arXiv subjects

Weixi Chen

Publications and source records attributed to Weixi Chen.

3 recordsLinked to original sources

arXiv2025

Eventually constant maps for two sets and nilpotent pairs

We give a bijective correspondence between the number of nilpotent matrices over a Boolean semiring and the number of directed acyclic graphs on ordered vertices. We then enumerate pairs of maps between two finite sets whose composites are eventually constant by forming a bijection that relates a pair of such maps with a spanning tree in a complete bipartite graph, and an edge of said tree. This generalizes the main principle of A. Joyal's proof of Cayley's formula. Finally, we generalize T. Leinster's work by considering a pair of finite-dimensional vector spaces and show a bijectivity between a nilpotent pair of maps and a balanced vector with the hom spaces between them. This leads us to an elegant formula for the number of nilpotent pairs.

math.CO↗

arXiv2025

Pairs of eventually constant maps and nilpotent pairs

Tom Leinster gave a bijective correspondence between the set of operators on a finite-dimensional vector space $V$ and the set of pairs consisting of a nilpotent operator and a vector in $V$. Over a finite field this bijection implies that the probability that an operator be nilpotent is the reciprocal of the number of vectors in $V$. We generalize this correspondence to pairs of operators between pairs of vector spaces and determine the probability that a random pair of operators be nilpotent. We also determine the set-theoretical counterpart of this construction and compute the number of eventually constant pairs of maps between two finite sets, closely related to the number of spanning trees in a complete bipartite graph.

math.RT↗

arXiv2025

Protecting Copyright of Medical Pre-trained Language Models: Training-Free Backdoor Model Watermarking

With the advancement of intelligent healthcare, medical pre-trained language models (Med-PLMs) have emerged and demonstrated significant effectiveness in downstream medical tasks. While these models are valuable assets, they are vulnerable to misuse and theft, requiring copyright protection. However, existing watermarking methods for pre-trained language models (PLMs) cannot be directly applied to Med-PLMs due to domain-task mismatch and inefficient watermark embedding. To fill this gap, we propose the first training-free backdoor model watermarking for Med-PLMs. Our method employs low-frequency words as triggers, embedding the watermark by replacing their embeddings in the model's word embedding layer with those of specific medical terms. The watermarked Med-PLMs produce the same output for triggers as for the corresponding specified medical terms. We leverage this unique mapping to design tailored watermark extraction schemes for different downstream tasks, thereby addressing the challenge of domain-task mismatch in previous methods. Experiments demonstrate superior effectiveness of our watermarking method across medical downstream tasks. Moreover, the method exhibits robustness against model extraction, pruning, fusion-based backdoor removal attacks, while maintaining high efficiency with 10-second watermark embedding.

cs.LG↗