Bernhard Schäfl¹, Lukas Gruber¹, Angela Bitto-Nemling^{1, 2}, Sepp Hochreiter^{1, 2}

¹ ELLIS Unit Linz and LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Austria
² Institute of Advanced Research in Artificial Intelligence (IARAI)

While Deep Learning excels in structured data as encountered in vision and natural language processing, it failed to meet its expectations on tabular data. For tabular data, Support Vector Machines (SVMs), Random Forests, and Gradient Boosting are the best performing techniques with Gradient Boosting in the lead. Recently, we saw a surge of Deep Learning methods that were tailored to tabular data but still underperformed compared to Gradient Boosting on small-sized datasets. We suggest "Hopular", a novel Deep Learning architecture for medium- and small-sized datasets, where each layer is equipped with continuous modern Hopfield networks. The modern Hopfield networks use stored data to identify feature-feature, feature-target, and sample-sample dependencies. Hopular's novelty is that every layer can directly access the original input as well as the whole training set via stored data in the Hopfield networks. Therefore, Hopular can step-wise update its current model and the resulting prediction at every layer like standard iterative learning algorithms. In experiments on small-sized tabular datasets with less than 1,000 samples, Hopular surpasses Gradient Boosting, Random Forests, SVMs, and in particular several Deep Learning methods. In experiments on medium-sized tabular data with about 10,000 samples, Hopular outperforms XGBoost, CatBoost, LightGBM and a state-of-the art Deep Learning method designed for tabular data. Thus, Hopular is a strong alternative to these methods on tabular data.

The full paper is available at: https://arxiv.org/abs/2206.00664.

The software was developed and tested on the following 64-bit operating systems:

• Rocky Linux 8.5 (Green Obsidian)
• macOS 12.4 (Monterey)

As the development environment, Python 3.8.3 in combination with PyTorch Lightning 1.4.9 was used. More details on how to install PyTorch Lightning are available on the official project page.

The recommended way to install the software is to use pip/pip3:

$ pip3 install git+https://github.com/ml-jku/hopular

Hopular has two modes of operation:

• list for displaying various information.
• optim for optimizing Hopular using specified hyperparameters.

More information regarding the operation modes is accessible via the -h flag (or, alternatively, by --help).

$ hopular -h

$ hopular <mode> -h

To display all available datasets, the --datasets flag has to be specified in the list mode.

$ hopular list --datasets 

Optimizing a Hopular model using the default hyperparameters is achieved by specifying the corresponding dataset in the optim mode.

$ hopular optim --dataset <dataset_name>

To optimize a Hopular model on the GlassIdentificationDataset using the default hyperparameters, only the dataset name itself needs to be specified. More details on the default values are available in the console interface implementation.

$ hopular optim --dataset "GlassIdentificationDataset"

Optimizing a smaller Hopular model on the GlassIdentificationDataset utilizing only 4 modern Hopfield networks, 2 iterative refinement blocks, and a scaling factor of 10 is achieved by manually specifying the respective hyperparameters.

$ hopular optim --dataset "GlassIdentificationDataset" --num_heads 4 --num_blocks 2 --scaling_factor 10

The datasets, which are part of this repository, are publicly available and may be licensed differently. Hence, the LICENSE of this repository does not apply to them. More details on the origin of the datasets are available in the accompanying paper.

This repository is MIT-style licensed (see LICENSE), except where noted otherwise.