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.

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.

The categorical compositional distributional (DisCoCat) model of meaning developed by [7] has been successful in modeling various aspects of meaning. However, it fails to model the fact that language can change. We give an approach to DisCoCat that allows us to represent language models and translations between them, enabling us to describe translations from one language to another, or changes within the same language. We unify the product space representation given in [7] and the functorial description in [16], in a way that allows us to view a language as a catalogue of meanings. We formalize the notion of a lexicon in DisCoCat, and define a dictionary of meanings between two lexicons. All this is done within the framework of monoidal categories. We give examples of how to apply our methods, and give a concrete suggestion for compositional translation in corpora.

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