# Informed deep hierarchical classification: a non-standard analysis inspired approach

arXiv: https://arxiv.org/abs/2409.16956 · HTML: https://mlsanity.com/paper/2409.16956/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 60 references that are in the map.
- First posted on arXiv 25 Sep 2024.

## Builds on (most cited first, 14 of 14)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [HDLTex: Hierarchical Deep Learning for Text Classification](https://mlsanity.com/paper/1709.08267/) (2017)
- [Coherent Hierarchical Multi-Label Classification Networks](https://mlsanity.com/paper/2010.10151/) (2020)
- [Deep Learning with Logical Constraints](https://mlsanity.com/paper/2205.00523/) (2022)
- [B-CNN: Branch Convolutional Neural Network for Hierarchical Classification](https://mlsanity.com/paper/1709.09890/) (2017)
- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [Towards Automated ICD Coding Using Deep Learning](https://mlsanity.com/paper/1711.04075/) (2017)
- [Hierarchical Taxonomy-Aware and Attentional Graph Capsule RCNNs for Large-Scale Multi-Label Text Classification](https://mlsanity.com/paper/1906.04898/) (2019)
- [Yoga-82: A New Dataset for Fine-grained Classification of Human Poses](https://mlsanity.com/paper/2004.10362/) (2020)
- [DeepGO: Predicting protein functions from sequence and interactions using a deep ontology-aware classifier](https://mlsanity.com/paper/1705.05919/) (2017)
- [Deep Hierarchical Classification for Category Prediction in E-commerce System](https://mlsanity.com/paper/2005.06692/) (2020)
- [A Non-Archimedean Interior Point Method for Solving Lexicographic Multi-Objective Quadratic Programming Problems](https://mlsanity.com/paper/2110.15658/) (2021)

## Built on by (most cited first, 2 of 2)

- [Multi-Label Plant Species Prediction with Metadata-Enhanced Multi-Head Vision Transformers](https://mlsanity.com/paper/2508.10457/) (2025)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)

## Abstract (arXiv)

This work proposes a novel approach to the deep hierarchical classification task, i.e., the problem of classifying data according to multiple labels organized in a rigid parent-child structure. It consists in a multi-output deep neural network equipped with specific projection operators placed before each output layer. The design of such an architecture, called lexicographic hybrid deep neural network (LH-DNN), has been possible by combining tools from different and quite distant research fields: lexicographic multi-objective optimization, non-standard analysis, and deep learning. To assess the efficacy of the approach, the resulting network is compared against the B-CNN, a convolutional neural network tailored for hierarchical classification tasks, on the CIFAR10, CIFAR100 (where it has been originally and recently proposed before being adopted and tuned for multiple real-world applications) and Fashion-MNIST benchmarks. Evidence states that an LH-DNN can achieve comparable if not superior performance, especially in the learning of the hierarchical relations, in the face of a drastic reduction of the learning parameters, training epochs, and computational time, without the need for ad-hoc loss functions weighting values.