Active simultaneously transmitting and reflecting surfaces (ASTARS) have attracted growing research interest due to its ability to alleviate multiplicative fading and reshape the electromagnetic environment across the entire space. In this paper, we utilise ASTARS to assist the federated learning (FL) uplink model transfer and further reduce the number of uploaded parameter counts through over-the-air (OTA) computing techniques. The impact of model aggregation errors on ASTARS-aided FL uplink networks is characterized. We derive an upper bound on the aggregation error of the OTA-FL model and quantify the training loss due to communication errors. Then, we define the performance of OTA-FL as a joint optimization problem that encompasses both the assignment of received beams and the phase shifting of ASTARS, aiming to achieve the maximum learning efficiency and high-quality signal transmission. Numerical results demonstrate that: i) The FL accuracy in ASTARS uplink networks are enhanced compared to that in state-of-the-art networks; ii) The ASTARS enabled FL system achieves the better learning accuracy using fewer active units than other baseline, especially when the dataset is more discrete; and iii) FL accuracy improves with higher amplification power, but excessive amplification makes thermal noise the dominant source of error.