# Symbolic Branch Networks: Tree-Inherited Neural Models for Interpretable Multiclass Classification

arXiv: https://arxiv.org/abs/2507.01781 · HTML: https://mlsanity.com/paper/2507.01781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 2 Jul 2025.

## Builds on (most cited first, 6 of 6)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (2019)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [When Do Neural Nets Outperform Boosted Trees on Tabular Data?](https://mlsanity.com/paper/2305.02997/) (2023)
- [Neural Random Forests](https://mlsanity.com/paper/1604.07143/) (2016)

## Abstract (arXiv)

Symbolic Branch Networks (SBNs) are neural models whose architecture is inherited directly from an ensemble of decision trees. Each root-to-parent-of-leaf decision path is mapped to a hidden neuron, and the matrices W1 (feature-to-branch) and W2 (branch-to-class) encode the symbolic structure of the ensemble. Because these matrices originate from the trees, SBNs preserve transparent feature relevance and branch-level semantics while enabling gradient-based learning. The primary contribution of this work is SBN, a semi-symbolic variant that preserves branch semantics by keeping W2 fixed, while allowing W1 to be refined through learning. This controlled relaxation improves predictive accuracy without altering the underlying symbolic structure. Across 28 multiclass tabular datasets from the OpenML CC-18 benchmark, SBN consistently matches or surpasses XGBoost while retaining human-interpretable branch attributions. We also analyze SBN*, a fully symbolic variant in which both W1 and W2 are frozen and only calibration layers are trained. Despite having no trainable symbolic parameters, SBN* achieves competitive performance on many benchmarks, highlighting the strength of tree-derived symbolic routing as an inductive bias. Overall, these results show that symbolic structure and neural optimization can be combined to achieve strong performance while maintaining stable and interpretable internal representations.