CayleyPy-4: AI-Holography. Towards analogs of holographic string dualities for AI tasks

CayleyPy is an open-source project that uses machine-learning and reinforcement-learning ideas to explore extremely large graphs arising in mathematics and physics. Many core ML tasks—such as prediction, planning, and optimization—can be viewed as path-finding problems on graphs, where complexity is measured by distances, areas, or accumulated costs. In CayleyPy, we study Cayley graphs of groups and develop AI-based methods to estimate diameters, shortest paths, and spectral properties that are otherwise computationally inaccessible.

We introduce a new discretized analogue of holographic string duality, where large graphs are mapped to simpler geometric objects such as polygons and lattice paths. In this dual picture, graph distances and algorithmic complexity correspond to areas under paths, echoing the “complexity = area” principle from theoretical physics. This viewpoint connects graph navigation to Young diagrams, tableaux, and integrable models, leading to concrete mathematical predictions. A simple example comes from machine learning itself: ROC curves are holographically dual to paths in a bubble-sort graph on binary strings. More generally, the duality suggests that hard graph problems can become easier when translated to their geometric counterparts.

We outline how these ideas extend to other graphs, languages, and reinforcement-learning environments. Overall, CayleyPy provides a playground where AI, graph theory, and ideas from string theory meet in a concrete and computational way.