Independent Manifolds in the Zebra Finch Song: A Strategy for Robust Social Interaction

The song of the male Zebra Finch is the primary means of identification of one individual from other males of the same species. In order to serve that purpose, it needs to have a statistical structure that allows robust separation from the rich acoustic environment in the bird colony, as well as enough degrees of freedom to allow specificity at the level of the individual bird. Since second-order structure cannot be used for source separation of linear mixtures—typical in the Zebra Finch acoustic environment—higher-order statistical structures must support the social function of the song. Here we study the dynamics of temporally localized elements of an adult male’s song, and find that, when viewed suitably through Poincare sections, the evolution of the sound lies close to a one-dimensional curved manifold, non-trivially embedded in a high-dimensional linear space. On one hand, the nonlinear property of the manifold generally survives linear mixtures, and the one-dimensionality places significant constraints on the structure that could serve as the basis for robust separation. On the other hand, the degrees freedom in the embedding into the high-dimensional space provide enough flexibility for biometric identification of individuals. Also, we discuss how the known properties of the sound-production apparatus of the Zebra Finch can be employed in support of this statistical structure.