Prevailing AI training 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 (Haynes 2026), which establishes stack-eligible gradient allocation and exact quire accumulation as design-time verifiable properties; the Program Hypergraph (Haynes 2026), which establishes grade preservation through geometric algebra computations as a type-level invariant; and the b-posit bounded-regime design (Jonnalagadda et al. 2025), 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 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AI训练普遍采用基于IEEE-754算术的反向模式自动微分。训练过程相对于推理的内存开销、优化器的复杂性以及几何属性在训练中的结构性退化，均是这一算术基底的直接后果。本文基于三项前期成果提出了一种替代性训练架构：维度类型系统与确定性内存管理框架（Haynes 2026），该框架将栈级梯度分配和精确quire累加确立为设计时可验证属性；程序超图（Haynes 2026），该框架通过几何代数计算将等级保持确立为类型级不变量；以及b-posit有界域设计（Jonnalagadda等，2025），该设计使得posit算术在传统上被视为仅推理型的硬件目标上变得可行。上述成果的融合实现了与推理内存占用约为两倍的深度无关训练内存、保持等级的权重更新及精确梯度累积，并可统一应用于损失函数优化型与脉冲时序依赖型神经形态模型。我们引入了*贝叶斯蒸馏*机制，通过ADM训练范式提取通用模型的潜在先验结构，从而解决特定领域训练的数据稀缺启动问题。在部署层面，我们提出了*热切换*操作模式——更新后的模型可在不中断服务的情况下过渡到活跃推理路径，并通过PHG证书与签名版本记录实现正确性形式化验证。最终成果是一类比通用模型更小巧、更精确的领域特定AI系统，具备持续自适应能力、针对领域物理结构的可验证正确性，且可从现有模型进行初始化。