# Loss Surface Modality of Feed-Forward Neural Network Architectures

## TL;DR

This paper investigates how the architecture of feed-forward neural networks affects the shape and complexity of their loss surfaces, revealing that width and depth influence the number of local minima and the landscape's exploitable features.

## Contribution

It provides a detailed analysis of how network width and depth impact loss surface modality using fitness landscape analysis, clarifying their roles in optimization difficulty.

## Key findings

- Increasing problem dimensionality makes the loss surface more searchable.
- Wider hidden layers reduce local minima and simplify the global attractor.
- Deeper architectures sharpen the global attractor, affecting exploitability.

## Abstract

It has been argued in the past that high-dimensional neural networks do not exhibit local minima capable of trapping an optimisation algorithm. However, the relationship between loss surface modality and the neural architecture parameters, such as the number of hidden neurons per layer and the number of hidden layers, remains poorly understood. This study employs fitness landscape analysis to study the modality of neural network loss surfaces under various feed-forward architecture settings. An increase in the problem dimensionality is shown to yield a more searchable and more exploitable loss surface. An increase in the hidden layer width is shown to effectively reduce the number of local minima, and simplify the shape of the global attractor. An increase in the architecture depth is shown to sharpen the global attractor, thus making it more exploitable.