The model-specific Markov embedding problem for symmetric group-based models

We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix exponential of a rate matrix, we additionally ask that the rate matrix follows the model structure. We provide a characterisation of model embeddable Markov matrices corresponding to symmetric group-based phylogenetic models. In particular, we provide necessary and sufficient conditions in terms of the eigenvalues of symmetric group-based matrices. To showcase our main result on model embeddability, we provide an application to hachimoji models, which are eight-state models for synthetic DNA. Moreover, our main result on model embeddability enables us to compute the volume of the set of model embeddable Markov matrices relative to the volume of other relevant sets of Markov matrices within the model.

Text-based Person Search via Multi-Granularity Embedding Learning

Most existing text-based person search methods highly depend on exploring the corresponding relations between the regions of the image and the words in the sentence. However, these methods correlated image regions and words in the same semantic granularity. It 1) results in irrelevant corresponding relations between image and text, 2) causes an ambiguity embedding problem. In this study, we propose a novel multi-granularity embedding learning model for text-based person search. It generates multi-granularity embeddings of partial person bodies in a coarse-to-fine manner by revisiting the person image at different spatial scales. Specifically, we distill the partial knowledge from image scrips to guide the model to select the semantically relevant words from the text description. It can learn discriminative and modality-invariant visual-textual embeddings. In addition, we integrate the partial embeddings at each granularity and perform multi-granularity image-text matching. Extensive experiments validate the effectiveness of our method, which can achieve new state-of-the-art performance by the learned discriminative partial embeddings.