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Operator Calculus for Population-Based Optimization: A Mean-Field Convergence Theory

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arXiv:2606. 14289v1 Announce Type: cross Abstract: Population-based and distributional optimization methods, from evolution strategies and consensus-based optimization to covariance-matrix adaptation and stochastic gradient methods viewed as distributional dynamics, are widely used for nonconvex or black-box problems, yet their convergence analyses remain fragmented across algorithm-specific techniques.

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Authors: Pekka Malo, Lauri Viitasaari, Patrik Nummi, Antti Suominen, Ankur Sinha, Olli Tahvonen
Released: 2026-06-15 (24d ago)
Topic: Related to current project
Relation to my work: Read next because Operator Calculus for Population-Based Optimization: A Mean-Field Convergence Theory overlaps with clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Only continuous soft prefixes hit both EM axes at once on Qwen-2.5-7B-Instruct: discrete prompt searches split between the alignment objective and the distributional objective, and both discretizations of the soft prefix collapse (MODERATE confidence)". Matching terms: class, under, distributional, rate, control, full, position. Source: arxiv stat.ML (Machine Learning).
arXiv: 2606.14289

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