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

Shintaro Yoshizawa

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 $\DKL(\cdot \,\|\, \mathbf{q})$. 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 $F_{β_1} = U + β_1^{-1} \DKL(\cdot \,\|\, \mathbf{q})$, we prove well-posedness, monotonic dependence on $β_1$, adaptation bounds via Jeffreys divergence, and a symmetry principle for static optimality. An entropic proximal-gradient method updates multiplicatively with a $|V|$-dim dual KL projection, achieving linear convergence.For time-varying traffic, a threshold policy yields regret $O(\sqrt{ΓC V_1 T})$ 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…