---
license: cc-by-4.0
task_categories:
  - graph-ml
tags:
  - graph-anomaly-detection
  - heterogeneous-graphs
  - non-adversarial-anomalies
  - billing-pipelines
size_categories:
  - 10K<n<100K
---

# BillSim — A Synthetic Heterogeneous Graph Benchmark for Non-Adversarial Anomaly Detection in Usage-Based Billing

Anonymous Authors
Submitted to NeurIPS 2026 Evaluations & Datasets Track
2026

## Overview

BillSim is a fully synthetic heterogeneous graph benchmark for non-adversarial anomaly detection in usage-based billing pipelines. Existing graph anomaly detection benchmarks (Amazon reviews, Bitcoin OTC/Alpha, Yelp, UNSW-NB15, DGraph) model adversarial behaviour: fraud, spam, attacks, intentional concealment. BillSim targets the complementary regime that dominates enterprise systems-of-record: configuration errors, integration drift, and timing mismatches that are economically consequential (revenue leakage, customer overbilling) yet not adversarial.

The headline finding the benchmark is built to expose: a 0.374 AUROC gap on peer-comparison anomalies between a hand-coded oracle (0.965) and the best GNN (0.591), localizing the limitation to message-passing aggregation rather than task ill-posedness. In abstract-level shorthand, this is the 0.37 AUROC oracle gap.

## Dataset At A Glance

- 63,155 nodes across 11 entity types
- 108,930 edges across 14 relationship types
- 6 anomaly types organized by graph reasoning pattern: structural / relational / peer-comparison
- 5 baselines benchmarked: MLP, GCN, GAT, RGCN, HGT
- 10 random seeds per configuration
- 4 anomaly injection rates: 0.01, 0.03, 0.05, 0.10
- 24 simulated billing months; temporal split for dynamic entities, deterministic 75/25 random split for static entities

## Schema

### Node Types (11)

| Type | Count | Features |
|------|-------|----------|
| customer | 200 | segment, is_active, num_sub_accounts |
| contract | 389 | duration_months, payment_terms, status, total_committed_value |
| sku | 50 | category, base_price, is_active |
| pricing_rule | 1,111 | rate_type, rate_value, is_current |
| usage_record | 14,601 | volume, unit_cost |
| rated_charge | 14,601 | amount |
| invoice | 3,547 | total_amount, status |
| line_item | 14,601 | amount |
| payment | 3,547 | amount, method |
| ar_record | 3,547 | status, amount |
| gl_entry | 6,961 | abs_amount |
| **Total** | **63,155** | |

All feature vectors are z-score normalized per node type. Categorical features are integer-encoded. The `gl_entry` feature deliberately omits the sign of the GL amount to prevent revenue/cash leakage into the learning task.

### Edge Types (14)

| Edge | Source -> Target | Count |
|------|------------------|-------|
| subscribes_to | customer -> contract | 389 |
| has_sku | contract -> sku | 1,111 |
| governs | pricing_rule -> sku | 1,111 |
| applies_to | pricing_rule -> contract | 1,111 |
| generates_usage | customer -> usage_record | 14,601 |
| for_sku | usage_record -> sku | 14,601 |
| rates_to | usage_record -> rated_charge | 14,601 |
| priced_by | rated_charge -> pricing_rule | 14,601 |
| billed_on | rated_charge -> line_item | 14,601 |
| part_of | line_item -> invoice | 14,601 |
| invoiced_to | invoice -> customer | 3,547 |
| settles | payment -> invoice | 3,547 |
| opens_ar | invoice -> ar_record | 3,547 |
| posts_to | invoice -> gl_entry | 6,961 |
| **Total** | | **108,930** |

The homogeneous view doubles edge count by adding reverse edges.

## Anomaly Taxonomy

Six anomaly types are organized into three graph-reasoning categories. The categorization is the analytical contribution of the benchmark: it makes the architectural success and failure modes of GNNs interpretable.

| # | Name | Target Node | Category | Mechanism |
|---|------|-------------|----------|-----------|
| 1 | Missing Metering | customer | relational | Usage stops while contract remains active |
| 2 | Orphaned Lines | line_item | relational | Invoice customer differs from charge customer (cross-path violation) |
| 3 | Pricing Mismatch | rated_charge | structural | Charge amount inconsistent with volume x rate from connected pricing rule |
| 4 | Stale Discount | pricing_rule | peer-comparison | Rate diverges from peer rules governing the same SKU |
| 5 | Revenue Recognition | gl_entry | structural | Invoice missing the expected cash GL entry (sibling-count check) |
| 6 | Premature AR | ar_record | structural | AR record closed despite incomplete payment sum |

Labels are provided per node type as a binary `y` (0 = normal, 1 = anomalous) and as `anomaly_type` (0 = normal, 1-6 = the type above). Each node carries at most one anomaly label; no overlap between types.

Injection signatures have been audited for feature leakage: per-type Cohen's d remains below 0.2, ensuring detection requires graph structure rather than feature shortcuts.

## Headline Result

At injection rate 0.05 across 10 seeds, the V4 result table is:

| Type | MLP | GCN | GAT | RGCN | HGT | Oracle | Best GNN | Gap |
|------|-----|-----|-----|------|-----|--------|----------|-----|
| Missing Metering | 0.512 | 0.730 | 0.398 | 0.784 | **0.827** | 0.866 | HGT | +0.038 |
| Pricing Mismatch | 0.684 | 0.571 | 0.867 | **0.980** | 0.979 | 0.881 | RGCN | -0.099 |
| Orphaned Lines | 0.505 | 0.967 | 0.968 | 0.922 | **0.988** | 1.000 | HGT | +0.012 |
| **Stale Discount** | 0.560 | 0.571 | 0.476 | **0.591** | 0.540 | **0.965** | RGCN | **+0.374** |
| Revenue Recognition | 0.509 | 0.965 | 0.928 | 0.497 | **0.987** | 1.000 | HGT | +0.013 |
| Premature AR | 0.509 | 0.519 | 0.533 | **0.996** | 0.991 | 1.000 | RGCN | +0.004 |

The 0.374 oracle-GNN gap on Stale Discount is an order of magnitude larger than any other gap. Because the gap is exposed by a hand-coded peer-comparison oracle that achieves 0.965 AUROC, the limitation is established as architectural — message-passing aggregation cannot represent peer-distribution comparison — rather than the task being ill-posed.

## Data Generation

The dataset is fully synthetic. No real billing data was used at any stage. The generation pipeline is a configurable Python module with deterministic NumPy seeding. Default parameters:

- Revenue distribution: lognormal contract sizes producing a Pareto-like tail
- Usage volumes: log-normal (mu = 6.0, sigma = 1.2)
- Customer arrivals: front-loaded declining Poisson
- Contract durations: uniform 6-36 months
- Pricing: uniform 0.01-10.0 base rate with +/-20% per-contract variation

All parameters are documented in the configuration module of the released code.

## Train / Test Split

- Dynamic entities (usage_record, rated_charge, invoice, line_item, payment, ar_record, gl_entry): temporal split. Months 1-18 -> train, months 19-24 -> test.
- Static entities (customer, contract, sku, pricing_rule): deterministic 75/25 random split keyed off `(seed + stable_offset(node_type))`. The stable offset is an MD5-derived integer per node type name, ensuring split reproducibility across seeds and node types.

## Preprocessing

- All features z-score normalized per column (mean 0, std 1)
- Categorical features integer-encoded
- No missing values; no NaN or Inf values (verified by automated integrity check)
- No out-of-bounds edge indices (verified)

## Intended Uses

- Benchmarking GNN methods for non-adversarial anomaly detection on heterogeneous temporal graphs
- Evaluating which graph reasoning patterns (structural sibling counting, multi-hop relational path matching, relation-specific traversal, peer-distribution comparison) different architectures can or cannot represent
- Diagnostic studies of message-passing limitations, including ablations against hand-coded oracle ceilings
- Research on architectural extensions that close the peer-comparison gap

## Not-Intended Uses

- Production billing system deployment. The synthetic distributions do not replicate the complexity of real billing data.
- Training fraud detection models. The anomalies in BillSim are non-adversarial system errors, not adversarial attack patterns. Fraud involves intentional concealment and shifting tactics; billing errors do not.
- Drawing conclusions about real-customer billing accuracy. The benchmark exists to evaluate model architectures, not to model any specific operator's billing platform.

## Format

PyTorch Geometric `HeteroData` objects serialized as `.pt` files, accompanied by Python generation scripts that reproduce the dataset deterministically from any seed and injection rate.

## Licenses

- Data: CC-BY-4.0
- Code: Apache-2.0

## Citation

Anonymous Authors. BillSim: A Synthetic Heterogeneous Graph Benchmark for Non-Adversarial Anomaly Detection in Usage-Based Billing. Submitted to NeurIPS 2026 Evaluations & Datasets Track, 2026.