Demand forecasting faces challenges induced by Peak Events (PEs) corresponding to special periods such as promotions and holidays. Peak events create significant spikes in demand followed by demand ramp down periods. Neural networks like MQCNN and MQT overreact to demand peaks by carrying over the elevated PE demand into subsequent Post-Peak-Event (PPE) periods, resulting in significantly over-biased forecasts. To tackle this challenge, we introduce a neural forecasting model called Split Peak Attention DEcomposition, SPADE. This model reduces the impact of PEs on subsequent forecasts by modeling forecasting as consisting of two separate tasks: one for PEs; and the other for the rest. Its architecture then uses masked convolution filters and a specialized Peak Attention module. We show SPADE's performance on a worldwide retail dataset with hundreds of millions of products. Our results reveal a reduction in PPE degradation by 4.5% and an improvement in PE accuracy by 3.9%, relative to current production models.