Self-Explaining Neural Networks (SENN)

The core architectural constraint of a SENN is that the final prediction is a linear combination of basis concepts. The model learns functions h(x) that transform raw inputs into interpretable, high-level features. The output is f(x) = Σ θ(x)_i * h(x)_i, where θ(x) are the locally relevant relevance scores. This additive decomposition ensures that the contribution of each concept is isolated and can be inspected independently, making the decision process transparent by design.

Unlike global linear models, a SENN generates input-dependent relevance scores θ(x) via a parameterized network. This means the explanation adapts to every single input. For a given instance, the network outputs a set of coefficients that weight the basis concepts. This allows the model to capture complex, non-linear decision boundaries while maintaining local linearity with respect to the concepts, providing a faithful, instance-specific explanation rather than a global approximation.

To ensure the explanations are stable and meaningful, SENNs are trained with a robustness loss that penalizes large variations in the relevance scores θ(x) for small, imperceptible changes to the input. This is achieved by minimizing the gradient of θ(x) with respect to x:

• Stability: Explanations do not fluctuate wildly for nearly identical inputs.
• Faithfulness: The penalty enforces that the explanation is a true function of the input's semantic content, not brittle noise.

The model learns a dictionary of basis concepts h(x) that serve as the vocabulary of the explanation. These concepts can be:

• Prototype-based: Similarity to learned prototypical examples.
• Domain-specific: Encoded to align with known, human-understandable attributes (e.g., 'fur texture', 'ear shape'). The architecture forces the model to reason using these high-level concepts, making the internal representation inherently more interpretable than raw feature detectors in standard deep networks.

The entire SENN architecture—including the concept encoder, relevance parameterizer, and final linear combination—is trained end-to-end using standard gradient-based optimization. There is no separate post-hoc explainer to train. The explanation is a direct, differentiable output of the model. This joint optimization ensures that the model's predictive accuracy and its explanatory fidelity are balanced during training, rather than having an explanation retrofitted onto a frozen, opaque model.