Application of lattice gauge theory to the detection of money laundering

Financial-transaction fraud subjects the global banking industry to daily risk of significant monetary loss, increased operating costs, potential damage to reputation, substantial regulatory challenges, and numerous legal consequences. As the volume and complexity of fraud schemes increases, new artificial intelligence methods have been devised to address the scale of this crime, as well as the need for reliable recognition of new and evolving patterns of fraudulent behavior. In this study we construct a physics-inspired compact U(1) lattice gauge theory (LGT) to identify money laundering, overlaying the lattice onto a graph of financial accounts as nodes and financial transactions as directed edges. Specifically, within our LGT framework, we define a quantum gauge field, a four-vector composed of a c-number compact phase and a Schwinger isospin operator, where the isospin resides on a directed edge. We apply the gauge field to the definition of a bilinear phase operator that serves as the exponential argument of a Hilbert-space link operator for each directed edge. In this way, we define a Wilson line as the product of link operators that correspond to a specific financial transaction path, and we utilize the local gauge-covariant behavior of the Wilson line to ascertain the extent of money laundering along the path. With a line-graph, path-preserving transformation to a new graph, where financial transactions are nodes, we introduce a graph-transformer model that we train to learn the expectation values of the Wilson lines. We apply the learned Wilson lines to path-dependent attention, introducing both a gating coefficient and an attention bias that depend on the expectation value of Wilson lines. We report on the training and inference results of our model, as applied to publicly available synthetic transaction datasets.