Atlantic Multidecadal Variability (AMV) describes fluctuations of North Atlantic sea surface temperature (SST) with a typical cycle of 60-70 years. Despite its numerous impacts on climate over the surrounding continents, the relative importance of oceanic and atmospheric drivers of AMV are still highly contested. Thus, both physical understanding and prediction of AMV, specifically its extreme states, is of great social relevance for anticipating the trajectory of North Atlantic climate in the coming decades. In this study, we train feed-forward (FNNs) and convolutional neural networks (CNNs) to predict the state of AMV (positive, negative, or neutral) up to 25 years ahead of time. The networks are trained with combinations of various atmospheric and oceanic predictors using output from the Community Earth System Model 1 Large Ensemble Project. We evaluate the sensitivity of skill to predictor combination, season, and subregion of the North Atlantic to gain insight on critical processes that contribute to high-confidence predictions. We find that the networks outperform traditional baseline persistence forecasts and multiple linear regression, particularly at decadal and longer timescales. Additionally, training the with more persistent oceanic predictors, such as sea surface salinity, yielded higher skill at these longer timescales. We additionally employ layer-wise relevance propagation (LRP) to retrieve the weights learned by these networks and identify the patterns in the predictors that lead to successful prediction of AMV states. These patterns are compared with known fingerprints of AMV drivers identified in the literature, such as the North Atlantic Oscillation and Atlantic Meriodional Overturning Circulation.