Temporal coherence

The fundamental results relating natural stimulus statistics to the structure and functionality of neurons in the primary visual cortex were obtained with static image data. These results suggested that the defining property of the static neural code at the simple-cell level is sparseness / statistical independence.

It is natural to ask what kind of temporal properties this neural code has. Our research has shown that the defining temporal property of the neural code at the simple-cell level seems to be that the output of a neuron consists of periods of high activity (burst code). This has also been called temporal coherence of activity levels. This principle is an alternative to sparseness in the sense that both result in the emergence of simple-cell-like receptive fields from natural image data. The following image shows the receptive fields estimated using temporal coherence:

We have also extended the concept of temporal dependencies of activity levels to a model which captures both temporal and spatiotemporal dependencies - that is, activity dependencies between two different neurons at nearby time points. This model can be formulated as a two-layer autoregressive model. The first layer is similar to the standard linear model of simple cells. The second layer, however, describes a connectivity pattern between simple cells and higher-level units; these higher-level units can be related to complex cells. When the model is estimated from natural image data, the result exhibits both simple-cell-like receptive fields (in the first layer), and a V1-like topography / complex-cell-like pooling of simple cells (in the second layer):

Finally, further work by us has resulted in a model which is able to unify the previously modelled spatial and temporal properties of the neural code: sparseness, spatial activity bubbles and temporal bursts. In this model, neural activity on the primary visual cortex is described by spatiotemporal bubbles of activity. The model is able to learn both simple-cell-like receptive fields and a topographic organization for these cells; the organization resembles that observed on the visual cortex.

References

• Jarmo Hurri and Aapo Hyvärinen: Simple-Cell-Like Receptive Fields Maximize Temporal Coherence in Natural Video. (final / draft) Neural Computation, volume 15, number 3, pages 663-691, 2003.
• Jarmo Hurri and Aapo Hyvärinen: Temporal and spatiotemporal coherence in simple-cell responses: A generative model of natural image sequences. (final / draft) Network: Computation in Neural Systems, volume 14, number 3, pages 527-551, 2003.
• Aapo Hyvärinen, Jarmo Hurri, and Jaakko Väyrynen: Bubbles: A Unifying Framework for Low-Level Statistical Properties of Natural Image Sequences. (final / draft) Journal of the Optical Society of America A, volume 20, number 7, pages 1237-1252, 2003.
• Jarmo Hurri: Computational Models Relating Properties of Visual Neurons to Natural Stimulus Statistics. PhD thesis, Helsinki University of Technology, 2003.