The present disclosure provides projection neural networks and example applications thereof. In particular, the present disclosure provides a number of different architectures for projection neural networks, including two example architectures which can be referred to as: Self-Governing Neural Networks (SGNNs) and Projection Sequence Networks (ProSeqoNets). Each projection neural network can include one or more projection layers that project an input into a different space. For example, each projection layer can use a set of projection functions to project the input into a bit-space, thereby greatly reducing the dimensionality of the input and enabling computation with lower resource usage. As such, the projection neural networks provided herein are highly useful for on-device inference in resource-constrained devices. For example, the provided SGNN and ProSeqoNet architectures are particularly beneficial for on-device inference such as, for example, solving natural language understanding tasks on-device.