Siamese Network

The defining characteristic of a Siamese network is its use of two identical subnetworks that process two distinct inputs. Critically, these subnetworks share the exact same weights and configuration. During training, weight updates are mirrored across both branches, ensuring that identical inputs produce identical output embeddings. This weight tying forces the network to learn a consistent feature extraction function, making the comparison between the resulting feature vectors semantically meaningful. Without shared weights, the network could map two identical inputs to different latent spaces, defeating the purpose of similarity learning.

Rather than classifying inputs directly, Siamese networks learn a distance function between data points. The twin subnetworks map inputs into an embedding space where the Euclidean distance or cosine similarity between vectors reflects semantic similarity. The goal is to create a representation where:

• Similar pairs (e.g., two signals from the same device) are mapped close together.
• Dissimilar pairs (e.g., signals from different devices) are mapped far apart. This approach excels in few-shot learning scenarios, where the network must verify identities against a single enrolled example without retraining for new classes.

The standard training objective for Siamese networks is contrastive loss, which operates on pairs of samples labeled as similar or dissimilar. The loss function is defined as:

• For a similar pair (Y=1): The loss penalizes large distances between embeddings, pulling them together.
• For a dissimilar pair (Y=0): The loss penalizes distances smaller than a predefined margin, pushing them apart. This margin parameter creates a boundary: once dissimilar pairs are separated beyond the margin, they no longer contribute to the loss, allowing the network to focus on harder cases. This is distinct from classification losses like cross-entropy.

A direct evolution of the Siamese architecture is the triplet network, which processes three inputs simultaneously: an anchor, a positive sample (same class as anchor), and a negative sample (different class). The network uses triplet loss to ensure the distance between the anchor and positive is smaller than the distance between the anchor and negative by at least a margin. This triplet structure provides richer training signals than pairwise contrastive loss because it considers relative distances within a triplet, often leading to more discriminative embeddings for fine-grained fingerprinting tasks.

Siamese networks are inherently designed for one-shot learning. Once trained, the network can verify whether two inputs belong to the same class even if that class was never seen during training. For RF fingerprinting, this means a model can authenticate a newly enrolled transmitter by comparing its live signal to a single stored reference embedding. This is achieved by computing the distance between the two embeddings and applying a verification threshold. If the distance is below the threshold, the pair is considered a match. This eliminates the need to retrain a classifier every time a new device is added to the network.

In wireless applications, a raw Siamese network is vulnerable to channel variability, where multipath fading can distort the signal more than the hardware impairments being fingerprinted. To address this, the twin subnetworks are often augmented with domain adversarial training or trained with heavily augmented data that simulates diverse channel conditions. The objective is to shape the embedding space to be invariant to channel effects while remaining sensitive to transmitter-specific impairments. This ensures that the distance between two signals from the same device remains small even when they traverse different propagation environments.

A metric learning loss function that extends the Siamese concept to three inputs: an anchor, a positive sample (same class), and a negative sample (different class). The loss minimizes the distance between the anchor and positive while enforcing a margin of separation from the negative. This is critical for learning fine-grained, channel-invariant fingerprint embeddings where intra-class variance must be smaller than inter-class variance.

The defining architectural constraint of a Siamese network where the subnetworks are identical clones—they share the exact same parameters and weights. This symmetry guarantees that both inputs are processed by the same function, ensuring the output embeddings reside in the same latent space. Without weight sharing, the network would be a pseudo-Siamese or Conjoined Network, which lacks the mathematical guarantee of consistent feature extraction.

The function applied to the two output embeddings to compute a similarity score. Common choices include:

• Euclidean Distance: Sensitive to absolute vector magnitudes.
• Cosine Similarity: Focuses on angular separation, often preferred for high-dimensional RF fingerprint embeddings.
• Manhattan Distance: Computationally cheaper L1 norm. The choice of metric directly impacts the geometry of the learned latent space.

A primary use case for Siamese networks where the model must recognize a device class given only a single enrollment example. Instead of retraining a classifier for every new device, the Siamese network compares the new sample against a stored reference signature. This is essential for few-shot device enrollment in IoT security, where capturing hundreds of rogue device transmissions is impractical.

An advanced training objective often paired with Siamese architectures to separate the learned embedding into independent factors. In RF fingerprinting, this forces the network to isolate device-specific hardware impairments from channel-induced distortions. By using adversarial branches or variational autoencoders alongside the Siamese structure, the similarity score becomes robust to multipath fading and Doppler shift.