We use the notation G= (V,E) to represent unweighted graphs, and G= (V,E,w) for weighted graphs. We use lowercase letters u,v to refer to vertices in V, and given a vertex v, we use dG(v) to refer to its degree in graph G. We use capital letters S,T to represent subsets of vertices, and given a vertex set S V, we use |S|to refer to its cardinality, S:= V \S to refer to its complement, and G[S] to refer to the subgraph of Ginduced by vertex set S. Furthermore, given two disjoint vertex sets S,T, we use wG(S,T):= P Given a graph G = (V,E), we use T to refer to a hierarchical clustering (tree) of the vertex set V, and costG(T) to refer to the cost of this clustering in graph G. Without loss of generality, we restrict our attention to just full binary hierarchical clustering trees, since the optimal tree is binary [20].

Unlike MI, some GEMINIs do not require regularisations when training.

Improving the generalization of deep networks is an important open challenge, particularly in domains without plentiful data. The mixup algorithm improves generalization by linearly interpolating a pair of examples and their corresponding labels. These interpolated examples augment the original training set. Mixup has shown promising results in various classification tasks, but systematic analysis of mixup in regression remains underexplored. Using mixup directly on regression labels can result in arbitrarily incorrect labels.