# Multi-Element Long Distance Dependencies: Using SPk Languages to Explore the Characteristics of Long-Distance Dependencies

## TL;DR

This paper investigates the characteristics of long-distance dependencies in datasets generated by Strictly k-Piecewise languages, revealing the importance of multiple interacting elements and suggesting attention mechanisms as a potential modeling approach.

## Contribution

It introduces a systematic analysis of LDDs using SPk languages and highlights the need for improved attention mechanisms to model multi-element dependencies effectively.

## Key findings

- Number of interacting elements is key in LDDs
- Attention mechanisms may help model multi-element LDDs
- More efficient attention mechanisms are needed

## Abstract

In order to successfully model Long Distance Dependencies (LDDs) it is necessary to understand the full-range of the characteristics of the LDDs exhibited in a target dataset. In this paper, we use Strictly k-Piecewise languages to generate datasets with various properties. We then compute the characteristics of the LDDs in these datasets using mutual information and analyze the impact of factors such as (i) k, (ii) length of LDDs, (iii) vocabulary size, (iv) forbidden subsequences, and (v) dataset size. This analysis reveal that the number of interacting elements in a dependency is an important characteristic of LDDs. This leads us to the challenge of modelling multi-element long-distance dependencies. Our results suggest that attention mechanisms in neural networks may aide in modeling datasets with multi-element long-distance dependencies. However, we conclude that there is a need to develop more efficient attention mechanisms to address this issue.