The Deterministic Horizon: Impossibility Results as Design Specifications for Trustworthy AI Systems
arXiv:2605.23024v1 Announce Type: cross Abstract: Large language models now write software, draft legal documents, and produce clinical notes, yet fundamental limits, from Turing and Arrow to the No Free Lunch theorems, shape what computation can do. This thesis turns such impossibility results from curiosities into design rules. Its flagship result proves an accuracy ceiling set by architecture alone: past a critical reasoning depth, no amount of training moves it, at any adapter rank, sample size, or loss function. Computable before deployment from layer count and embedding width, this Deter
This research emerges as AI models become pervasive in critical applications, making fundamental limitations a pressing concern for ethical and reliable deployment.
It fundamentally re-frames impossibility results as critical design specifications, offering pre-deployment computability of AI accuracy ceilings based purely on architecture.
AI development shifts from an 'unlimited scaling' mindset to one bounded by architectural constraints, enabling proactive design for trustworthy systems rather than reactive problem-solving.
- · AI ethics and safety researchers
- · Developers of specialized AI
- · Regulators and policy makers
- · Users of critical AI applications
- · AI firms prioritizing scale over architectural understanding
- · Researchers ignoring fundamental limits
- · General-purpose AI over-promisers
Architectural design becomes a more critical and informed phase in AI system development, with early-stage limitation analysis.
This framework could lead to the development of 'certifiably honest' or 'provably limited' AI systems, fostering trust in specific domains.
It might influence hardware design, with specialized architectures being developed to optimize for specific reasoning depths and known accuracy ceilings.
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Read at arXiv cs.LG