The FE Algorithm: Strategic Elimination with Paradox Retention

Background: Protein folding remains one of computational biology's grand challenges, with the search space growing exponentially with sequence length. ⁵Monte Carlo methods have dominated stochastic optimization since 1946, but struggle with the rugged energy landscapes characteristic of protein folding problems. ⁶Methods: We introduce the Forgetting Engine (FE), a novel optimization algorithm that treats elimination as an active computational primitive rather than a limitation. ⁷FE strategically eliminates the worst-performing 30% of candidate solutions each generation while paradoxically retaining a small subset of these "contradictory" states that show structural promise despite high energy. ⁸We validated FE against standard Monte Carlo (MC) methods using the 3D hydrophobic-polar (HP) lattice model with a 20-residue test sequence (HPHPHPHΗΡΗΗΗΡHPPPHPH) across 4,000 independent trials. ⁹Results: FE achieved a 25.4% success rate compared to MC's 5.5%, representing a 362% improvement (4.62-fold increase). ¹⁰This superiority was statistically overwhelming ($p<10^{-12},$ Cohen's d = 1.056, 99% confidence intervals non-overlapping). ¹¹FE also achieved 19.5% better mean energy (-8.408 vs -7.037) and 12.8% lower standard deviation. ¹²Mechanistic analysis revealed that paradox retention was active in 100% of FE trials (mean 15 retentions per trial) and correlated with improved energy optimization ($r=-0.087$, $p=0.0001$). ¹³Conclusions: The Forgetting Engine represents a paradigm shift in optimization by making "forgetting" an active tool rather than a limitation. ¹⁴The 362% improvement over Monte Carlo, combined with pharmaceutical-grade statistical validation ($p<10^{-12}$), establishes FE as a transformative approach for protein folding and potentially other NP-hard optimization problems. ¹⁵Our pre-registered protocol and fixed random seeds ensure full reproducibility.