Sparse and Continuous Attention Mechanisms
This work addresses the need for more flexible and interpretable attention mechanisms in machine learning, particularly for applications requiring continuous inputs, though it is incremental by building on existing sparse attention methods.
The paper extends sparse attention mechanisms from finite to continuous domains, linking them to Tsallis statistics, and introduces continuous-domain attention with efficient gradient algorithms for alpha in {1,2}. Experiments on tasks like text classification and machine translation demonstrate that continuous attention can attend to intervals and regions, improving model flexibility.
Exponential families are widely used in machine learning; they include many distributions in continuous and discrete domains (e.g., Gaussian, Dirichlet, Poisson, and categorical distributions via the softmax transformation). Distributions in each of these families have fixed support. In contrast, for finite domains, there has been recent work on sparse alternatives to softmax (e.g. sparsemax and alpha-entmax), which have varying support, being able to assign zero probability to irrelevant categories. This paper expands that work in two directions: first, we extend alpha-entmax to continuous domains, revealing a link with Tsallis statistics and deformed exponential families. Second, we introduce continuous-domain attention mechanisms, deriving efficient gradient backpropagation algorithms for alpha in {1,2}. Experiments on attention-based text classification, machine translation, and visual question answering illustrate the use of continuous attention in 1D and 2D, showing that it allows attending to time intervals and compact regions.