用符号回归找新优化器，25个任务表现超现有方法
Searching the Space of Feed-Forward Neural-Network Weight-Update Rules with Fixed Depth Symbolic Regression
- 固定深度符号表达式搜索优化器更新规则
- 25/30任务优于调优后经典优化器，均方误差降44.47%
- 发现规则融合自适应归一化与非线性变换，适合算法探索者
我们研究符号回归能否发现显式的神经网络权重更新规则，使其在小型符号回归基准上超越标准手工设计的优化器。候选更新规则以常见优化器量（如梯度、动量、自适应梯度和矩估计）为操作数，构建固定深度的符号表达式。在30个基准/神经网络组合中，符号回归在25个案例中找到了优于最佳调参优化器的更新规则，改善案例的总均方误差降低44.47%。发现的规则无统一形式，但多数结合了自适应归一化、类动量项、非线性变换和有理表达式。结果表明符号回归可作为发现紧凑优化器变体的轻量机制，同时凸显大规模验证的必要性。
原文摘要 · Abstract (English)
We investigate whether symbolic regression can discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks. Candidate update rules are represented as fixed-depth symbolic expressions over operands derived from common optimizers, including gradient, momentum, adaptive-gradient, and moment-estimate quantities. Across 30 benchmark/neural network combinations, the symbolic regression procedure found an update rule outperforming the best hyperparameter-tuned established optimizer in 25 cases, with an aggregate MSE reduction of 44.47\% over the improved cases. The discovered rules do not all share a single common symbolic form, but many combine adaptive normalization, momentum-like quantities, nonlinear transformations, and rational expressions. These results suggest that symbolic regression can serve as a lightweight mechanism for discovering compact optimizer variants, while also highlighting the need for larger-scale validation.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。