# Adaptive Domain Models: Bayesian Evolution, Warm Rotation, and Principled Training for Geometric and Neuromorphic AI

arXiv: https://arxiv.org/abs/2603.18104 · HTML: https://mlsanity.com/paper/2603.18104/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [BitNet: Scaling 1-bit Transformers for Large Language Models](https://mlsanity.com/paper/2310.11453/) (2023)
- [Gradients without Backpropagation](https://mlsanity.com/paper/2202.08587/) (2022)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Bayesian Teaching Enables Probabilistic Reasoning in Large Language Models](https://mlsanity.com/paper/2503.17523/) (2025)
- [Clifford-Steerable Convolutional Neural Networks](https://mlsanity.com/paper/2402.14730/) (2024)
- [Beyond Backpropagation: Optimization with Multi-Tangent Forward Gradients](https://mlsanity.com/paper/2410.17764/) (2024)
- [Closing the Gap Between Float and Posit Hardware Efficiency](https://mlsanity.com/paper/2603.01615/) (2026)
- [HIF: The hypergraph interchange format for higher-order networks](https://mlsanity.com/paper/2507.11520/) (2025)
- [Dimensional Type Systems and Deterministic Memory Management: Design-Time Semantic Preservation in Native Compilation](https://mlsanity.com/paper/2603.16437/) (2026)
- [WAMI: Compilation to WebAssembly through MLIR without Losing Abstraction](https://mlsanity.com/paper/2506.16048/) (2025)
- [Clean up your Mesh! Part 1: Plane and simplex](https://mlsanity.com/paper/2511.08058/) (2025)

## Built on by (most cited first, 1 of 1)

- [Decidable By Construction: Design-Time Verification for Truly Fearless Systems](https://mlsanity.com/paper/2603.25414/) (2026)

## Abstract (arXiv)

Transformer-based large language models have become a prominent focus of machine learning. We develop adaptive domain models to supply domain-specific predictions and checks within language-model pipelines, as well as to serve direct machine automation efficiently. Their predictions can inform generation, while declared constraints and error bounds support checks on the calculations underlying proposed responses and actions. These feedforward and feedback paths aim to reduce domain errors while supporting use cases such as constraint solving for machine processes as well as preserving accuracy in a language model's conversational setting. Physical dimensions and geometric support restrict admissible computation, while a probability model expresses uncertainty. Our type and program hypergraph work connects these relationships to numerical and deployment obligations. We derive a natural-gradient calculation over forward tangent directions using a declared program metric, with a calibration example and a bound separating metric, derivative and solve errors. Forward differentiation and posit accumulation expose complementary resource and error tradeoffs. Our worked linear-Gaussian update connects posterior computation to error and a distribution-shift decision. Recent results from Urschel bound elimination growth probabilistically under distinct Gaussian-input and random-preconditioning hypotheses. Our unique approach to warm rotation binds candidate parameters to their numerical evidence and destination while each request observes a coherent model and state. We propose Bayesian distillation as a source of prior information. Our architecture offers a route to domain computations with explicit guarantees that can guide automated decisions and model responses. We specify experiments to evaluate prediction quality, domain errors across conversational turns, and total resource cost.