  We explore element-wise convex combinations of two permutation-aligned neural
network parameter vectors $\Theta_A$ and $\Theta_B$ of size $d$. We conduct
extensive experiments by examining various distributions of such model
combinations parametrized by elements of the hypercube $[0,1]^{d}$ and its
vicinity. Our findings reveal that broad regions of the hypercube form surfaces
of low loss values, indicating that the notion of linear mode connectivity
extends to a more general phenomenon which we call mode combinability. We also
make several novel observations regarding linear mode connectivity and model
re-basin. We demonstrate a transitivity property: two models re-based to a
common third model are also linear mode connected, and a robustness property:
even with significant perturbations of the neuron matchings the resulting
combinations continue to form a working model. Moreover, we analyze the
functional and weight similarity of model combinations and show that such
combinations are non-vacuous in the sense that there are significant functional
differences between the resulting models.
