The Deterministic Horizon: Impossibility Results as Design Specifications for Trustworthy AI Systems

Architectural limits are fundamental, not fixable: The paper proves that transformer models have an accuracy ceiling determined solely by their architecture (layer count and embedding width)—called the "Deterministic Horizon"—that cannot be overcome through more training data, better loss functions, or parameter-efficient fine-tuning methods, measured between 19-31 layers across tested architectures.

These limits are predictable and measurable before deployment: Organizations can compute a model's maximum performance ceiling before deploying it, enabling more honest assessment of what tasks a system can reliably handle and preventing overconfidence in AI capabilities for high-stakes applications like legal documents or clinical notes.

Impossibility results should guide AI design choices: Rather than treating mathematical impossibility theorems as abstract curiosities, the paper argues they should directly inform how we build trustworthy AI systems—essentially using fundamental computational limits as design specifications to set realistic expectations.

Trustworthiness requires acknowledging multiple failure modes: The paper identifies cascading problems across different AI applications: preference learning systems have discontinuous performance jumps under model misspecification, multi-stage retrieval systems need independent verification at each stage, and zero-knowledge verification of neural networks carries substantial computational overhead (110-190x per activation).

Transparency about computational constraints builds trust: By making architectural limitations explicit and measurable, developers can communicate honestly about what their systems can and cannot do, which is essential for responsible deployment in domains like healthcare, law, and finance.