Hyper-Adaptive Momentum Dynamics for Native Cubic Portfolio Optimization: Avoiding Quadratization Distortion in Higher-Order Cardinality-Constrained Search

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The paper addresses portfolio optimization with cardinality constraints and higher-order (cubic) sector co-movement terms, which are relevant to quantitative portfolio construction. However, the contribution is primarily methodological (native vs. surrogate optimization) rather than directly producing trading signals or strategies. The cubic interaction modeling of three-way sector co-movement is relevant to realistic portfolio risk modeling. The 60-second CPU budget constraint makes it applicable to near-real-time portfolio rebalancing. The work is more relevant to portfolio construction and risk management than to high-frequency trading or signal generation.

The HAMD pipeline involves four distinct stages (continuous Hamiltonian dynamics with HVP, exact top-K projection, vectorized K-swap local search, and ILS with 2-pair perturbations). The continuous phase requires analytical gradient and Hessian-vector product computation for cubic terms, bifurcation potential with time-varying ramp, transverse geometric force, and damped-elastic reflection boundary handling. The K-swap polish requires evaluating K(n-K) swap moves simultaneously. The Rosenberg quadratization for baselines adds complexity. However, the code is publicly available and the mathematical formulations are explicitly provided. CPU-only implementation reduces hardware requirements but increases wall-clock time for large instances.

Code and benchmark instance files are publicly available on GitHub. Deterministic instance generation from seeds is described. CPU-only computation ensures hardware reproducibility. However, scaling results at n≥300 use single seed (seed 42) only, limiting statistical confidence. The multi-seed study is restricted to n=200. Fixed hyperparameters (α_cubic=4.0, n_sectors=10, λ_R=10.0) are disclosed. A λ_K sensitivity study is included. The repository is noncommercial-use only.