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 $α$ 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.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Rivera, M. (2026). Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computation. https://omanscience.com/en/articles/beyond-affine-transformations-a-soft-dominance-layer-for-coordinate-wise-neural-computation
MLA 9
Rivera, Mariano. "Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computation." https://omanscience.com/en/articles/beyond-affine-transformations-a-soft-dominance-layer-for-coordinate-wise-neural-computation.
Chicago (author–date)
Rivera, Mariano. 2026. "Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computation." https://omanscience.com/en/articles/beyond-affine-transformations-a-soft-dominance-layer-for-coordinate-wise-neural-computation.
Harvard
Rivera, M. (2026) 'Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computation', Available at: https://omanscience.com/en/articles/beyond-affine-transformations-a-soft-dominance-layer-for-coordinate-wise-neural-computation.
Vancouver
Rivera M. Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computation. https://omanscience.com/en/articles/beyond-affine-transformations-a-soft-dominance-layer-for-coordinate-wise-neural-computation
IEEE
M. Rivera, "Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computation," https://omanscience.com/en/articles/beyond-affine-transformations-a-soft-dominance-layer-for-coordinate-wise-neural-computation.