How a Neural Network Learned Its Own Fraud Rules: A Neuro-Symbolic AI Experiment
Most neuro-symbolic systems inject rules written by humans. But what if a neural network could discover those rules itself?
In this experiment, a hybrid neural network was extended with a differentiable rule-learning module that automatically extracts IF-THEN fraud rules during training. The model was tested on the Kaggle Credit Card Fraud dataset, which has a fraud rate of 0.17%. The model learned interpretable rules such as:
IF V14 < −1.5σ AND V4 > +0.5σ → Fraud
Here, σ denotes the feature standard deviation after normalization. The rule learner achieved a ROC-AUC of 0.933 ± 0.029, while maintaining 99.3% fidelity to the neural network’s predictions.
Most interestingly, the model independently rediscovered V14 — a feature long known by analysts to correlate strongly with fraud — without being instructed to look for it.
What the Model Discovered
This section outlines the findings after up to 80 epochs of training. The rule learner produced clear rules in two seeds:
- Seed 42 — Cleanest Rule (5 conditions, conf=0.95)
Learned Fraud Rule: IF V14 < −1.5σ AND V4 > +0.5σ AND V12 < −0.9σ AND V11 > +0.5σ AND V10 < −0.8σ THEN FRAUD - Seed 7 — Complementary Rule (8 conditions, conf=0.74)
Learned Fraud Rule: IF V14 < −1.6σ AND V12 < −1.3σ AND V4 > +0.3σ AND V11 > +0.5σ AND V10 < −1.0σ AND V3 < −0.8σ AND V17 < −1.5σ AND V16 < −1.0σ THEN FRAUD
In both cases, low values of V14 sit at the heart of the logic — a striking convergence given zero prior guidance.
From Injected Rules to Learned Rules — Why It Matters
Every fraud model has a decision boundary. Fraud teams, however, operate using rules. The gap between them—what the model learned and what analysts can read, audit, and defend to a regulator—is critical for compliance.
Hand-coded rules encode existing knowledge, which works well when fraud patterns are stable. However, when fraud patterns shift or features are anonymized, it becomes essential for the model to surface signals that haven’t been previously identified.
The Architecture: Three Learnable Pieces
The architecture keeps a standard neural network intact while adding a second path that learns symbolic rules explaining the network’s decisions. The two paths run in parallel:
- Learnable Discretizer: Converts continuous features into binary inputs using a soft sigmoid threshold.
- Rule Learner Layer: Produces rules as weighted combinations of binarized features.
- Temperature Annealing: Controls the learning process, allowing rules to crystallize into readable formats.
Three-Part Loss: Detection + Consistency + Sparsity
The full training objective includes:
- L_BCE: Weighted Binary Cross-Entropy to focus on fraud samples.
- L_consistency: Ensures rules agree with the MLP’s predictions where confidence is high.
- L_sparsity: Encourages the model to keep rules simple by applying L1 penalties on raw weights.
Results: Does Rule Learning Work — and What Did It Find?
The experimental setup used the Kaggle Credit Card Fraud dataset, comprising 284,807 transactions. The results showed that the rule learner performed slightly below the pure neural baseline but provided valuable explainability.
Rule Fidelity: 0.993 ± 0.001 — Excellent
Rule Coverage: 0.811 ± 0.031 — Good
Rule Simplicity: 1.7 ± 2.1 — With active seeds using 5 and 8 conditions, comfortably readable.
The Extracted Rules — What the Gradient Found
Both rules produced by the model highlighted V14, confirming its significance without prior instruction. The model demonstrated the capacity to rediscover important features autonomously.
Four Things to Watch Before Deploying This
Considerations include:
- Annealing speed: Too fast or slow can adversely affect rule clarity.
- n_rules: Sets interpretability; balance to avoid too few or excessive rules.
- Consistency threshold: Ensure the MLP is well-calibrated for effective rule extraction.
- Rule auditing: Required after each retrain cycle to maintain compliance.
Rule Injection vs. Rule Learning — When to Use Which
The rule learner adds minimal code but requires careful validation for meaningful rule extraction. This approach serves as a tool rather than a solution, highlighting the need for multi-seed evaluation in claims about learned rule behavior.
Overall, this experiment demonstrates the potential of neuro-symbolic AI to combine statistical learning with human-readable logic, paving the way for more transparent and adaptable fraud detection systems.
