Wiktor Młynarski

Wiktor Młynarski, Josh H. McDermott

Interaction with the world requires an organism to transform sensory signals into representations in which behaviorally meaningful properties of the environment are made explicit. These representations are derived through cascades of neuronal processing stages in which neurons at each stage recode the output of preceding stages. Explanations of sensory coding may thus involve understanding how low-level patterns are combined into more complex structures. Although models exist in the visual domain to explain how mid-level features such as junctions and curves might be derived from oriented filters in early visual cortex, little is known about analogous grouping principles for mid-level auditory representations. We propose a hierarchical generative model of natural sounds that learns combinations of spectrotemporal features from natural stimulus statistics. In the first layer the model forms a sparse convolutional code of spectrograms using a dictionary of learned spectrotemporal kernels. To generalize from specific kernel activation patterns, the second layer encodes patterns of time-varying magnitude of multiple first layer coefficients. Because second-layer features are sensitive to combinations of spectrotemporal features, the representation they support encodes more complex acoustic patterns than the first layer. When trained on corpora of speech and environmental sounds, some second-layer units learned to group spectrotemporal features that occur together in natural sounds. Others instantiate opponency between dissimilar sets of spectrotemporal features. Such groupings might be instantiated by neurons in the auditory cortex, providing a hypothesis for mid-level neuronal computation.

Wiktor Mlynarski

Complex-valued sparse coding is a data representation which employs a dictionary of two-dimensional subspaces, while imposing a sparse, factorial prior on complex amplitudes. When trained on a dataset of natural image patches, it learns phase invariant features which closely resemble receptive fields of complex cells in the visual cortex. Features trained on natural sounds however, rarely reveal phase invariance and capture other aspects of the data. This observation is a starting point of the present work. As its first contribution, it provides an analysis of natural sound statistics by means of learning sparse, complex representations of short speech intervals. Secondly, it proposes priors over the basis function set, which bias them towards phase-invariant solutions. In this way, a dictionary of complex basis functions can be learned from the data statistics, while preserving the phase invariance property. Finally, representations trained on speech sounds with and without priors are compared. Prior-based basis functions reveal performance comparable to unconstrained sparse coding, while explicitely representing phase as a temporal shift. Such representations can find applications in many perceptual and machine learning tasks.