← 研踪 PaperTrailarXiv:2605.12326 · v4
Black-Box Optimization of Mixed Binary-Continuous Variables: Challenges and Opportunities in Evolutionary Model Merging
首次提交 2026-05-13 00:08
版本更新 2026-11-12 13:51
雷达观测 2026-11-13 14:16
摘要
Model merging has emerged as a cost-effective paradigm for combining capabilities of multiple large language models (LLMs) without additional training. Among existing approaches, Data Flow Space (DFS) merging operates by selectively activating parameter groups across model layers, offering greater flexibility than naive parameter averaging. However, the optimization challenges underlying DFS merging remain poorly understood. In this paper, we formally characterize the DFS merging problem as a mixed binary-continuous black-box optimization problem, identifying three fundamental challenges: (1) mixed binary-continuous variable types, (2) high-dimensional search spaces with up to 291 parameter groups, and (3) conditional variable dependencies corresponding to Type-I interaction as characterized by Akimoto et al. [1]. We empirically evaluate seven merging methods on Mistral-7B models across official GSM8K (1,319 questions) and MMLU (14,042 questions, 57 subjects) benchmarks. Our structured approach achieves a 49.5% reduction in effective search space. Results reveal that all tested merging methods fail to surpass the stronger source model on official benchmarks, with TIES (13.72%) and DELLA (4.12%) performing catastrophically on GSM8K. Notably, DELLA scores below even the base model (6.67%), demonstrating that standard parameter space methods fail when merging base and instruction-tuned models. These findings directly validate the difficulty of the Type-I interaction structure we identify, and motivate the application of algorithms specifically designed for this challenge such as the concurrent IGBD work of Ong et al. [2].
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v4 · 2026-11-12 13:51 · 最新观测版本
Black-Box Optimization of Mixed Binary-Continuous Variables: Challenges and Opportunities in Evolutionary Model Merging
Model merging has emerged as a cost-effective paradigm for combining capabilities of multiple large language models (LLMs) without additional training. Among existing approaches, Data Flow Space (DFS) merging operates by selectively activating parameter groups across model layers, offering greater flexibility than naive parameter averaging. However, the optimization challenges underlying DFS merging remain poorly understood. In this paper, we formally characterize the DFS merging problem as a mixed binary-continuous black-box optimization problem, identifying three fundamental challenges: (1) mixed binary-continuous variable types, (2) high-dimensional search spaces with up to 291 parameter groups, and (3) conditional variable dependencies corresponding to Type-I interaction as characterized by Akimoto et al. [1]. We empirically evaluate seven merging methods on Mistral-7B models across official GSM8K (1,319 questions) and MMLU (14,042 questions, 57 subjects) benchmarks. Our structured approach achieves a 49.5% reduction in effective search space. Results reveal that all tested merging methods fail to surpass the stronger source model on official benchmarks, with TIES (13.72%) and DELLA (4.12%) performing catastrophically on GSM8K. Notably, DELLA scores below even the base model (6.67%), demonstrating that standard parameter space methods fail when merging base and instruction-tuned models. These findings directly validate the difficulty of the Type-I interaction structure we identify, and motivate the application of algorithms specifically designed for this challenge such as the concurrent IGBD work of Ong et al. [2].
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