Prevailing AI training infrastructure assumes reverse-mode automatic differentiation over IEEE-754 arithmetic. The memory overhead of training relative to inference, optimizer complexity, and structural degradation of geometric properties through training are consequences of this arithmetic substrate. This paper develops an alternative training architecture grounded in three prior results: the Dimensional Type System and Deterministic Memory Management framework [6], which establishes stack-eligible gradient allocation and exact quire accumulation as design-time verifiable properties; the Program Hypergraph [8], which establishes grade preservation through geometric algebra computations as a type-level invariant; and the b-posit 2026 standard [10], which makes posit arithmetic tractable across hardware targets conventionally considered inference-only. Their composition enables depth-independent training memory bounded to approximately twice the inference footprint, grade-preserving weight updates, and exact gradient accumulation, applicable uniformly to loss-function-optimized and spike-timing-dependent neuromorphic models. We introduce Bayesian distillation, a mechanism by which the latent prior structure of a general-purpose model is extracted through the ADM training regime, resolving the data-scarcity bootstrapping problem for domain-specific training. For deployment, we introduce warm rotation, an operational pattern in which an updated model transitions into an active inference pathway without service interruption, with structural correctness formalized through PHG certificates and signed version records. The result is a class of domain-specific AI systems that are smaller and more precise than general-purpose models, continuously adaptive, verifiably correct with respect to the physical structure of their domains, and initializable from existing models.

翻译：当前主流AI训练体系以IEEE-754算术上的反向模式自动微分为基础。训练相对于推理的内存开销、优化器的复杂性、以及训练过程中几何特性的结构退化，均植根于此算术基板。本文提出一种基于三项前期成果的替代性训练架构：维度类型系统与确定性内存管理框架[6]，该框架将栈可分配梯度与精确四元组累加确立为设计时可验证属性；程序超图[8]，该框架将几何代数计算中的阶数保持性确立为类型级不变量；以及b-posit 2026标准[10]，该标准使posit算术在传统上被视为仅推理型硬件目标上变得可行。三者组合实现了：训练内存深度无关性（约等于推理足迹的两倍）、阶数保持的权重更新、以及精确梯度累加——这些特性可统一应用于损失函数优化模型与脉冲时序依赖神经形态模型。我们提出贝叶斯蒸馏机制，通过ADM训练范式提取通用模型中的隐式先验结构，从而解决领域特定训练的数据匮乏自举问题。在部署层面，我们引入热切换操作模式：更新后的模型可在不中断服务的情况下切换至活跃推理路径，其结构正确性通过PHG证书与签名版本记录进行形式化验证。最终成果是一类比通用模型更小、精度更高的领域特定AI系统，具备持续自适应能力、与领域物理结构保持可验证一致性、且可从现有模型初始化。