on the diversity of interaction patterns observed during training, thereby encompassing a wide variety of real-world domains. In addition, we validate our theoretical insights through experiments demonstrating that self-attention learns interaction functions and generalizes across both population distributions and out-of-distribution scenarios. Building on our theories, we introduce HyperFeatureAttention, a novel neural network module designed to learn couplings of different feature-level interactions between entities. Furthermore, we propose HyperAttention, a new module that extends beyond pairwise interactions to capture multi-entity dependencies, such as three-way, four-way, or general n-way interactions.