SPECTRA: Sparse Prototype-Encoded Classification Trees with Routing Attribution

Differentiable decision trees aim to combine the transparent structure of trees with the optimization flexibility of neural models. However, the discrete paths presented as explanations do not always reflect the soft routing computation that actually produces a prediction. We introduce SPECTRA, a sparse multiway classification tree that learns prototype-based branches, structural gates, and leaf predictors through differentiable optimization. Its central mechanism is routing attribution, which expresses each branch decision as a combination of feature-level evidence and an explicit structural-gate contribution. Based on the model’s native routing flow, SPECTRA constructs an executable dominant path that identifies the most influential features, quantifies their support for competing branches, and connects local decisions to the final prediction without fitting a post-hoc surrogate. This formulation makes the learned tree structure, routing process, and explanation share the same computational semantics. SPECTRA therefore provides a unified framework for predictive modeling and auditable decision analysis on tabular data, enabling its behavior to be examined in terms of predictive quality, explanation fidelity, structural sparsity, stability, and computational efficiency.