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Self-attention can be viewed as message passing on a fully connected graph where each token (node) sends a weighted message to every other token.
A graph models relationships between items using vertices (nodes) and edges (links).
Matrix exponentiation turns repeated linear transitions into fast O(n^{3} log k) computation using exponentiation by squaring.
Matrix exponentiation turns repeated linear transitions into a single fast power of a matrix using exponentiation by squaring.
Prim's algorithm builds a Minimum Spanning Tree (MST) by growing a tree from an arbitrary start vertex, always adding the lightest edge that connects the tree to a new vertex.