Systems, methods, devices, and other techniques are described herein for training and using neural networks to encode inputs and to process encoded inputs, e.g., to reconstruct inputs from the encoded inputs. A neural network system can include an encoder neural network, a trusted decoder neural network, and an adversary decoder neural network. The encoder neural network processes a primary neural network input and a key input to generate an encoded representation of the primary neural network input. The trusted decoder neural network processes the encoded representation and the key input to generate a first estimated reconstruction of the primary neural network input. The adversary decoder neural network processes the encoded representation without the key input to generate a second estimated reconstruction of the primary neural network input. The encoder and trusted decoder neural networks can be trained jointly, and these networks trained adversarially to the adversary decoder neural network.