Feedback processes are believed to play an important role in the Arctic region and to be responsible for the polar amplification of global warming found in climate models. However, it is difficult to quantify the important feedback loops because of the many interactions among the relevant climate variables, particularly the nonlinear behavior of these interactions. A neural network technique are used to examine the relationships in cloud-radiation feedback with the measurements at SHEBA site in the Beaufort Sea. Climate sensitivities are represented as the Jacobians of a neural network, which are the first derivatives of one variable with respect to another variable. Quantitative relationships between climate variables, including longwave cloud radiative forcing, cloud fraction, liquid water path, cloud base height, and cloud base temperature, are obtained at these two sites. Results from a nonlinear approach using the neural network is compared with that from Shupe and Intrieri (2004).