Prototype Learning

The foundational architecture computes a class prototype as the mean embedding vector of its support examples. A query signal is classified by finding the nearest prototype in the embedding space using a distance metric, typically squared Euclidean distance.

• Produces a distribution over classes via a softmax over distances
• Naturally episodic training mimics few-shot scenarios
• Distance to the nearest prototype serves as a direct novelty score

Unlike closed-set softmax classifiers that force a decision, prototype networks reject unknown modulations by thresholding the minimum distance to any known class prototype.

• If min_distance > threshold, the signal is flagged as unknown
• Threshold can be calibrated using Extreme Value Theory on known-class distances
• Avoids the feature collapse problem common in discriminative models

An extension where each known class is represented by a reciprocal point rather than a central prototype. Classification uses the maximum distance to these points, creating a more robust open space risk boundary.

• Unknown samples are pushed away from all reciprocal points simultaneously
• Provides stronger theoretical guarantees against open space risk
• Integrates naturally with deep convolutional feature extractors for IQ samples

Training is regularized by exposing the network to auxiliary outlier datasets during prototype learning. This forces prototypes to be compact and well-separated from potential unknown signal regions.

• Outlier samples are pushed to a background prototype or uniform distribution
• Improves AUROC for novelty detection by 10-15% in spectrum monitoring tasks
• Prevents prototype drift toward ambiguous feature space regions

Replaces Euclidean distance with the Mahalanobis distance, which accounts for the covariance structure of each class's embedding distribution. This provides a statistically informed metric that adapts to the spread of each modulation type.

• Class-specific covariance matrices are learned during training
• Handles anisotropic clusters common in high-SNR signal representations
• More robust to distributional shift in channel conditions

Supports open world learning by allowing new modulation classes to be registered without retraining the entire network. A new prototype is computed from a few labeled examples and added to the gallery.

• Enables field-updatable signal libraries for SIGINT platforms
• Avoids catastrophic forgetting of previously learned modulations
• Compatible with few-shot and one-shot registration scenarios

The overarching classification paradigm where a model must accurately identify known classes while simultaneously detecting and rejecting unknown classes not seen during training. Prototype learning provides a natural mechanism for this by measuring distance to learned class representatives. In a spectrum monitoring context, this means a classifier can identify standard modulations like QPSK and 16QAM while flagging a novel, proprietary waveform as 'unknown' rather than forcing a misclassification.

The specific task of identifying input samples that differ significantly from the training data distribution. Prototype networks enable this by establishing a distance threshold in the embedding space. Key mechanisms include:

• Mahalanobis Distance: Accounts for class covariance structure, providing a more statistically informed metric than Euclidean distance
• Feature Magnitude Thresholding: Unknown samples often produce embeddings with smaller norms, creating a natural rejection boundary
• Energy-Based Scoring: Assigns high energy to OOD samples based on their distance from all known prototypes

A statistical framework for modeling the tail behavior of distance distributions. The OpenMax layer replaces standard SoftMax by fitting a Weibull distribution to the distances of correctly classified samples from their class mean. This recalibrates activation vectors to estimate the probability of an input belonging to an unknown class. For modulation recognition, EVT provides a principled way to set rejection thresholds that adapt to the geometry of each class's embedding space.

An alternative classification strategy where each known class is represented by a reciprocal point in the embedding space rather than a central prototype. Unknown samples are identified by their maximum distance to these reciprocal points. The key insight: known samples cluster near their class prototype but far from reciprocal points, while unknown samples maintain similar distances to all reciprocal points, creating a detectable signature for novelty.

The model's uncertainty arising from a lack of knowledge or data, which is reducible with more training samples. Prototype distance directly quantifies epistemic uncertainty—a sample far from all prototypes indicates the model has insufficient knowledge to classify it. This is distinct from aleatoric uncertainty (inherent noise). Techniques for measuring this include:

• Evidence Deep Learning: Places a Dirichlet distribution over class probabilities
• Deep Ensembles: Variance across multiple networks signals uncertainty
• Distance to Nearest Prototype: The simplest and most direct metric

A specialized loss function that creates a distinct separation in feature magnitude between known and unknown samples. It maximizes the feature norm for known samples while minimizing it for unknown samples, creating a thresholdable rejection space. When combined with prototype learning, this loss ensures that known modulation embeddings have large magnitudes and cluster tightly around their prototypes, while unknown signals produce low-magnitude embeddings that fall below a rejection threshold.