Realizing Common Random Numbers: Event-Keyed Hashing for Causally Valid Stochastic Models

2026-03-10

AI Summary

This work addresses a critical issue in counterfactual simulation: traditional state-based pseudorandom number generators (PRNGs) break the correspondence between events and their associated random numbers when interventions alter execution paths, leading to causal inconsistencies in counterfactual comparisons. To resolve this, the authors propose an event-keyed hashing mechanism that integrates counter-based PRNGs—such as Philox or Threefry—with unique event identifiers. This approach decouples random number generation from execution order and explicitly binds stochasticity to the modeled events themselves. By doing so, it restores the stable exogenous structure required by structural causal models, enabling causally consistent paired counterfactual simulations. The method effectively mitigates variance control failure and bias in causal inference caused by changes in simulation execution paths.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Agent-based models (ABMs) are widely used to estimate causal treatment effects via paired counterfactual simulation. A standard variance reduction technique is common random numbers (CRNs), which couples replicates across intervention scenarios by sharing the same random inputs. In practice, CRNs are implemented by reusing the same base seed, but this relies on a critical assumption: that the same draw index corresponds to the same modeled event across scenarios. Stateful pseudorandom number generators (PRNGs) violate this assumption whenever interventions alter the simulation's execution path, because any change in control flow shifts the draw index used for all downstream events. We argue that this execution-path-dependent draw indexing is not only a variance-reduction nuisance, but represents a fundamental mismatch between the scientific causal structure ABMs are intended to encode and the program-level causal structure induced by stateful PRNG implementations. Formalizing this through the lens of structural causal models (SCMs), we show that standard PRNG practices yield causally incoherent paired counterfactual comparisons even when the mechanistic specification is otherwise sound. We show that a remedy is to combine counter-based random number generators (e.g., Philox/Threefry) with event identifiers. This decouples random number generation from simulation execution order by making random draws explicit functions of the particular modeled event that called them, restoring the stable event-indexed exogenous structure assumed by SCMs.

Problem

• common random numbers
• agent-based models
• causal inference
• pseudorandom number generators
• counterfactual simulation

Innovation

• Common Random Numbers
• Counterfactual Simulation
• Structural Causal Models
• Counter-based PRNGs
• Event-Keyed Hashing