{Twisted Poincar\'e Series and Geometric Factorization of Affine Weyl Groups

We study the relation between the alternating product of twisted Poincar'e series of parabolic subgroups of affine Weyl groups and hyperbolic stabilizers of geodesic tubes. Moreover, from such relation, we find a length-preserving factorization of affine Weyl groups of type $\tilde{A}_n$ and $\tilde{C}_n$

Interactive Multi-Head Self-Attention with Linear Complexity

We propose an efficient interactive method for multi-head self-attention via decomposition. For existing methods using multi-head self-attention, the attention operation of each head is computed independently. However, we show that the interactions between cross-heads of the attention matrix enhance the information flow of the attention operation. Considering that the attention matrix of each head can be seen as a feature of networks, it is beneficial to establish connectivity between them to capture interactions better. However, a straightforward approach to capture the interactions between the cross-heads is computationally prohibitive as the complexity grows substantially with the high dimension of an attention matrix. In this work, we propose an effective method to decompose the attention operation into query- and key-less components. This will result in a more manageable size for the attention matrix, specifically for the cross-head interactions. Expensive experimental results show that the proposed cross-head interaction approach performs favorably against existing efficient attention methods and state-of-the-art backbone models