Integrated Gradients

The sum of all feature attributions equals the difference between the model's output at the input and the output at the baseline. This conservation property ensures no importance is created or destroyed during the attribution process.

• If a feature differs from the baseline and changes the output, it receives non-zero attribution
• If the input and baseline produce identical outputs, all attributions are zero
• Provides a global accounting of prediction responsibility

Two functionally equivalent networks—networks that produce identical outputs for all possible inputs—always receive identical attributions. This property is critical for model auditing because it guarantees the explanation reflects the mathematical function learned, not the arbitrary structural choices of the implementation.

• Attributions are invariant to architectural differences
• Eliminates gaming of explanations through network restructuring
• Ensures consistency across different framework implementations

If a model is a linear combination of two sub-models, the attribution is the same linear combination of the individual attributions. This compositional property enables attribution for ensemble models and simplifies analysis of modular architectures.

• Supports attribution for stacked or ensembled models
• Preserves mathematical relationships between model components
• Enables decomposition of complex predictions into sub-component explanations

Two input variables that play identical roles in the network and have identical values receive identical attributions. This fairness axiom prevents the attribution method from arbitrarily favoring one symmetric feature over another.

• Guarantees equal treatment of functionally equivalent features
• Critical for applications where feature parity is legally mandated
• Prevents spurious attribution asymmetries in symmetric architectures

Attributions are computed by accumulating gradients along a straight-line path from a baseline input to the actual input. This path integral satisfies the fundamental theorem of calculus for multivariate functions and is the mechanism that enforces the Sensitivity axiom.

• The baseline represents an informationless reference point (e.g., black image, zero signal)
• Gradients are sampled at interpolated points: baseline + α × (input - baseline)
• The number of interpolation steps controls the approximation accuracy

The choice of baseline fundamentally shapes the attribution. A baseline should represent the absence of signal for the domain. For RF applications, common baselines include zero-valued IQ samples, thermal noise, or a carrier-only signal.

• Poor baseline choice produces misleading attributions
• Domain expertise is required to define a meaningful neutral reference
• Multiple baselines can be averaged to improve robustness

A visualization technique that uses gradients flowing into the final convolutional layer to produce a coarse localization map highlighting important regions. For RF applications, Grad-CAM can identify which time-frequency bins in a spectrogram most influenced a modulation classification decision. Unlike Integrated Gradients, Grad-CAM is specifically designed for CNN architectures and produces spatial heatmaps rather than per-pixel attributions.

A causal explanation method that identifies the minimal change to an input required to alter a prediction to a predefined alternative. In RF contexts, this answers: 'What minimal shift in frequency or power would change the emitter identification?' Key contrast with Integrated Gradients:

• IG explains why a prediction was made
• Counterfactuals explain how to change the prediction
• Useful for adversarial robustness testing of RF fingerprinting models

A global interpretability tool showing the marginal effect of one or two features on the predicted outcome, averaged over all other features. While Integrated Gradients provides local explanations for individual predictions, PDPs reveal global behavior across the entire dataset. For RF ML, PDPs can show how a model's classification confidence changes as signal-to-noise ratio (SNR) varies across its full range.

An optimization-based technique that generates synthetic inputs to maximally activate specific neurons or channels. For RF models, this can reveal what I/Q patterns a neural receiver has learned to detect. Unlike Integrated Gradients which explains existing inputs, feature visualization synthesizes idealized inputs that represent a model's learned concepts. Often used alongside activation maximization and diversity regularization.