Kernel Deformed Exponential Families for Sparse Continuous Attention

Alexander Moreno, Supriya Nagesh, Zhenke Wu, Walter Dempsey, James Matthew Rehg

Keywords: kernel methods, attention mechanism, theory, exponential families, deformed exponential families

Abstract: Attention mechanisms take an expectation of a data representation with respect to probability weights. This creates summary statistics that focus on important features. Recently, Martins et al. (2020, 2021) proposed continuous attention mechanisms, focusing on unimodal attention densities from the exponential and deformed exponential families: the latter has sparse support. Farinhas et al. (2021) extended this to use Gaussian mixture attention densities, which are a flexible class with dense support. In this paper, we extend this to two general flexible classes: kernel exponential families and our new sparse counterpart kernel deformed exponential families. Theoretically, we show new existence results for both kernel exponential and deformed exponential families, and that the deformed case has similar approximation capabilities to kernel exponential families. Experiments show that kernel deformed exponential families can attend to non-overlapping intervals of time.

One-sentence Summary: We introduce a new flexible non-parametric density class for use as a continuous attention mechanism and show novel theoretical existence and approximation results for this class.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2111.01222/code)