  Learning using statistical invariants (LUSI) is a new learning paradigm,
which adopts weak convergence mechanism, and can be applied to a wider range of
classification problems. However, the computation cost of invariant matrices in
LUSI is high for large-scale datasets during training. To settle this issue,
this paper introduces a granularity statistical invariant for LUSI, and
develops a new learning paradigm called learning using granularity statistical
invariants (LUGSI). LUGSI employs both strong and weak convergence mechanisms,
taking a perspective of minimizing expected risk. As far as we know, it is the
first time to construct granularity statistical invariants. Compared to LUSI,
the introduction of this new statistical invariant brings two advantages.
Firstly, it enhances the structural information of the data. Secondly, LUGSI
transforms a large invariant matrix into a smaller one by maximizing the
distance between classes, achieving feasibility for large-scale datasets
classification problems and significantly enhancing the training speed of model
operations. Experimental results indicate that LUGSI not only exhibits improved
generalization capabilities but also demonstrates faster training speed,
particularly for large-scale datasets.
