Safety & GovernanceFebruary 12, 202642 min read

Responsibility-Tiered RAG Output Control: A Mathematical Framework for Gate-Governed Retrieval Accuracy

Why controlling RAG accuracy through responsibility structure outperforms Top-k optimization alone

Many RAG systems optimize retrieval quality primarily through Top-k tuning and embedding similarity. This paper adds a governance-oriented approach: responsibility-tiered gates that adjust validation intensity by risk classification. The framework reports an 82% hallucination-rate reduction on enterprise document corpora while maintaining sub-second response times for low-risk queries.

RAGresponsibility-gatesrisk-tiershallucination-reductionHITLmathematical-models
MathematicsJanuary 22, 202626 min read

The Lagrange Problem of Gate Optimization: Finding the Optimal Point Between Safety and Speed

Constrained optimization of governance gates using Lagrange multipliers and KKT conditions

Every governance gate imposes two costs: the cost of errors it fails to catch (misjudgment cost) and the cost of delays it introduces (latency cost). These costs move in opposite directions. Stronger gates catch more errors but delay more decisions. This paper formulates the tradeoff as a constrained optimization problem, derives optimal gate strength per risk tier using Lagrange multipliers, and provides closed-form solutions under practical assumptions.

optimizationlagrange-multipliersgate-designrisk-tiersKKT-conditionssafety-speed-tradeoff
Safety & GovernanceJanuary 2, 202636 min read

Mathematical Criteria for RiskTier Design: Impact, Irreversibility, and Regulatory Pressure

A principled scoring function T(d) = f(impact, irreversibility, regulation) with rational threshold derivation and domain calibration

Risk tiers in AI governance are often assigned heuristically. This paper proposes a formal scoring function `T(d)` based on three continuous variables: impact scope, irreversibility degree, and regulatory intensity. We derive threshold boundaries from loss-function analysis, characterize optimality under a quadratic loss model, and provide calibration examples for finance, healthcare, and software engineering.

risk-tiersscoring-functionsthreshold-designregulatory-compliancedecision-classificationloss-functions