On the distribution of performance from multiple neural-network trials

The performance of neural-network simulations is often reported in terms of the mean and standard deviation of a number of simulations performed with different starting conditions. However, in many cases, the distribution of the individual results does not approximate a Gaussian distribution, may not be symmetric, and may be multimodal. We present the distribution of results for practical problems and show that assuming Gaussian distributions can significantly affect the interpretation of results, especially those of comparison studies. For a controlled task which we consider, we find that the distribution of performance is skewed toward better performance for smoother target functions and skewed toward worse performance for more complex target functions. We propose new guidelines for reporting performance which provide more information about the actual distribution.