# Dynamic multilayer growth: Parallel vs. sequential approaches

## TL;DR

This paper explores whether adding hidden units to a neural network should happen in parallel or sequentially across layers, finding that parallel growth can lead to better performance.

## Contribution

The paper introduces a modified constructive algorithm for parallel growth of hidden units in multilayer networks and compares it with sequential approaches.

## Key findings

- Parallel growth of hidden units in multiple layers can achieve comparable or better performance than sequential growth.
- Parallel growth encourages the development of narrower, deeper architectures suited to specific tasks.
- Dynamic growth inspired by population dynamics can adapt both width and depth of neural networks effectively.

## Abstract

The decision of when to add a new hidden unit or layer is a fundamental challenge for constructive algorithms. It becomes even more complex in the context of multiple hidden layers. Growing both network width and depth offers a robust framework for leveraging the ability to capture more information from the data and model more complex representations. In the context of multiple hidden layers, should growing units occur sequentially with hidden units only being grown in one layer at a time or in parallel with hidden units growing across multiple layers simultaneously? The effects of growing sequentially or in parallel are investigated using a population dynamics-inspired growing algorithm in a multilayer context. A modified version of the constructive growing algorithm capable of growing in parallel is presented. Sequential and parallel growth methodologies are compared in a three-hidden layer multilayer perceptron on several benchmark classification tasks. Several variants of these approaches are developed for a more in-depth comparison based on the type of hidden layer initialization and the weight update methods employed. Comparisons are then made to another sequential growing approach, Dynamic Node Creation. Growing hidden layers in parallel resulted in comparable or higher performances than sequential approaches. Growing hidden layers in parallel promotes growing narrower deep architectures tailored to the task. Dynamic growth inspired by population dynamics offers the potential to grow the width and depth of deeper neural networks in either a sequential or parallel fashion.