Brain Economy-Aligned Graph Transformers

Graph neural networks for brain connectomics treat every connection as topologically equivalent, ignoring the brain-economy trade-off between the metabolic cost of maintaining a connection and the topological value it delivers to the network. We argue that this trade-off is a property of the channel (i.e., edge) between two brain regions, not of the regions themselves, and should therefore shape how regions interact during attention computation rather than being appended as a node feature or auxiliary loss. We introduce the ecospace, a two-dimensional coordinate system that characterizes each brain connection by its economy—the trade-off between connectivity strength and anatomical cost—and uses it to guide how brain regions attend to one another. We further introduce EcoSpace Rotary Encoding (ESRE), an attention mechanism that injects the ecospace dimensions through asymmetric rotations of the query-key subspace, guaranteeing by mathematical identity that the attention score between two brain regions depends on the economy of the edge connecting them. Together, these two contributions form the Brain Graph Transformer with EcoSpace Rotary Encoding (BGT-ESRE). On brain graph classification, BGT-ESRE outperforms classical, general-purpose, and brain-graph-specific baselines by a substantial margin in both accuracy and AUC. Ablations confirm that the rotary mechanism and the brain economy-aligned transformation each contribute independently, and that asymmetric rotary injection is superior to additive bias injection of the same economy measure.