Learning useful information across long time lags is a critical and difficult problem for temporal neural models in tasks such as language modeling. Existing architectures that address the issue are often complex and costly to train. The differential state framework (DSF) is a simple and high-performing design that unifies previously introduced gated neural models. DSF models maintain longer-term memory by learning to interpolate between a fast-changing data-driven representation and a slowly changing, implicitly stable state. Within the DSF framework, a new architecture is presented, the delta-RNN. This model requires hardly any more parameters than a classical, simple recurrent network. In language modeling at the word and character levels, the delta-RNN outperforms popular complex architectures, such as the long short-term memory (LSTM) and the gated recurrent unit (GRU), and, when regularized, performs comparably to several state-of-the-art baselines. At the subword level, the delta-RNN's performance is comparable to that of complex gated architectures.