HuggingFace Daily Papers（社区热门论文）· HuggingFace Daily Papers（社区热门论文）·· 10 天前AI 评分34
不改参数改乘积：面向 Transformer 的结合代数层
AI 导读
研究者提出用结合代数中的稀疏交互表替代 Transformer 投影层的普通矩阵乘法，在物理块大小固定时实现矩阵维度上的二次算术复杂度，并给出适配 GPU 执行的形状约束。
正文
Abstract:Fast matrix multiplication algorithms keep the product fixed and search for a cheaper way to evaluate it. We instead ask whether a Transformer's learned projections can use a different, cheaper product altogether. Building on an associative-algebra construction that replaces ordinary matrix multiplication with a sparser interaction table over the same weight blocks, we construct a family with quadratic arithmetic in the matrix dimension when the physical block size remains fixed, and derive finite-shape constraints for GPU execution. The construction is provably optimal for its bilinear rank by the Alder--Strassen bound and can be realized as row-typed rectangular projections compatible with causal masking and KV-cached decoding. We provide an empirical test of this approach by training two approximately 110M-parameter decoder-only Transformer LMs from the same recipe and 12.3B-token budget, differing only in their feed-forward layer: one uses ordinary dense matrix multiplication and the other uses the associative-algebra product. Across four prompt domains, the algebraic model achieves a 6.2--7.8\% increase in end-to-end generation throughput, while obtaining lower scores on all three reported downstream metrics. We treat these results as a feasibility and trainability check for the proposed approach at small scale, leaving further investigation to future work.
| Comments: | Under review |
| Subjects: | Machine Learning (cs.LG); Performance (cs.PF) |
| Cite as: | arXiv:2609.32814 [cs.LG] |
| (or arXiv:2609.32814v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.32814 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ilya Koziev [view email]
[v1]
Sat, 26 Sep 2026 17:39:58 UTC (129 KB)
来源：HuggingFace Daily Papers（社区热门论文） · arxiv.org