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：主流AI训练基础设施依赖于基于IEEE-754算术的反向模式自动微分。相对于推理而言，训练带来的内存开销、优化器的复杂度以及训练过程中几何属性的结构性退化，均是这一算术基底的直接后果。本文基于三项前期成果，构建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[6]（在栈上可行梯度分配与精确累加器累积被确立为设计时可验证属性）、程序超图[8]（通过几何代数计算将等级保持性确立为类型级不变量），以及b-posit 2026标准[10]（使posit算术在传统上被视为仅推理适用的各类硬件目标上变得可行）。这些成果的组合实现了训练内存与推理足迹的近似两倍解耦、等级保持的权重更新、以及精确梯度累积，并统一适用于损失函数优化型模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训练体制提取通用模型的潜在先验结构，从而解决了特定领域训练中的数据稀缺自举问题。在部署方面，我们提出了热旋转操作模式，允许更新后的模型在不中断服务的情况下过渡至活跃推理路径，其结构正确性通过PHG证书与签名版本记录得到形式化保证。最终成果是一类特定领域AI系统：其规模较通用模型更小、精度更高、具备持续自适应能力，在领域物理结构层面具备可验证的正确性，且可基于现有模型进行初始化。