Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for training a neural network including a first subnetwork followed by a second subnetwork on training inputs by optimizing an objective function. In one aspect, a method includes processing a training input using the neural network to generate a training model output, including processing a subnetwork input for the training input using the first subnetwork to generate a subnetwork activation for the training input in accordance with current values of parameters of the first subnetwork, and providing the subnetwork activation as input to the second subnetwork; determining a synthetic gradient of the objective function for the first subnetwork by processing the subnetwork activation using a synthetic gradient model in accordance with current values of parameters of the synthetic gradient model; and updating the current values of the parameters of the first subnetwork using the synthetic gradient.

Abstract: A halfshaft assembly in a vehicle is disclosed. The halfshaft assembly includes a hub and a mating universal joint, such as a constant-velocity joint. The hub has a plurality of hub-teeth arranged annularly about an axis. The constant-velocity joint has a plurality of joint-teeth arranged annularly about the axis and engaged with the hub-teeth. Between each joint-tooth is a joint-root. The top, outermost surface of each tooth facing away from adjacent roots extends at a first angle with respect to the central axis. The root extends at a second angle with respect to the central axis. The angles are different such that the height of the tooth varies along the same tooth along the length of the tooth. Each tooth has involute side surfaces. The joint-teeth form a conical or inverse-conical shape.