iSTAR: an algebraic-collapse framework for variational reduction in quantum-inspired continuous Ising solvers

• URL: http://arxiv.org/abs/2607.05448v1
• Date: Sun, 05 Jul 2026 02:02:19 GMT
• Title: iSTAR: an algebraic-collapse framework for variational reduction in quantum-inspired continuous Ising solvers
• Abstract summary: Continuous Ising solvers embed a discrete optimization problem into a continuous dynamical system and recover the spin configuration by sign readout.<n>We show that this cost is not intrinsic; during late-stage simulated bifurcation the trajectory collapses onto a lower-dimensional active subspace.<n>An online certified implementation on the G-set benchmark preserves the same-seed baseline in all runs and removes on average 64.4% of the dense interaction work.
• Score: 0.9704960686964833
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Continuous Ising solvers embed a discrete optimization problem into a continuous dynamical system and recover the spin configuration by sign readout, but dense interaction evaluation gives an $O(N^2)$-per-step cost. We show that this cost is not intrinsic: during late-stage simulated bifurcation the trajectory collapses onto a lower-dimensional active subspace, and saturated coordinates can be eliminated exactly by a variational frozen-set identity whose couplings fold into an induced field on the unresolved subsystem. We prove large-parameter recovery for the external-field quartic model, the hard-box limit of ballistic confinement, and a robust-margin freezing criterion. The resulting algorithm, iSTAR (Ising Stable-set Tail-Aware Reduction), exploits this collapse by detecting stabilized coordinates and continuing only on the active tail. An online certified implementation on the G-set benchmark preserves the same-seed baseline in all runs and removes on average 64.4% of the dense interaction work.

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