Softmax注意力的量子路线图：概率单纯形上Softmax注意力的精确玻恩规则类比
A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex
- University of Alabama（阿拉巴马大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出了概率单纯形上Softmax注意力的量子实现方案，将其各组件映射为量子操作，且其代数核心经Lean 4机器验证。
AI中文摘要：
注意力机制是Transformer等众多现代AI模型的基础。在一类注意力被使用的问题中，输入和输出被限定在概率单纯形上，使得所有输出之和为1。在该设定下，Softmax注意力存在精确的逐分量量子实现：注意力分数是振幅编码输入的块编码投影上的Hadamard测试统计量；指数Softmax是由精确双射下的玻恩规则测量生成的余弦平方族的内部，其边界表示有限参数值下带有精确零的稀疏注意力；Softmax温度是重复次数，后选测量轮次精确实现离散化的逆温度；值聚合是确定性的列加载通道，会扩张列随机值矩阵；门控残差是单个辅助量子比特的制备角度，加性恒等式位于混合角π/2处；所有可学习参数均为旋转门角度。该复合层在无限采样次数极限下是精确的，每个注意力分数对应一次测量-重加载步骤；完全相干变体在无限深度极限下通过量子奇异值变换实现ε近似。其代数核心在Lean 4中经过机器验证。
英文摘要：
The attention mechanism forms the foundation of many modern AI models such as the Transformer. In one subclass of problems where attention is used, inputs and outputs are bound to the probability simplex so that all outputs sum to one. In this setting, softmax attention admits an exact, component-by-component quantum realization. Attention scores are Hadamard-test statistics on block-encoded projections of amplitude-encoded inputs. The exponential softmax is the interior of a cosine-squared family generated by Born-rule measurement under an exact bijection, whose boundary expresses sparse attention with exact zeros at finite parameter values. The softmax temperature is a repetition count where post-selected measurement rounds realize discretized inverse temperature exactly. Value aggregation is a deterministic column-loading channel that dilates the column-stochastic value matrix. The gated residual is the preparation angle of a single ancilla, with the additive identity at a mixing angle of π/2. Every learnable parameter is a rotation-gate angle. The composed layer is exact in the infinite-shot limit with one measure-and-reload step per attention score; a fully-coherent variant is ε-approximate via quantum singular value transformation in the infinite depth limit. The algebraic core is machine-checked in Lean 4.
