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In this paper we propose a real-time and robust solution to large-scale multiple rotation averaging. Until recently, Multiple rotation averaging problem had been solved using conventional iterative optimization algorithms. Such methods employed robust cost functions that were chosen based on assumptions made about the sensor noise and outlier distribution. In practice, these assumptions do not always fit real datasets very well. A recent work showed that the noise distribution could be learnt using a graph neural network. This solution required a second network for outlier detection and removal as the averaging network was sensitive to a poor initialization. In this paper we propose a single-stage graph neural network that can robustly perform rotation averaging in the presence of noise and outliers. Our method uses all observations, suppressing outliers effects through the use of weighted averaging and an attention mechanism within the network design. The result is a network that is faster, more robust and can be trained with less samples than the previous neural approach, ultimately outperforming conventional iterative algorithms in accuracy and in inference times.