# Ghost Features and Spooky Transfer Learning for Hypercomplex-Valued Neural Networks

arXiv: https://arxiv.org/abs/2608.07735 · HTML: https://mlsanity.com/paper/2608.07735/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 10 of 10)

- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [GhostNet: More Features from Cheap Operations](https://mlsanity.com/paper/1911.11907/) (2019)
- [Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with 1/n Parameters](https://mlsanity.com/paper/2102.08597/) (2021)
- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)
- [Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2401.02277/) (2024)
- [A General Framework for Hypercomplex-valued Extreme Learning Machines](https://mlsanity.com/paper/2101.06166/) (2021)
- [Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2209.02456/) (2022)
- [Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2309.07716/) (2023)
- [Novel computational workflows for natural and biomedical image processing based on hypercomplex algebras](https://mlsanity.com/paper/2502.07758/) (2025)

## Abstract (arXiv)

Hypercomplex numbers extend the concept of complex numbers by introducing additional imaginary components. Besides increasing dimensionality, operations on the imaginary parts provide algebraic and geometrical properties that can be beneficial for solving machine learning problems. In this paper, we show how to create hypercomplex-valued neural network layers where the real part corresponds to the output of a traditional real-valued layer. The additional imaginary parts of these hypercomplex-valued layers produce what we call ``ghost features,'' which contain enhanced information that is not present in the output of the real-valued layer. Moreover, ghost features can be effectively integrated into a trained neural network through a process we refer to as ``spooky transfer learning.'' This approach allows us to harness the richness of ghost features, leading to more efficient neural networks. The source code and Jupyter Notebook are available at https://github.com/mevalle/v-nets/.