Adaptive Domain Models: Bayesian Evolution, Warm Rotation, and Principled Training for Geometric and Neuromorphic AI
Summary: arXiv:2603.18104v3 Announce Type: replace
Abstract: 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, 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, 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.
Key Innovations in Adaptive Domain Models
The paper outlines several key innovations in the field of AI training and deployment, which include:
- Dimensional Type System and Deterministic Memory Management: This framework allows for efficient memory allocation and the preservation of geometric properties during training.
- Program Hypergraph: This concept ensures that geometric algebra computations maintain their integrity, supporting reliable model performance.
- b-posit 2026 Standard: By making posit arithmetic usable across different hardware platforms, this standard enhances the flexibility of AI model deployment.
Advantages of Bayesian Distillation and Warm Rotation
The introduction of Bayesian distillation and warm rotation offers several advantages for AI systems:
- Data Scarcity Resolution: Bayesian distillation effectively addresses the challenges of training domain-specific models in environments with limited data.
- Seamless Model Updates: Warm rotation facilitates uninterrupted service during model updates, ensuring that users experience minimal disruption.
- Structural Correctness: The use of PHG certificates and signed version records guarantees that the AI models remain verifiably correct, maintaining their operational integrity.
Conclusion
In conclusion, the advancements outlined in the paper pave the way for a new generation of adaptive domain models that are not only efficient and precise but also capable of continuous improvement. By leveraging Bayesian evolution and warm rotation, these models promise to enhance the landscape of geometric and neuromorphic AI, making them more applicable across various domains.