📄 中文摘要
当前的人工智能训练基础设施假设采用IEEE-754算术的反向模式自动微分。这种算术基础导致了训练相对于推理的内存开销、优化器复杂性以及通过训练导致的几何属性结构退化。研究提出了一种替代训练架构，基于三个先前的研究成果：维度类型系统和确定性内存管理框架，建立了可堆栈的梯度分配和精确的累加作为设计时可验证的属性；程序超图，建立了通过几何代数计算保持等级的类型级不变性；以及b-posit 2026标准。这些成果为构建更高效的AI训练提供了理论基础。
自适应领域模型：贝叶斯演化、温暖旋转与几何和神经形态人工智能的原则性训练
📄 English Summary
Adaptive Domain Models: Bayesian Evolution, Warm Rotation, and Principled Training for Geometric and Neuromorphic AI
The prevailing AI training infrastructure assumes reverse-mode automatic differentiation over IEEE-754 arithmetic, leading to memory overhead during training compared to inference, optimizer complexity, and structural degradation of geometric properties through training. An alternative training architecture is developed based on three prior results: the Dimensional Type System and Deterministic Memory Management framework, which establishes stack-eligible gradient allocation and exact quire accumulation as design-time verifiable properties; the Program Hypergraph, which establishes grade preservation through geometric algebra computations as a type-level invariant; and the b-posit 2026 standard. These results provide a theoretical foundation for building more efficient AI training.