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Understanding the non-linear functional systems of neural networks at multiple scales with dimensionality reduction techniques

白石, 祥之 大阪大学 DOI:10.18910/82352

2021.03.24

概要

An objective of systems neuroscience is to clarify the functional significance of single neuron and neural networks and to identify task-related neural activities in real brains and artificial neural networks at various hierarchies, but there are several challenges. First, the input-output relationship of networks is usually nonlinear. Second, internal and measurement noise complicates measurement of the neuronal response.

Finally, the neuronal outputs are usually high-dimensional. These factors make it difficult to interpret the functional significance of the corresponding neural networks. Applying dimensionality reduction techniques to high-dimensional neural data will help clarify the underlying mechanisms and functional significance of the neural networks and remove the noise components. This framework works at various hierarchical layers, such as the responses of a single neuron, small neural network, and whole brain. To examine this hypothesis, in this study, I applied reverse correlation analysis for the activity of a single unit in a Deep Convolutional Neural Network (DCNN), which is considered a good model for the ventral visual pathway, and also applied dynamic mode decomposition (DMD) analysis to the electrocorticography (ECoG) recorded from electrodes placed just above the motor cortex. Using the reverse correlation technique, I successfully reconstructed the spatial profiles of receptive fields of DCNN units as clusters of excitatory and suppressive linear sub-filters. Using the sub-filters with a simple liner-nonlinear model, I predicted the responses of the units to Cartesian gratings and natural image stimuli to some extent. However, the model did not work at output layers in DCNNs, which may be attributed to the arbitrarily chosen nonlinear function. In contrast, DMD analysis successfully extracted ECoG patterns corresponding to a particular motor movement task by the Koopman operator as the composition operator of dynamics and observation function. In the DMD analysis, system nonlinearities were identified in a data-driven manner, and no arbitrary nonlinear functions needed to be introduced. Taken together, the findings strongly suggested that dimensionality reduction techniques, especially DMD, can be effective tools for understanding the functional significance of neural networks at various levels of hierarchy.

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