Implicit Kernel Attention
This work addresses the need for more flexible and effective attention mechanisms in machine learning models for sequential and graph-structured data, though it is incremental as it builds on existing attention paradigms.
The paper tackles the problem of generalizing attention mechanisms in Transformer and GAT by proposing implicit kernel attention, which replaces manual kernel selection with an implicit kernel, generalizes norms, and extends to structured multi-head attention, resulting in improved performance on classification, translation, and regression tasks.
\textit{Attention} computes the dependency between representations, and it encourages the model to focus on the important selective features. Attention-based models, such as Transformer and graph attention network (GAT), are widely utilized for sequential data and graph-structured data. This paper suggests a new interpretation and generalized structure of the attention in Transformer and GAT. For the attention in Transformer and GAT, we derive that the attention is a product of two parts: 1) the RBF kernel to measure the similarity of two instances and 2) the exponential of $L^{2}$ norm to compute the importance of individual instances. From this decomposition, we generalize the attention in three ways. First, we propose implicit kernel attention with an implicit kernel function instead of manual kernel selection. Second, we generalize $L^{2}$ norm as the $L^{p}$ norm. Third, we extend our attention to structured multi-head attention. Our generalized attention shows better performance on classification, translation, and regression tasks.