Learning to adapt voluntary movements to an external perturbation, whether mechanical or visual, is faster during a second encounter than during the first. The mechanisms underlying this phenomenon, known as savings, remain unclear. Recent studies propose that the high dimensionality of neural control enables the retention of learning traces that may facilitate savings. To test this idea we used MotorNet, a framework for training recurrent neural networks (RNNs) to control biomechanical models of the human upper limb. RNNs were trained to perform reaching movements with a velocity-dependent force field (FF) and without (NF) in the sequence NF1 (baseline), FF1 (adaptation), NF2 (washout), and FF2 (re-adaptation). RNNs showed behavioural signatures of savings in the absence of any explicit contextual input signalling the presence or absence of the FF. Savings was more robust in RNNs with larger numbers of units. We identified a component of RNN activity associated with savings--a shift in preparatory activity that persisted even after washout. Displacing this preparatory activity in the direction of the shift enhanced savings, whereas perturbations in the opposite direction reduced or eliminated savings. These findings suggest a potential neural basis for motor memory retention underlying savings that is reliant on the high dimensionality of neural space, and is independent of cognitive or strategic learning.