Title: Improving Zero-Shot Neural Architecture Search with Parameters Scoring. Abstract: The exceptional success of deep learning comes at the cost of long training sessions, and a slow iterative process of  proposing new architectures that have to be hand-engineered through years of experience. Neural Architecture Search (NAS) is the line of research that tries to automatically design architectures with better performances at a given task. The performance of a network in a task can be predicted by a score, even before the network is trained: this is referred to as zero-shot NAS. However, the existing score remains unreliable for architectures with high accuracy. We develop in this direction by exploring different related scores. We study their time efficiency and we improve on their dependence with the final accuracy, especially for high values of the score.  We propose a monotonicity metric to evaluate the adequate relative scoring of the architectures, as a way to avoid imposing a linearity assumption too early. We find that our use of noise improves the score, but a more substantial improvement comes when the evaluation of the score is done in the parameter space. We hope this effort will help clarify promising directions to speed up automatic discovery of good neural architectures without training.