Biomedical subjects

Xiaohui Xie

Publications and source records attributed to Xiaohui Xie.

5 recordsLinked to original sources

PubMed2003

Equivalence of backpropagation and contrastive Hebbian learning in a layered network.

Backpropagation and contrastive Hebbian learning are two methods of training networks with hidden neurons. Backpropagation computes an error signal for the output neurons and spreads it over the hidden neurons. Contrastive Hebbian learning involves clamping the output neurons at desired values and letting the effect spread through feedback connections over the entire network. To investigate the relationship between these two forms of learning, we consider a special case in which they are identical: a multilayer perceptron with linear output units, to which weak feedback connections have been added. In this case, the change in network state caused by clamping the output neurons turns out to be the same as the error signal spread by backpropagation, except for a scalar prefactor. This suggests that the functionality of backpropagation can be realized alternatively by a Hebbian-type learning algorithm, which is suitable for implementation in biological networks.

Algorithms↗

PubMed2002

Double-ring network model of the head-direction system.

In the head-direction system, the orientation of an animal's head in space is encoded internally by persistent activities of a pool of cells whose firing rates are tuned to the animal's directional heading. To maintain an accurate representation of the heading information when the animal moves, the system integrates horizontal angular head-velocity signals from the vestibular nuclei and updates the representation of directional heading. The integration is a difficult process, given that head velocities can vary over a large range and the neural system is highly nonlinear. Previous models of integration have relied on biologically unrealistic mechanisms, such as instantaneous changes in synaptic strength, or very fast synaptic dynamics. In this paper, we propose a different integration model with two populations of neurons, which performs integration based on the differential input of the vestibular nuclei to these two populations. We mathematically analyze the dynamics of the model and demonstrate that with carefully tuned synaptic connections it can accurately integrate a large range of the vestibular input, with potentially slow synapses.

Animals↗

PubMed2002

Nonlinear dynamics of direction-selective recurrent neural media.

The direction selectivity of cortical neurons can be accounted for by asymmetric lateral connections. Such lateral connectivity leads to a network dynamics with characteristic properties that can be exploited for distinguishing in neurophysiological experiments this mechanism for direction selectivity from other possible mechanisms. We present a mathematical analysis for a class of direction-selective neural models with asymmetric lateral connections. Contrasting with earlier theoretical studies that have analyzed approximations of the network dynamics by neglecting nonlinearities using methods from linear systems theory, we study the network dynamics with nonlinearity taken into consideration. We show that asymmetrically coupled networks can stabilize stimulus-locked traveling pulse solutions that are appropriate for the modeling of the responses of direction-selective neurons. In addition, our analysis shows that outside a certain regime of stimulus speeds the stability of these solutions breaks down, giving rise to lurching activity waves with specific spatiotemporal periodicity. These solutions, and the bifurcation by which they arise, cannot be easily accounted for by classical models for direction selectivity.

Animals↗

PubMed2002

Selectively grouping neurons in recurrent networks of lateral inhibition.

Winner-take-all networks have been proposed to underlie many of the brain's fundamental computational abilities. However, not much is known about how to extend the grouping of potential winners in these networks beyond single neuron or uniformly arranged groups of neurons. We show that competition between arbitrary groups of neurons can be realized by organizing lateral inhibition in linear threshold networks. Given a collection of potentially overlapping groups (with the exception of some degenerate cases), the lateral inhibition results in network dynamics such that any permitted set of neurons that can be coactivated by some input at a stable steady state is contained in one of the groups. The information about the input is preserved in this operation. The activity level of a neuron in a permitted set corresponds to its stimulus strength, amplified by some constant. Sets of neurons that are not part of a group cannot be coactivated by any input at a stable steady state. We analyze the storage capacity of such a network for random groups--the number of random groups the network can store as permitted sets without creating too many spurious ones. In this framework, we calculate the optimal sparsity of the groups (maximizing group entropy). We find that for dense inputs, the optimal sparsity is unphysiologically small. However, when the inputs and the groups are equally sparse, we derive a more plausible optimal sparsity. We believe our results are the first steps toward attractor theories in hybrid analog-digital networks.

Brain↗

PubMed2002

Threshold behaviour of the maximum likelihood method in population decoding.

We study the performance of the maximum likelihood (ML) method in population decoding as a function of the population size. Assuming uncorrelated noise in neural responses, the ML performance, quantified by the expected square difference between the estimated and the actual quantity, follows closely the optimal Cramer-Rao bound, provided that the population size is sufficiently large. However, when the population size decreases below a certain threshold, the performance of the ML method undergoes a rapid deterioration, experiencing a large deviation from the optimal bound. We explain the cause of such threshold behaviour, and present a phenomenological approach for estimating the threshold population size, which is found to be linearly proportional to the inverse of the square of the system's signal-to-noise ratio. If the ML method is used by neural systems, we expect the number of neurons involved in population coding to be above this threshold.

Artifacts↗