Differentiable decision trees stop spreading across dozens of features: a Euclidean penalty cuts Wine's effective node features from 8.94 to 1.54

Each internal node of a differentiable decision tree can now be pushed toward dominance by a small number of input features while continuous soft splits and explicit root-to-leaf paths remain. Earlier differentiable decision trees used oblique soft splits, so one node's weight vector could spread across many input dimensions and the features behind a node decision stayed unclear. Averages over five matched random seeds show mean effective features dropping from 8.94 to 1.54 on Wine and from 45.28 to 9.06 on Digits, with no collapsed nodes reported for any variant under the given threshold.

The change is a training term that measures how far each node's normalised absolute feature weights sit from a uniform distribution. This normalised squared Euclidean concentration regulariser first turns weights into feature shares and then takes their squared Euclidean distance from uniform; L1 and L2 constrain parameter magnitude rather than relative shares inside a node. On Wine and Digits the four variants share tree depth, leaf representation, initialisation and a full-batch Adam optimiser and differ only in the regulariser, with 7 internal nodes on Wine and 63 on Digits, each run over five random seeds.

The same mechanism also parameterises a PPO policy directly, so the policy tree's nodes depend on fewer state variables. Earlier tree policies faced the same diffuse node dependence, while value estimation stayed with a separate MLP critic. CartPole-v1 and MiniPacman each ran two random seeds; in the representative runs EU-DDT reached 100% final evaluation success and mean node concentration rose from 0.1272 to 0.7179 and from 0.0437 to 0.7237.

The demonstrated scope is supervised classification on the Wine and Digits datasets and PPO policy parameterisation in CartPole-v1 and MiniPacman; interpreting node weights depends on a uniform scaling strategy, standardisation for Wine and MinMax scaling for Digits, with scaling parameters fitted on the training set only.

The reinforcement-learning experiments use only two random seeds per environment, which the authors say assesses directional consistency rather than supporting statistical inference; the supervised experiments use five seeds, and the authors note that more repetitions and a broader set of datasets would give more reliable variance estimates and stronger generalisability evidence. The interpretability analysis rests on structural tree properties and node-weight concentration, and the authors propose human-subject evaluation or fidelity checks of single-feature rules derived from learned nodes as future work.