  Graph neural networks (GNNs) for link prediction can loosely be divided into
two broad categories. First, \emph{node-wise} architectures pre-compute
individual embeddings for each node that are later combined by a simple decoder
to make predictions. While extremely efficient at inference time (since node
embeddings are only computed once and repeatedly reused), model expressiveness
is limited such that isomorphic nodes contributing to candidate edges may not
be distinguishable, compromising accuracy. In contrast, \emph{edge-wise}
methods rely on the formation of edge-specific subgraph embeddings to enrich
the representation of pair-wise relationships, disambiguating isomorphic nodes
to improve accuracy, but with the cost of increased model complexity. To better
navigate this trade-off, we propose a novel GNN architecture whereby the
\emph{forward pass} explicitly depends on \emph{both} positive (as is typical)
and negative (unique to our approach) edges to inform more flexible, yet still
cheap node-wise embeddings. This is achieved by recasting the embeddings
themselves as minimizers of a forward-pass-specific energy function (distinct
from the actual training loss) that favors separation of positive and negative
samples. As demonstrated by extensive empirical evaluations, the resulting
architecture retains the inference speed of node-wise models, while producing
competitive accuracy with edge-wise alternatives.
