  The recent emergence of new algorithms for permuting models into functionally
equivalent regions of the solution space has shed some light on the complexity
of error surfaces, and some promising properties like mode connectivity.
However, finding the right permutation is challenging, and current optimization
techniques are not differentiable, which makes it difficult to integrate into a
gradient-based optimization, and often leads to sub-optimal solutions. In this
paper, we propose a Sinkhorn re-basin network with the ability to obtain the
transportation plan that better suits a given objective. Unlike the current
state-of-art, our method is differentiable and, therefore, easy to adapt to any
task within the deep learning domain. Furthermore, we show the advantage of our
re-basin method by proposing a new cost function that allows performing
incremental learning by exploiting the linear mode connectivity property. The
benefit of our method is compared against similar approaches from the
literature, under several conditions for both optimal transport finding and
linear mode connectivity. The effectiveness of our continual learning method
based on re-basin is also shown for several common benchmark datasets,
providing experimental results that are competitive with state-of-art results
from the literature.
