Deep learning in random neural fields: Numerical experiments via neural tangent kernel.

A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but highly correlated when they are in close proximity in receptive fields. In this paper, we investigate such neural fields in a multilayer architecture to investigate the supervised learning of the fields. We empirically compare the performances of our field model with those of randomly connected deep networks. The behavior of a randomly connected network is investigated on the basis of the key idea of the neural tangent kernel regime, a recent development in the machine learning theory of over-parameterized networks; for most randomly connected neural networks, it is shown that global minima always exist in their small neighborhoods. We numerically show that this claim also holds for our neural fields. In more detail, our model has two structures: (i) each neuron in a field has a continuously distributed receptive field, and (ii) the initial connection weights are random but not independent, having correlations when the positions of neurons are close in each layer. We show that such a multilayer neural field is more robust than conventional models when input patterns are deformed by noise disturbances. Moreover, its generalization ability can be slightly superior to that of conventional models.

EEG dipole source localization with information criteria for multiple particle filters.

Electroencephalography (EEG) is a non-invasive brain imaging technique that describes neural electrical activation with good temporal resolution. Source localization is required for clinical and functional interpretations of EEG signals, and most commonly is achieved via the dipole model; however, the number of dipoles in the brain should be determined for a reasonably accurate interpretation. In this paper, we propose a dipole source localization (DSL) method that adaptively estimates the dipole number by using a novel information criterion. Since the particle filtering process is nonparametric, it is not clear whether conventional information criteria such as Akaike's information criterion (AIC) and Bayesian information criterion (BIC) can be applied. In the proposed method, multiple particle filters run in parallel, each of which respectively estimates the dipole locations and moments, with the assumption that the dipole number is known and fixed; at every time step, the most predictive particle filter is selected by using an information criterion tailored for particle filters. We tested the proposed information criterion first through experiments on artificial datasets; these experiments supported the hypothesis that the proposed information criterion would outperform both AIC and BIC. We then analyzed real human EEG datasets collected during an auditory short-term memory task using the proposed method. We found that the alpha-band dipoles were localized to the right and left auditory areas during the auditory short-term memory task, which is consistent with previous physiological findings. These analyses suggest the proposed information criterion can work well in both model and real-world situations.