发表机构
Centro de Investigación en Matemáticas, A.C.（数学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出软支配层作为仿射变换的替代，通过可微不等式比较实现坐标级计算，初步实验显示其可训练性但准确率低于MLP基线，需进一步验证。
AI 中文摘要
本文对传统神经网络层所基于的仿射变换提出了一种替代方案的初步研究。在所提出的软支配层中，每个输出单元将输入坐标与一个可学习的参考向量进行比较，并聚合平滑的不等式响应。sigmoid松弛使比较可微，而锐度参数α控制其向硬阈值决策的过渡。其目的是检验这一原语的可训练性和直接阈值解释，而非声称替代仿射层。在单次运行的MNIST实验中，观察到的软支配层最高准确率为0.9061（无退火）和0.9173（有退火），而MLP基线为0.9827。这些描述性结果并未确立可靠的配置排名或统计上支持的退火优势。学习到的参考向量表现出空间结构，提供了结构化学习的定性证据。需要重复种子实验和更广泛的数据集来评估鲁棒性和超出概念验证的实际相关性。
英文摘要
This paper presents a preliminary study of an alternative to the affine transformation underlying conventional neural-network layers. In the proposed Soft Dominance Layer, each output unit compares input coordinates with a learnable reference vector and aggregates smooth inequality responses. A sigmoid relaxation makes the comparisons differentiable, while a sharpness parameter $α$ controls their transition toward hard threshold decisions. The aim is to examine the trainability and direct threshold interpretation of this primitive, not to claim a replacement for affine layers. In single-run MNIST experiments, the highest observed Soft Dominance accuracy is $0.9061$ without annealing and $0.9173$ with annealing, compared with $0.9827$ for the MLP baseline. These descriptive results do not establish reliable configuration rankings or a statistically supported annealing benefit. Learned reference vectors exhibit spatial structure, providing qualitative evidence of structured learning. Repeated-seed experiments and broader datasets are required to assess robustness and practical relevance beyond this proof of concept.
Comments14 pages, 4 figures
