# Multitask Hopfield Networks

## TL;DR

This paper introduces HoMTask, a novel multitask Hopfield Network model that leverages task sharing to improve classification accuracy, demonstrating competitive results with existing semi-supervised graph algorithms.

## Contribution

First multitask model based on Hopfield Networks that effectively integrates multiple tasks into a single energy-based framework.

## Key findings

- HoMTask improves classification over single-task Hopfield Networks.
- Achieves competitive performance with state-of-the-art semi-supervised algorithms.
- Provides theoretical guarantees on model coherence and convergence.

## Abstract

Multitask algorithms typically use task similarity information as a bias to speed up and improve the performance of learning processes. Tasks are learned jointly, sharing information across them, in order to construct models more accurate than those learned separately over single tasks. In this contribution, we present the first multitask model, to our knowledge, based on Hopfield Networks (HNs), named HoMTask. We show that by appropriately building a unique HN embedding all tasks, a more robust and effective classification model can be learned. HoMTask is a transductive semi-supervised parametric HN, that minimizes an energy function extended to all nodes and to all tasks under study. We provide theoretical evidence that the optimal parameters automatically estimated by HoMTask make coherent the model itself with the prior knowledge (connection weights and node labels). The convergence properties of HNs are preserved, and the fixed point reached by the network dynamics gives rise to the prediction of unlabeled nodes. The proposed model improves the classification abilities of singletask HNs on a preliminary benchmark comparison, and achieves competitive performance with state-of-the-art semi-supervised graph-based algorithms.