Neural Additive Models (NAM)

The core architecture of a NAM is expressed as:

y = β₀ + f₁(x₁) + f₂(x₂) + ... + fₚ(xₚ)

Each fᵢ is a distinct, independently trained neural network attending to a single input feature xᵢ. The final prediction is the unweighted sum of these individual network outputs. This structural constraint enforces additivity, eliminating complex feature interactions by design and ensuring that the contribution of each feature is mathematically isolated and independently auditable.

Because each feature is processed by its own dedicated network, the learned relationship can be plotted as a shape function. This is a 2D graph where the x-axis is the input feature value and the y-axis is the model's output contribution for that feature.

• Direct Visualization: Unlike SHAP or LIME which approximate explanations, NAM shape functions are the exact, ground-truth logic of the model.
• Auditability: A domain expert can visually inspect the graph to verify that the model has learned a medically, financially, or physically plausible relationship.
• Example: For a credit model, the shape function for 'age' might show a smooth, monotonically increasing risk score up to a point, which a regulator can instantly validate.

NAMs enforce a strict modular architecture where each feature network is a self-contained unit. This provides several engineering advantages:

• Independent Training: Feature networks can be trained in parallel, distributing the computational load.
• Selective Retraining: If a data distribution shift is detected for a single feature, only that specific network needs to be retrained, leaving the rest of the model untouched.
• Feature Surgery: A problematic or biased shape function can be surgically removed or replaced without degrading the performance of other features, enabling precise model editing for compliance.

The structural additivity constraint is the source of both NAM's interpretability and its primary limitation. By design, a NAM cannot learn feature interactions.

• Expressiveness Gap: A standard deep neural network (DNN) can model complex, non-linear interactions between features (e.g., the combined effect of 'age' and 'income'). A pure NAM cannot.
• NAMs with Interactions (NA²M): To bridge this gap, the architecture can be extended to include two-way interaction terms, learning separate networks for pairs of features: fᵢⱼ(xᵢ, xⱼ). This improves accuracy while retaining partial interpretability, as the pairwise shape functions can still be visualized as heatmaps.

Standard activation functions like ReLU produce smooth, piecewise-linear functions. To learn highly jagged, non-smooth shape functions common in real-world data, NAMs often employ Exp-centered Units (ExU) in the first hidden layer.

An ExU is defined as: ExU(x) = exp(w) * (x - b)

• High Curvature: The exponential weight term allows the network to create sharp, high-frequency variations in the shape function without requiring an excessively deep architecture.
• Practical Use: This is critical for modeling phenomena like mortality risk, which has a sharp spike in infancy, a drop in early adulthood, and an exponential increase in old age—a shape a standard ReLU network struggles to fit precisely.

NAMs provide both global and local explanations without additional computation:

• Global Explanation: The entire set of shape functions constitutes a complete, global explanation of the model's logic. This serves as a Global Surrogate Model that is the actual model itself.
• Local Explanation: For a single prediction, the explanation is a simple bar chart showing the additive contribution of each feature: f₁(x₁_instance), f₂(x₂_instance), .... This is mathematically identical to the model's own internal computation, providing 100% faithful local feature attribution.
• Comparison: This contrasts with post-hoc methods like LIME, which generate a local approximation that may not perfectly reflect the underlying model's true reasoning.

A glass-box model that is the closest sibling to NAM. Like NAM, EBM learns a generalized additive model where each feature contributes independently via a learned shape function. The key difference: EBM uses gradient boosting with bagging and detects pairwise interactions automatically, while NAM uses deep neural networks for each feature. Both produce fully intelligible graphs showing exactly how each variable influences the prediction.

A global visualization tool that shows the marginal effect of one or two features on a model's predictions. PDP works by averaging over the distribution of all other features, revealing the average relationship. NAM renders PDPs obsolete for single features because its learned shape functions are the exact partial dependence curves, computed directly without estimation or averaging artifacts.

An unbiased alternative to PDP that handles correlated features correctly. While PDP averages over the marginal distribution (creating unrealistic data points), ALE computes effects by accumulating local differences within conditional distributions. NAM avoids this problem entirely: its feature-specific subnetworks learn effects in isolation, and the additive structure prevents correlated features from contaminating each other's shape functions.

A game-theoretic framework that assigns each feature an importance value for a specific prediction. SHAP values satisfy desirable axioms: efficiency, symmetry, dummy, and additivity. While SHAP can explain any black-box model post-hoc, NAM provides inherent feature-level explanations without approximation. The additive structure of NAM means the contribution of each feature is directly readable from its neural network's output—no Shapley sampling required.

A class of models that learn to produce both a prediction and an explanation simultaneously. SENN generates locally relevant feature coefficients that are stable and interpretable. NAM takes a different architectural approach: instead of forcing a single network to output explanations, NAM structurally decomposes the problem into independent sub-networks, making the explanation a direct consequence of the architecture rather than an auxiliary output.

Explanations that answer: 'What would need to change to get a different outcome?' They identify the minimal feature perturbations that flip a prediction. NAM complements counterfactuals perfectly: by inspecting the learned shape functions, you can immediately see how much a feature must shift to cross a decision threshold. The monotonic or smooth curves learned by NAM make counterfactual search deterministic and instantaneous.