The capacity for sensory systems to encode relevant information that is invariant to many stimulus changes is central to normal, real-world, cognitive function. This invariance is thought to be reflected in the complex spatiotemporal activity patterns of neural populations, but our understanding of population-level representational invariance remains coarse. Applied topology is a promising tool to discover invariant structure in large datasets. Here, we use topological techniques to characterize and compare the spatiotemporal pattern of coactive spiking within populations of simultaneously recorded neurons in the secondary auditory region caudal medial neostriatum of European starlings (Sturnus vulgaris). We show that the pattern of population spike train coactivity carries stimulus-specific structure that is not reducible to that of individual neurons. We then introduce a topology-based similarity measure for population coactivity that is sensitive to invariant stimulus structure and show that this measure captures invariant neural representations tied to the learned relationships between natural vocalizations. This demonstrates one mechanism whereby emergent stimulus properties can be encoded in population activity, and shows the potential of applied topology for understanding invariant representations in neural populations.SIGNIFICANCE STATEMENT Information in neural populations is carried by the temporal patterns of spikes. We applied novel mathematical tools from the field of algebraic topology to quantify the structure of these temporal patterns. We found that, in a secondary auditory region of a songbird, these patterns reflected invariant information about a learned stimulus relationship. These results demonstrate that topology provides a novel approach for characterizing neural responses that is sensitive to invariant relationships that are critical for the perception of natural stimuli.

Human speech possesses a rich hierarchical structure that allows for meaning to be altered by words spaced far apart in time. Conversely, the sequential structure of nonhuman communication is thought to follow non-hierarchical Markovian dynamics operating over only short distances. Here, we show that human speech and birdsong share a similar sequential structure indicative of both hierarchical and Markovian organization. We analyze the sequential dynamics of song from multiple songbird species and speech from multiple languages by modeling the information content of signals as a function of the sequential distance between vocal elements. Across short sequence-distances, an exponential decay dominates the information in speech and birdsong, consistent with underlying Markovian processes. At longer sequence-distances, the decay in information follows a power law, consistent with underlying hierarchical processes. Thus, the sequential organization of acoustic elements in two learned vocal communication signals (speech and birdsong) shows functionally equivalent dynamics, governed by similar processes.