Mode combinability: Exploring convex combinations of permutation aligned models

Abstract

We explore element-wise convex combinations of two permutation-aligned neural network parameter vectors Θ_A and Θ_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.

Keywords: Deep learning; Linear mode connectivity; Representation learning; Representational similarity.