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This paper adds a regulariser to differentiable decision trees that pushes each split toward relying on a few input features, which makes individual nodes easier to read. The tabular results are the strongest evidence: effective feature counts drop sharply, with accuracy falling on Wine and rising slightly on Digits. The reinforcement-learning results rest on only two seeds, so readers should treat them as preliminary.
Improving the Intrinsic Interpretability of Differentiable Decision Trees through Euclidean Feature-Concentration Regularisation
arXiv:2610.39596v1 Announce Type: new Abstract: Differentiable decision trees (DDTs) support end-to-end optimisation and explicit decision paths, but dense oblique splits can obscure the role of individual input features. We propose the Euclidean-Concentrated Differentiable Decision Tree (EU-DDT), which regularises the relative absolute feature weights at each internal node using their normalised squared Euclidean distance from the uniform distribution. This encourages dominance by a small number of features while retaining probabilistic soft routing. Across five matched random seeds, EU-DDT reduces the mean effective number of features from 8.94 to 1.54 on Wine and from 45.28 to 9.06 on Digits. Mean test accuracy changes from 100.0% to 93.9% on Wine and from 92.3% to 94.6% on Digits, illustrating the dataset-dependent trade-off between concentration and predictive performance. We also use EU-DDT to parameterise a PPO actor with an MLP critic. Two random-seed runs per environment show a consistent qualitative increase in concentration while preserving effective task performance. In representative CartPole-v1 and MiniPacman runs, EU-DDT reaches 100% final evaluation success, while mean node concentration increases from 0.1272 to 0.7179 and from 0.0437 to 0.7237, respectively. These results support EU regularisation as a mechanism for reducing node-level feature complexity; the reinforcement-learning evidence remains preliminary because only two seeds are evaluated.
Abstract:Differentiable decision trees (DDTs) support end-to-end optimisation and explicit decision paths, but dense oblique splits can obscure the role of individual input features. We propose the Euclidean-Concentrated Differentiable Decision Tree (EU-DDT), which regularises the relative absolute feature weights at each internal node using their normalised squared Euclidean distance from the uniform distribution. This encourages dominance by a small number of features while retaining probabilistic soft routing. Across five matched random seeds, EU-DDT reduces the mean effective number of features from 8.94 to 1.54 on Wine and from 45.28 to 9.06 on Digits. Mean test accuracy changes from 100.0% to 93.9% on Wine and from 92.3% to 94.6% on Digits, illustrating the dataset-dependent trade-off between concentration and predictive performance. We also use EU-DDT to parameterise a PPO actor with an MLP critic. Two random-seed runs per environment show a consistent qualitative increase in concentration while preserving effective task performance. In representative CartPole-v1 and MiniPacman runs, EU-DDT reaches 100% final evaluation success, while mean node concentration increases from 0.1272 to 0.7179 and from 0.0437 to 0.7237, respectively. These results support EU regularisation as a mechanism for reducing node-level feature complexity; the reinforcement-learning evidence remains preliminary because only two seeds are evaluated.
17 pages, 3 figures, 5 tables. Based on the author's MSc dissertation, University of Birmingham
Machine Learning (cs.LG)
arXiv:2610.39596 [cs.LG]
(or arXiv:2610.39596v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.39596 Focus to learn more arXiv-issued DOI via DataCite
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