MRRO

Mechanism

A method of optimizing a non-convex objective by iterative application of a renormalization-group-derived smoothing operator at a finite descending schedule of scales, with warm-starting between scales and a deterministic inverse-renormalization refinement step at the terminal scale that maps the converged coarse-grained coordinate back to the fine-grained continuous manifold by deterministic gradient-based descent without any generative probabilistic sampling.

The unified operator family includes three preferred embodiments under a common scheme: a frequency-domain low-pass cascade variant; a Gaussian convolution variant with a Monte Carlo estimator; and a block-decimation renormalization-group flow variant adapted from spin-lattice physics to continuous-objective optimization.

Prior-art differentiator

Evolutionary metaheuristic baselines (CMA-ES family, Differential Evolution, Particle Swarm) carry covariance updates that are computationally infeasible at problem dimension D greater than approximately one thousand. On the load-bearing phased-array antenna sidelobe minimization benchmark, all four strongest evolutionary baselines under-perform a textbook uniform-spacing baseline across 30 seeds (the Phase 12 negative-evidence record).

Graduated-optimization and scale-space prior art lacks the unified operator family, the deterministic inverse-RG step, and the renormalization-group-theory framework as unifying mathematics. Recent RG-physics-machine-learning constructions apply RG to data distributions or generative diffusion probability spaces; MRRO operates directly on the deterministic objective function.

Empirical validation

The phased-array antenna sidelobe transfer provides a concrete real-world engineering anchor: a statistically significant antenna-array advantage at production scale (N=60 elements) over an AdamW-with-restart baseline. The foundational one-dimensional benchmarks hold strong across Rastrigin-1D, Ackley-1D, Styblinski-Tang-1D, and deceptive multi-minima landscapes. A production-scale continual fine-tuning anchor on a 7B-class open-weights instruction model is honestly disclosed as near-oracle but underpowered at its current sample size.

Counsel posture

Provisional self-filed. Twelve-month conversion and PCT deadline 2027-05-07. Track One Prioritized Examination at non-provisional conversion recommended to capitalize on the favorable USPTO Section 101 environment. PCT geographic scope tailored to satisfy the European Patent Office COMVIK technical-character requirement, emphasizing the empirical hardware metrics as undeniable physical technical effect. Joint-inventor USPTO assignment recordation in progress under 37 CFR Section 3.11.