Search papers, labs, and topics across Lattice.
This paper introduces Adaptive Domain Models (ADMs), a novel training architecture that leverages deterministic memory management, program hypergraphs, and b-posit arithmetic to overcome limitations of standard reverse-mode autodiff. ADMs achieve depth-independent training memory, grade-preserving weight updates, and exact gradient accumulation for both loss-function-optimized and neuromorphic models. The authors introduce Bayesian distillation for bootstrapping domain-specific training and warm rotation for seamless model updates, resulting in smaller, more precise, and verifiably correct AI systems.
Forget training behemoths: ADMs slash memory overhead to just twice the inference footprint while guaranteeing geometric correctness and continuous adaptation.
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.
