Accurate perception of objects within the environment independent of context is essential for the survival of an organism. While neurons that respond in an invariant manner to identity-preserving transformations of objects are thought to provide a neural correlate of context-independent perception, how these emerge in the brain remains poorly understood. Here we demonstrate that burst firing in neural populations can give rise to an invariant representation of highly heterogeneous natural communication stimuli. Multi-unit recordings from central sensory neural populations showed that considering burst spike trains led to invariant representations at the population but not the single neuron level. Computational modeling further revealed that optimal invariance is achieved for levels of burst firing seen experimentally. Taken together, our results demonstrate a novel function for burst firing towards establishing invariant representations of sensory input in neural populations.