arXiv：cs.LG· Mariano Rivera·· 2 天前AI 评分24
超越仿射变换：面向逐坐标神经计算的 Soft Dominance Layer
Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computation
AI 导读
一篇 arXiv 论文提出 Soft Dominance Layer，用可学习参考向量对输入坐标做平滑不等式比较，并以 sigmoid 松弛保证可微、用锐度参数 α 控制向硬阈值决策的过渡。单次 MNIST 实验中，该层最高准确率为无退火 0.9061、有退火 0.9173，MLP 基线为 0.9827。作者称这只是初步研究，不主张替代仿射层，退火收益与配置排序均未获统计支持。
正文
Abstract: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 $\alpha$ 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.
| Comments: | 14 pages, 4 figures |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| MSC classes: | 68T07 |
| ACM classes: | I.2.4; I.2.4 |
| Cite as: | arXiv:2610.00563 [cs.LG] |
| (or arXiv:2610.00563v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.00563 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Mariano Rivera [view email]
[v1]
Wed, 30 Sep 2026 18:38:05 UTC (343 KB)
来源：arXiv：cs.LG · arxiv.org