{"ID":6024191,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-08T01:49:45.009310586Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.05448","arxiv_id":"2607.05448","title":"iSTAR: an algebraic-collapse framework for variational reduction in quantum-inspired continuous Ising solvers","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.","short_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 collapse...","url_abs":"https://arxiv.org/abs/2607.05448","url_pdf":"https://arxiv.org/pdf/2607.05448v1","authors":"[\"Bowen Liu\",\"Dongmei Xiao\"]","published":"2026-07-05T02:02:19Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.OC\",\"quant-ph\"]","methods":"[]","has_code":false}