SLICE: Building Models from Structured Single-Feature Perturbation Effects

Single-feature perturbation analysis is a fundamental method for investigating how a predictive model behaves when a single feature is varied while the remaining features are held fixed. Existing visualization approaches analyze these effects after a model has been fitted, typically by aggregating responses across dataset samples or by visualizing individual response curves. However, aggregation can obscure heterogeneous responses across samples, while the individual curves may be numerous, complex, and heavily interleaving, making the overall perturbation behavior difficult to characterize globally. Moreover, these approaches provide no structural guarantee on behavior under other unseen feature values. We reverse this workflow: rather than first fitting a model and subsequently attempting to understand its perturbation effects, we explicitly constrain the form these effects may take and build the model around those constraints. We introduce SLICE (Structured Laminar Individual Conditional Effects), a class of models whose centered single-feature perturbation curves form structured, laminar families. In such families, perturbation curves form an ordered family rather than crossing and interleaving arbitrarily, making the full range of possible single-feature responses easy to characterize globally while still allowing the underlying predictor to capture interactions of arbitrary order. We characterize the prediction functions compatible with these perturbation requirements and develop a differentiable parameterization that satisfies them by construction. Across benchmark datasets, SLICE outperforms additive models and often approaches or matches fully flexible baselines, while preserving globally comprehensible single-feature perturbation behavior. SLICE thus shifts single-feature perturbation analysis from merely post-training inspection to explicit control during model construction.