An Information-Geometric Framework for OCS-Reconfigurable Interconnect Topology in Large-Scale AI Clusters

Optical Circuit Switches (OCS) make inter-pod wiring in AI clusters programmable, posing design questions on wiring choice, symmetry departure, and reconfigurations. We present a unified information-geometric framework to address these issues.A wiring is a point in a probability simplex over circuits within a degree polytope. Departure from a symmetric Fat-Tree prior $\mathbf{q}$ is measured by $\text{DKL}(\cdot \mathrm{\parallel }\mathbf{q})$. The cost $U$ is the smoothed DAG critical-path length, whose gradient equals path marginals of a Gibbs distribution via forward–backward recursion.For free energy $F_{{\beta }_1}=U+{\beta }_1^{-1}\text{DKL}(\cdot \mathrm{\parallel }\mathbf{q})$, we prove well-posedness, monotonic dependence on ${\beta }_1$, adaptation bounds via Jeffreys divergence, and a symmetry principle for static optimality. An entropic proximal-gradient method updates multiplicatively with a $\mathrm{\mid }V\mathrm{\mid }$-dim dual KL projection, achieving linear convergence.For time-varying traffic, a threshold policy yields regret $O(\sqrt{\mathrm{\Gamma }C{V}_{1}T})$ against the switching-free optimum. Traffic changes are detected by a multinomial GLR–CUSUM detector with non-asymptotic false-alarm bounds. Multi-job generalized-mean fairness aligns with $\alpha$-fairness ($\alpha \ge 2$). Experiments on pipeline, data, and MoE workloads validate the framework against integer programming.