Capacity Studies for a Differential Growing Neural Gas

TL;DR

This paper evaluates the capacity of a Differential Growing Neural Gas (DGNG) model in representing complex input data, analyzing how network parameters affect its ability to distinguish inputs, with implications for computational neuroscience.

Contribution

It provides an empirical analysis of how layer sizes influence the capacity of DGNG models on the Fashion-MNIST dataset, including parameter discussions and plausibility checks.

Findings

DGNG can effectively represent complex datasets like Fashion-MNIST.

Layer size variation impacts the capacity and scalability of DGNG.

The model maintains meaningful input representations at moderate sizes.

Abstract

In 2019 Kerdels and Peters proposed a grid cell model (GCM) based on a Differential Growing Neural Gas (DGNG) network architecture as a computationally efficient way to model an Autoassociative Memory Cell (AMC) \cite{Kerdels_Peters_2019}. An important feature of the DGNG architecture with respect to possible applications in the field of computational neuroscience is its \textit{capacity} refering to its capability to process and uniquely distinguish input signals and therefore obtain a valid representation of the input space. This study evaluates the capacity of a two layered DGNG grid cell model on the Fashion-MNIST dataset. The focus on the study lies on the variation of layer sizes to improve the understanding of capacity properties in relation to network parameters as well as its scaling properties. Additionally, parameter discussions and a plausability check with a pixel/segment variation method are provided. It is concluded, that the DGNG model is able to obtain a meaningful and plausible representation of the input space and to cope with the complexity of the Fashion-MNIST dataset even at moderate layer sizes.