An alternative formulation of attention pooling function in translation

The aim of this paper is to present an alternative formulation of the attention scoring function in translation tasks. Generally speaking, language is deeply structured, and this is reflected in the attention scoring matrix. We exploit this property to define the attention pooling function, taking this aspect into account. In the first chapters, we introduce the attention mechanism in mathematical terms and explain its limitations and alternative formulations. Next, we focus on the experimental session that led to the alternative formulation. Essentially, we guide queries and keys to interact in a specific manner, encoding the distinct roles of attention heads and directing values on where to seek context. In mathematical terms, we can think of this formula as projecting the attention scores matrix, say H, onto the space of band matrices with fixed bandwidth. This convex subspace is clearly finite-dimensional and therefore closed. As a consequence, the projection on this space is well-posed and unique. However, at the price of losing the uniqueness of the projection (i.e., the best approximation for H), we defined a new space consisting of band matrices plus error sparse matrices. We prove that this is a compact subspace which guarantees the existence of a matrix that best approximates H. We conclude the thesis by validating the new formula, namely calculating how well the new formula for attention scores approximates the original one. Additionally, we explore the impact of different parameters such as w (context windows) and num-pos (number of relevant words in a sentence). These analyses provide deeper insights into how languages are processed and translated, revealing nuances in the roles of context and word relevance.