The neural code that represents the world is transformed at each stage of a sensory pathway. These transformations enable downstream neurons to recode information they receive from earlier stages. Using the retinothalamic synapse as a model system, we developed a theoretical framework to identify stimulus features that are inherited, gained, or lost across stages. Specifically, we observed that thalamic spikes encode novel, emergent, temporal features not conveyed by single retinal spikes. Furthermore, we found that thalamic spikes are not only more informative than retinal ones, as expected, but also more independent. Next, we asked how thalamic spikes gain sensitivity to the emergent features. Explicitly, we found that the emergent features are encoded by retinal spike pairs and then recoded into independent thalamic spikes. Finally, we built a model of synaptic transmission that reproduced our observations. Thus, our results established a link between synaptic mechanisms and the recoding of sensory information.