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

Key points

• Optical Circuit Switches (OCS) make inter-pod wiring in AI clusters programmable, posing design questions on wiring choice, symmetry departure, and reconfigurations.1
• Departure from a symmetric Fat-Tree prior $q$ is measured by $\DKL(\cdot \,\|\, q)$.1
• 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 $F{β1} = U + β1^{-1} \DKL(\cdot \,\|\, q)$, we prove well-posedness, monotonic dependence on $β1$, adaptation bounds via Jeffreys divergence, and a symmetry principle for static optimality.1
• 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 $O(\sqrt{ΓC V1 T})$ against the switching-free optimum.1

Sources (1)

• [1]An Information-Geometric Framework for OCS-Reconfigurable Interconnect Topology in Large-Scale AI Clusters
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 18, 10:55 AM

  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.

  Optical Circuit Switches (OCS) make inter-pod wiring in AI clusters programmable, posing design questions on wiring choice, symmetry departure, and reconfigurations.

Extractive summary: sentences quoted from the sources.