Siamese Networks

The defining structural feature: two identical subnetworks with shared weights process two distinct inputs in parallel. This weight-tying guarantees that both inputs are encoded by the exact same function, ensuring that the resulting embedding vectors reside in a comparable feature space. Any architectural change to one branch is automatically reflected in the other, enforcing symmetry.

The network is trained not to classify, but to pull similar pairs together and push dissimilar pairs apart in the embedding space. The original contrastive loss is defined as:

• L = (1-Y) * D² + Y * max(0, margin - D)²
• Where Y=0 for genuine pairs and Y=1 for impostor pairs
• D is the Euclidean distance between the two output embeddings
• The margin hyperparameter defines the minimum separation for dissimilar pairs

After the twin subnetworks produce their respective embeddings, a distance layer computes the similarity between them. Common metrics include:

• Euclidean distance: Straight-line distance in the embedding space
• Cosine similarity: Measures the angle between vectors, ignoring magnitude
• Manhattan distance: Sum of absolute differences This distance score is the final output, thresholded to make a binary same/different decision.

Training data is organized into pairs, not individual samples. Each pair is labeled as genuine (same class) or impostor (different class). The network learns a manifold where:

• Genuine pairs map to nearby points
• Impostor pairs map to distant points This pair-based paradigm is what enables one-shot learning at inference time—the network compares a new sample against a single enrolled template.

Siamese networks were introduced by Bromley et al. in 1993 for signature verification as a form of metric learning. The original application compared a test signature against a reference to determine authenticity. This legacy directly maps to modern RF fingerprinting, where a newly captured waveform is compared against an enrolled device signature to verify physical-layer identity.

A powerful extension that uses three inputs per training example:

• Anchor: The reference sample
• Positive: A sample from the same class as the anchor
• Negative: A sample from a different class The loss minimizes distance(anchor, positive) while maximizing distance(anchor, negative) by a margin. This provides richer gradient signals than pairwise contrastive loss and often yields more discriminative embeddings for few-shot enrollment scenarios.

The canonical loss function for training Siamese networks. It operates on triplets of samples: an anchor, a positive (same class), and a negative (different class). The objective is to minimize the distance between the anchor and positive while enforcing a margin between the anchor and negative.

• Hard negative mining selects the most challenging negative samples to accelerate convergence
• Prevents the model from collapsing all embeddings to a single point
• Directly optimizes for a structured embedding space where distance equals dissimilarity

A metric-based few-shot architecture that extends Siamese principles. Instead of pairwise comparisons, it computes a prototype—the mean embedding vector—for each class from the support set. Query samples are classified by finding the nearest prototype in embedding space.

• Uses Euclidean distance rather than cosine similarity
• Naturally handles variable numbers of support examples per class
• Provides a probabilistic output via a softmax over distances to all prototypes

The lower-dimensional continuous vector space where Siamese networks map inputs. The geometry of this space is the network's learned knowledge: similar devices cluster together, while dissimilar ones are pushed apart.

• Dimensionality typically ranges from 64 to 512 for RF fingerprinting tasks
• Distance metrics include L2 (Euclidean), cosine similarity, and angular distance
• Quality is measured by cluster separation and intra-class compactness
• Visualized using t-SNE or UMAP for debugging model behavior

The meta-learning strategy used to train Siamese networks for few-shot generalization. Each training iteration simulates a deployment scenario by sampling a small N-way, K-shot task: N classes with K examples each.

• The model never sees the same class configuration twice during training
• Forces the network to learn a generalizable comparison function, not memorize classes
• Validation episodes use classes held out entirely from training to measure true generalization

The deployment scenario where a device is registered using only a single RF transmission. The Siamese network extracts an embedding from this one sample and stores it as the reference template.

• Eliminates the need for lengthy multi-sample calibration procedures
• Critical for rapid IoT onboarding at scale
• Requires highly discriminative embeddings to prevent false acceptances from a single reference
• Often paired with confidence thresholds to flag ambiguous matches for manual review

A self-supervised pre-training paradigm closely related to Siamese architectures. Modern variants like SimCLR and MoCo learn representations by maximizing agreement between differently augmented views of the same sample.

• Can pre-train an RF fingerprinting encoder on unlabeled spectrum data
• Reduces reliance on expensive labeled device datasets
• The pre-trained encoder is then fine-tuned with Triplet Loss on a small labeled enrollment set
• Particularly valuable for open set emitter recognition where labeled adversaries are scarce