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Structural Enforcement of Statistical Rigor in AI-Driven Discovery: A Functional Architecture

Karen Sargsyan

TL;DR

Problem: AI-Scientist systems generate and test many hypotheses, risking spurious discoveries without guaranteed sequential error control. Approach: a functional, two-level architecture— the Research monad enforcing macro-level sequential statistics and Declarative Scaffolding constraining LLM-generated imperative code at the IO boundary. Contributions: a type-class StatisticalProtocol, a LORD++ instance for online FDR control, a DataContract scaffold and harness, large-scale simulation with $N=2000$ hypotheses and an end-to-end case study, providing defense-in-depth across macro and micro levels. Significance: improves integrity and reliability of automated scientific discovery in hybrid AI-Scientist stacks and provides a foundation for extending to parallel settings using STM.

Abstract

Sequential statistical protocols require meticulous state management and robust error handling -- challenges naturally suited to functional programming. We present a functional architecture for structural enforcement of statistical rigor in automated research systems (AI-Scientists). These LLM-driven systems risk generating spurious discoveries through dynamic hypothesis testing. We introduce the Research monad, a Haskell eDSL that enforces sequential statistical protocols (e.g., Online FDR (false discovery rate) control) using a monad transformer stack. To address risks in hybrid architectures where LLMs generate imperative code, we employ Declarative Scaffolding -- generating rigid harnesses that structurally constrain execution and prevent methodological errors like data leakage. We validate this approach through large-scale simulation (N=2000 hypotheses) and an end-to-end case study, demonstrating essential defense-in-depth for automated science integrity.

Structural Enforcement of Statistical Rigor in AI-Driven Discovery: A Functional Architecture

TL;DR

Problem: AI-Scientist systems generate and test many hypotheses, risking spurious discoveries without guaranteed sequential error control. Approach: a functional, two-level architecture— the Research monad enforcing macro-level sequential statistics and Declarative Scaffolding constraining LLM-generated imperative code at the IO boundary. Contributions: a type-class StatisticalProtocol, a LORD++ instance for online FDR control, a DataContract scaffold and harness, large-scale simulation with hypotheses and an end-to-end case study, providing defense-in-depth across macro and micro levels. Significance: improves integrity and reliability of automated scientific discovery in hybrid AI-Scientist stacks and provides a foundation for extending to parallel settings using STM.

Abstract

Sequential statistical protocols require meticulous state management and robust error handling -- challenges naturally suited to functional programming. We present a functional architecture for structural enforcement of statistical rigor in automated research systems (AI-Scientists). These LLM-driven systems risk generating spurious discoveries through dynamic hypothesis testing. We introduce the Research monad, a Haskell eDSL that enforces sequential statistical protocols (e.g., Online FDR (false discovery rate) control) using a monad transformer stack. To address risks in hybrid architectures where LLMs generate imperative code, we employ Declarative Scaffolding -- generating rigid harnesses that structurally constrain execution and prevent methodological errors like data leakage. We validate this approach through large-scale simulation (N=2000 hypotheses) and an end-to-end case study, demonstrating essential defense-in-depth for automated science integrity.

Paper Structure

This paper contains 19 sections, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Architecture and Challenges
  3. The Hybrid Workflow
  4. The Two Levels of Risk
  5. The Generalized Research Monad (Macro-Level Control)
  6. Abstracting the Protocol
  7. The Monadic Architecture: State and Exceptions
  8. The Guarded Operation: testHypothesis
  9. Declarative Scaffolding (Micro-Level Control)
  10. The Strategy: Standardized Methodology Enforcement
  11. Defining the Contract:
  12. Generating the Scaffold and LLM Adaptation:
  13. Evaluation
  14. Simulation Study: Necessity of FDR Control at Scale
  15. Case Study: End-to-End Architecture Demonstration
  16. ...and 4 more sections

Figures (1)

  • Figure 1: The Hybrid AI-Scientist Architecture. The functional core manages the global statistical state, while the imperative environment executes experiments. The IO boundary represents the critical trust boundary.