Linear rank preservers of tensor products of rank one matrices

Let $n_1,\ldots,n_k$ be integers larger than or equal to 2. We characterize linear maps $\phi: M_{n_1\cdots n_k}\rightarrow M_{n_1\cdots n_k}$ such that $${\mathrm rank}\,(\phi(A_1\otimes \cdots \otimes A_k))=1\quad\hbox{whenever}\quad{\mathrm rank}\, (A_1\otimes \cdots \otimes A_k)=1 \quad \hbox{for all}\quad A_i \in M_{n_i},\, i = 1,\dots,k.$$ Applying this result, we extend two recent results on linear maps that preserving the rank of special classes of matrices.Comment: 12 page

Incremental Prompting: Episodic Memory Prompt for Lifelong Event Detection

Lifelong event detection aims to incrementally update a model with new event types and data while retaining the capability on previously learned old types. One critical challenge is that the model would catastrophically forget old types when continually trained on new data. In this paper, we introduce Episodic Memory Prompts (EMP) to explicitly preserve the learned task-specific knowledge. Our method adopts continuous prompt for each task and they are optimized to instruct the model prediction and learn event-specific representation. The EMPs learned in previous tasks are carried along with the model in subsequent tasks, and can serve as a memory module that keeps the old knowledge and transferring to new tasks. Experiment results demonstrate the effectiveness of our method. Furthermore, we also conduct a comprehensive analysis of the new and old event types in lifelong learning.Comment: Accepted to COLING'22 Main Conference (Short paper). 9 pages, 2 figures, 3 table