# Backpropagation Neural Tree

arXiv: https://arxiv.org/abs/2202.02248 · HTML: https://mlsanity.com/paper/2202.02248/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Adaptive Neural Trees](https://mlsanity.com/paper/1807.06699/) (2018)
- [Generalizing Pooling Functions in Convolutional Neural Networks: Mixed, Gated, and Tree](https://mlsanity.com/paper/1509.08985/) (2015)
- [An Experimental Comparison of Old and New Decision Tree Algorithms](https://mlsanity.com/paper/1911.03054/) (2019)
- [Multi-Objective Optimisation of Multi-Output Neural Trees](https://mlsanity.com/paper/2010.04524/) (2020)
- [Ensemble of heterogeneous flexible neural trees using multiobjective genetic programming](https://mlsanity.com/paper/1705.05592/) (2017)

## Built on by (most cited first, 3 of 3)

- [Fragility, Robustness and Antifragility in Deep Learning](https://mlsanity.com/paper/2312.09821/) (2023)
- [Dendritic Integration Based Quadratic Neural Networks Outperform Traditional Aritificial Ones](https://mlsanity.com/paper/2307.13609/) (2023)
- [Learning local discrete features in explainable-by-design convolutional neural networks](https://mlsanity.com/paper/2411.00139/) (2024)

## Abstract (arXiv)

We propose a novel algorithm called Backpropagation Neural Tree (BNeuralT), which is a stochastic computational dendritic tree. BNeuralT takes random repeated inputs through its leaves and imposes dendritic nonlinearities through its internal connections like a biological dendritic tree would do. Considering the dendritic-tree like plausible biological properties, BNeuralT is a single neuron neural tree model with its internal sub-trees resembling dendritic nonlinearities. BNeuralT algorithm produces an ad hoc neural tree which is trained using a stochastic gradient descent optimizer like gradient descent (GD), momentum GD, Nesterov accelerated GD, Adagrad, RMSprop, or Adam. BNeuralT training has two phases, each computed in a depth-first search manner: the forward pass computes neural tree's output in a post-order traversal, while the error backpropagation during the backward pass is performed recursively in a pre-order traversal. A BNeuralT model can be considered a minimal subset of a neural network (NN), meaning it is a "thinned" NN whose complexity is lower than an ordinary NN. Our algorithm produces high-performing and parsimonious models balancing the complexity with descriptive ability on a wide variety of machine learning problems: classification, regression, and pattern recognition.