Dropout and DropConnect are well-known techniques that apply a consistent drop rate to randomly deactivate neurons or edges in a neural network layer during training. This paper introduces a novel methodology that assigns dynamic drop rates to each edge within a layer, uniquely tailoring the dropping process without incorporating additional learning parameters. We perform experiments on synthetic and openly available datasets to validate the effectiveness of our approach. The results demonstrate that our method outperforms Dropout, DropConnect, and Standout, a classic mechanism known for its adaptive dropout capabilities. Furthermore, our approach improves the robustness and generalization of neural network training without increasing computational complexity. The complete implementation of our methodology is publicly accessible for research and replication purposes at https://github.com/ericabd888/Adjusting-the-drop-probability-in-DropConnect-based-on-the-magnitude-of-the-gradient/.