The effect of the choice of neural network depth and breadth on the size of its hypothesis space
arXiv:1806.02460v1
Originality Synthesis-oriented
AI Analysis
This provides a theoretical insight into neural network design for researchers, but it is incremental as it builds on existing hypothesis space analysis.
The paper investigates how neural network depth and breadth affect the size of the hypothesis space, finding that the number of unique function mappings is inversely proportional to the product of factorials of neuron counts per hidden layer.
We show that the number of unique function mappings in a neural network hypothesis space is inversely proportional to $\prod_lU_l!$, where $U_{l}$ is the number of neurons in the hidden layer $l$.