We explore the possibility of improving probabilistic models in structured prediction.Specifically, we combine the models with constrained decoding approaches in the context of token classification for information extraction.The decoding methods search for constraintsatisfying label-assignments while maximizing the total probability.To do this, we evaluate several existing approaches, as well as propose a novel decoding method called Lazy-k.Our findings demonstrate that constrained decoding approaches can significantly improve the models' performances, especially when using smaller models.The Lazy-k approach allows for more flexibility between decoding time and accuracy.The code for using Lazy-k decoding can be found here https://github.com/ ArthurDevNL/lazyk.

In the paper, we address the important problem of tensor decomposition which can be seen as a generalisation of Singular Value Decomposition for matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated moment matrix problem and we give a new criterion for flat extension of Quasi-Hankel matrices. We connect this criterion to the commutation characterisation of border bases. A new algorithm is described: it applies for general multihomogeneous tensors, extending the approach of J.J. Sylvester on binary forms. An example illustrates the algebraic operations involved in this approach and how the decomposition can be recovered from eigenvector computation.