Neural network pruning can be formulated as a combinatorial optimization problem, yet most existing approaches rely on greedy heuristics that ignore complex interactions between filters. Formal optimization methods such as Quadratic Unconstrained Binary Optimization (QUBO) provide a principled alternative but have so far underperformed due to oversimplified objective formulations based on metrics like the L1-norm. In this work, we propose a unified Hybrid QUBO framework that bridges heuristic importance estimation with global combinatorial optimization. Our formulation integrates gradient-aware sensitivity metrics - specifically first-order Taylor and second-order Fisher information - into the linear term, while utilizing data-driven activation similarity in the quadratic term. This allows the QUBO objective to jointly capture individual filter relevance and inter-filter functional redundancy. We further introduce a dynamic capacity-driven search to strictly enforce target sparsity without distorting the optimization landscape. Finally, we employ a two-stage pipeline featuring a Tensor-Train (TT) Refinement stage - a gradient-free optimizer that fine-tunes the QUBO-derived solution directly against the true evaluation metric. Experiments on the SIDD image denoising dataset demonstrate that the proposed Hybrid QUBO significantly outperforms both greedy Taylor pruning and traditional L1-based QUBO, with TT Refinement providing further consistent gains at appropriate combinatorial scales. This highlights the potential of hybrid combinatorial formulations for robust, scalable, and interpretable neural network compression.

翻译：神经网络剪枝可被形式化为组合优化问题，但现有方法大多依赖忽略滤波器间复杂交互的贪婪启发式算法。二次无约束二元优化（QUBO）等正式优化方法提供了原则性替代方案，但由于采用基于L1范数等指标的过度简化目标函数，其表现迄今欠佳。本文提出统一的混合QUBO框架，将启发式重要性估计与全局组合优化相衔接。该框架在线性项中整合了梯度感知灵敏度指标（具体为一阶泰勒展开与二阶Fisher信息），同时在二次项中引入数据驱动的激活相似性，使QUBO目标能同时捕捉单个滤波器重要性与滤波器间功能冗余。我们进一步引入动态容量驱动搜索机制，在不扭曲优化景观的前提下严格实现目标稀疏度。最终采用包含张量列（TT）精炼阶段的两阶段流水线——该梯度无关优化器可直接依据真实评估指标微调QUBO求解结果。在SIDD图像去噪数据集上的实验表明，所提出的混合QUBO方法显著优于贪婪泰勒剪枝与传统L1基QUBO方法，而TT精炼方法在适当组合尺度下能提供持续增益。这彰显了混合组合公式在实现稳健、可扩展且可解释的神经网络压缩中的潜力。