APRM: Learning Binary Function Representations with Radially Ordered Context

Node-level graph representation learning often requires encoding a directed, variable-size neighborhood into a fixed-dimensional representation. We study this problem in binary code similarity detection (BCSD), where compiled instances of the same source-level function are mapped to comparable representations. Compilation can change the target function and its surrounding function call graph (FCG). Therefore, absolute depth and node membership can differ across compilation pairs. However, among source-matched function nodes present in both FCGs, relative radial order and the directions of pairwise ancestor relations are often preserved. We introduce Augmented Predecessor-Radial Moments (APRM), a graph readout conditioned on the root function. APRM combines a normalized root-relative radial coordinate with signed contrasts between each node and its shortest-path predecessors within the same FCG. Across four fixed upstream encoders and four compilation conditions, APRM improves mean Macro Recall@1 from 6.48% to 14.75% on galleries containing 10,000 functions. APRM also outperforms four matched message-passing baselines, with the strongest baseline reaching 12.75% under the same retrieval protocol. On Dataset-1, an external BCSD benchmark introduced by Marcelli et al., APRM improves retrieval without using target data for training, checkpoint selection, or adaptation.