{"ID":5675329,"CreatedAt":"2026-07-03T01:40:09.565152011Z","UpdatedAt":"2026-07-07T01:06:03.009715918Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.02069","arxiv_id":"2607.02069","title":"Algebraic Model Counting for Global Analysis of Optimal Decision Trees","abstract":"Ensuring model reliability in Explainable AI requires a global assessment of the hypothesis space. We propose a formal framework for the exhaustive analysis of optimal and near-optimal decision trees, called Algebraic Decision Tree Counting (ADTC). Inspired by Algebraic Model Counting (AMC) in knowledge representation, ADTC reformulates diverse analytical tasks, such as optimization, counting, and sampling, into a unified sum-of-products computation over a semiring $R$. While the hypothesis space of decision trees is doubly exponential with respect to the maximum depth $Δ$, our dynamic programming algorithm achieves $O^*(n^{O(Δ)})$ time complexity in the number of features $n$, where $O^*$ suppresses polynomial factors. To handle complex constraints consisting of multiple tree metrics, we introduce model behavior tensors that aggregate semiring values via convolution products over a tensor semiring. This algebraic approach efficiently constructs a model profile that captures the global landscape and trade-offs between criteria such as accuracy, size, and fairness. We demonstrate the utility of our software, emtrees, on real-world datasets, illustrating how ADTC facilitates evidence-based model selection in sensitive domains.","short_abstract":"Ensuring model reliability in Explainable AI requires a global assessment of the hypothesis space. We propose a formal framework for the exhaustive analysis of optimal and near-optimal decision trees, called Algebraic Decision Tree Counting (ADTC). Inspired by Algebraic Model Counting (AMC) in knowledge representation,...","url_abs":"https://arxiv.org/abs/2607.02069","url_pdf":"https://arxiv.org/pdf/2607.02069v1","authors":"[\"Hiroki Arimura\"]","published":"2026-07-02T12:03:11Z","proceeding":"cs.AI","tasks":"[\"cs.AI\"]","methods":"[]","has_code":false}