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Rule-State Inference (RSI): A Bayesian Framework for Compliance Monitoring in Rule-Governed Domains

Abdou-Raouf Atarmla

Abstract

Existing machine learning frameworks for compliance monitoring -- Markov Logic Networks, Probabilistic Soft Logic, supervised models -- share a fundamental paradigm: they treat observed data as ground truth and attempt to approximate rules from it. This assumption breaks down in rule-governed domains such as taxation or regulatory compliance, where authoritative rules are known a priori and the true challenge is to infer the latent state of rule activation, compliance, and parametric drift from partial and noisy observations. We propose Rule-State Inference (RSI), a Bayesian framework that inverts this paradigm by encoding regulatory rules as structured priors and casting compliance monitoring as posterior inference over a latent rule-state space S = {(a_i, c_i, delta_i)}, where a_i captures rule activation, c_i models the compliance rate, and delta_i quantifies parametric drift. We prove three theoretical guarantees: (T1) RSI absorbs regulatory changes in O(1) time via a prior ratio correction, independently of dataset size; (T2) the posterior is Bernstein-von Mises consistent, converging to the true rule state as observations accumulate; (T3) mean-field variational inference monotonically maximizes the Evidence Lower BOund (ELBO). We instantiate RSI on the Togolese fiscal system and introduce RSI-Togo-Fiscal-Synthetic v1.0, a benchmark of 2,000 synthetic enterprises grounded in real OTR regulatory rules (2022-2025). Without any labeled training data, RSI achieves F1=0.519 and AUC=0.599, while absorbing regulatory changes in under 1ms versus 683-1082ms for full model retraining -- at least a 600x speedup.

Rule-State Inference (RSI): A Bayesian Framework for Compliance Monitoring in Rule-Governed Domains

Abstract

Existing machine learning frameworks for compliance monitoring -- Markov Logic Networks, Probabilistic Soft Logic, supervised models -- share a fundamental paradigm: they treat observed data as ground truth and attempt to approximate rules from it. This assumption breaks down in rule-governed domains such as taxation or regulatory compliance, where authoritative rules are known a priori and the true challenge is to infer the latent state of rule activation, compliance, and parametric drift from partial and noisy observations. We propose Rule-State Inference (RSI), a Bayesian framework that inverts this paradigm by encoding regulatory rules as structured priors and casting compliance monitoring as posterior inference over a latent rule-state space S = {(a_i, c_i, delta_i)}, where a_i captures rule activation, c_i models the compliance rate, and delta_i quantifies parametric drift. We prove three theoretical guarantees: (T1) RSI absorbs regulatory changes in O(1) time via a prior ratio correction, independently of dataset size; (T2) the posterior is Bernstein-von Mises consistent, converging to the true rule state as observations accumulate; (T3) mean-field variational inference monotonically maximizes the Evidence Lower BOund (ELBO). We instantiate RSI on the Togolese fiscal system and introduce RSI-Togo-Fiscal-Synthetic v1.0, a benchmark of 2,000 synthetic enterprises grounded in real OTR regulatory rules (2022-2025). Without any labeled training data, RSI achieves F1=0.519 and AUC=0.599, while absorbing regulatory changes in under 1ms versus 683-1082ms for full model retraining -- at least a 600x speedup.
Paper Structure (51 sections, 11 theorems, 25 equations, 5 tables, 1 algorithm)

This paper contains 51 sections, 11 theorems, 25 equations, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Probabilistic logic.
  4. Neurosymbolic AI.
  5. Interpretable rule learning.
  6. AI and tax compliance.
  7. Missing data and low-resource learning.
  8. The RSI Framework
  9. Problem Formulation
  10. The Latent Rule-State Space
  11. The Prior $P(\mathbf{S})$: Rules as Structured Priors
  12. The Likelihood $P(\mathbf{D} \mid \mathbf{S})$
  13. Posterior Inference
  14. Mean-Field Variational Inference
  15. Theoretical Guarantees
  16. ...and 36 more sections

Key Result

Theorem 1

For any regulatory update $\mathcal{U}_k$, RSI update cost is $\mathcal{C}^{\mathrm{RSI}}(\mathcal{U}_k) = O(1)$, independently of $|\mathbf{D}|$ and $n$.

Theorems & Definitions (22)

  • Definition 1: Rule-Governed Domain
  • Definition 2: Rule State
  • Definition 3: Regulatory Update
  • Theorem 1: $O(1)$ Adaptability
  • proof
  • Corollary 1.1
  • Theorem 2: BvM Consistency
  • proof : Proof sketch
  • Corollary 2.1: Prior Robustness
  • Theorem 3: Monotone ELBO
  • ...and 12 more