Graph Autoencoder (GAE)

The GAE consists of two core components working in tandem. The encoder uses a GNN—typically a Graph Convolutional Network (GCN) or Graph Attention Network (GAT)—to map each node to a low-dimensional latent vector z. The decoder reconstructs the original graph structure from these embeddings, usually by computing the inner product σ(z_i^T z_j) to predict edge probabilities. This bottleneck forces the model to learn a compressed, information-rich representation of the graph's topology.

GAEs excel at link prediction without labeled data. By masking a subset of edges during training and tasking the decoder with reconstructing them, the model learns to score the likelihood of connections between any node pair. In cellular networks, this enables:

• Forecasting future handover relationships as users move
• Predicting latent interference edges not captured by static propagation models
• Identifying missing neighbor relations in Automatic Neighbor Relation (ANR) tables

GAEs are inherently suited for graph anomaly detection. After training on normal network topologies, the model learns a characteristic reconstruction error distribution. When presented with a new graph snapshot, nodes or edges with anomalously high reconstruction error signal deviations from expected behavior. This enables:

• Detection of rogue base stations or unauthorized network elements
• Identification of cell outages where expected connections disappear
• Flagging unusual interference patterns indicating hardware faults or external jamming

The Variational Graph Autoencoder (VGAE) extends the standard GAE by introducing a probabilistic latent space. Instead of learning deterministic embeddings, the encoder outputs parameters of a Gaussian distribution—mean μ and variance σ—from which latent vectors are sampled. This variational inference framework regularizes the latent space, making it smoother and more interpretable. The loss function combines a reconstruction term with a KL divergence term that pushes the latent distribution toward a standard normal prior, preventing overfitting and enabling generative capabilities.

The smooth latent space of a VGAE enables generative modeling of graphs. By sampling new points from the latent distribution and passing them through the decoder, the model can generate entirely new, plausible graph structures. For cellular networks, this supports:

• Synthetic topology generation for simulation and stress-testing
• Graph completion tasks where missing portions of a network map are inferred from partial observations
• What-if scenario modeling by interpolating between known network states in latent space

The choice of reconstruction loss defines what structural properties the GAE prioritizes. Common formulations include:

• Binary cross-entropy on adjacency matrix entries, treating edge prediction as independent binary classification
• Area Under the Curve (AUC) optimization for ranking edges by likelihood
• Mean squared error on continuous adjacency weights, useful when edges carry signal strength or path loss values
• Multi-task losses that jointly reconstruct both topology and node attributes, forcing the latent space to capture richer semantics