Figure 1.
Architecture of 2-layer neural network model. The layer of input neurons on the left are projecting to the competitive output layer on the right. During learning, the strengths of the feedforward synaptic connections from the input layer to the output layer are modified by a trace learning rule.
Figure 2.
Simulated movements of the eyes and head-centered locations of visual targets during training and testing. (A) Scatter plot in which each point corresponds to a single fixation during either training (red) or testing (blue). The fixation points are plotted as a function of the eye position (abscissa) and the retinal location of the visual target (ordinate). Each of the diagonal lines of red points corresponds to a period during training when the visual target was fixed in one of the eight head-centered target locations while the eyes moved. The vertical lines of blue points correspond to the four eye positions in which the network was tested. (B) Multiple plots showing how the eye position is shifted through time in a randomised manner during training. Each plot corresponds to a different period during which the visual target is maintained in a fixed head centered location.
Table 1.
Parameters of self-organizing model.
Figure 3.
Neuron #79 firing responses and weight vector before and after training.
The development of the firing responses and synaptic weights of output neuron #79 before and after training. Results are presented before training (top row), after 10 training epochs (middle row) and after training epochs (bottom row). Plots in the left column show the firing rate responses of neuron #79 during testing. Within each plot, each curve corresponds to a fixed eye position while a visual target is presented in a range of head-centered locations. The vertical line shows the decoded head-centered receptive field location, and the grey bar shows the decoded receptive field size of the neuron. The minature scatter plot shows the response characteristics of all neurons in the output layer, where each neuron is plotted as a point corresponding to that neuron's particular combination of head-centeredness (ordinate) and eye-centeredness (abscissa). The neuron whose firing rate responses have been plotted is shown in the scatter plot by a red mark. Plots in the right column show the synaptic weights of synapses afferent to neuron #79. Within each plot the synapses have been arranged topographically by the effective preference of the input neuron for retinal location
and eye position
.
Figure 4.
Population analysis of receptive field properties.
Population analyses of receptive field properties of output neurons during succcessive stages of training of the self-organizing model. Results are presented before training, after ten training epochs, and after training epochs. (A) Scatter plot shows the reference frame response characteristics of all neurons in the output layer, where each neuron is plotted as a point corresponding to that neuron's particular combination of head-centeredness and eye-centeredness. Neurons from the untrained model are shown in blue, neurons from the trained model are shown in red. (B) Distributions for receptive field index values before and after training. (C) Scatter plot showing the combination of head centered receptive field size and head-centered receptive field location of all head-centered output neurons before and after training. (D) Histograms showing the frequency distribution of the numbers of output neurons that responded preferentially to each of the head-centered locations which were used to train the model.
Table 2.
Results for self-organization experiment.
Figure 5.
Population analysis for varying number of epochs of training.
Population analyses of receptive field properties of output neurons in the self-organizing model during succcessive training epochs. There are four plots as follows. The average receptive field size curve (black) shows the average size of the head centered receptive field among head-centered neurons, and the error bars represent the standard deviations. The head-centeredness rate (blue) was the fraction of output neurons that were head-centered. The coverage curve (green) was the coverage of the head-centered training locations by the output neuron population after the given number of epochs of training, where missing data points before epoch 5 were due to at least one of the eight head-centered training locations not being represented by the output cells. The average head-centeredness curve (red) was the average head-centeredness value among all head-centered neurons, and the error bars were the standard deviations.
Figure 6.
Neuron #170 firing responses and weight vector.
Analysis of one of the output neurons #170 from the model with input neurons with decoupled visual and eye position receptive fields. Results are presented after training. (A) The firing rate responses of the output neuron. (B) and (C) Histograms of afferent synaptic weights onto the output neuron from input cells that represent the retinal target location and eye position, respectively. The histograms in (B) and (C) were produced by finding the sum of all synaptic weights from input neurons with the given retinal location () or eye position preference (
) respectively. Both histograms have bin sizes of
.
Table 3.
Results for experiment with input neurons with decoupled receptive fields.
Figure 7.
Neuron #409 firing response and weight vector.
Results from a simulation without competitive interactions between output neurons. The Figure shows the firing responses and synaptic weights of one the output neurons #409 before training (top row) and after training epochs (bottom row).
Figure 8.
Population analysis in experiment without competition in output layer.
Simulation results without competitive interactions between output neurons. Population analyses of the receptive field properties of output neurons are presented before training (blue) and after training (red). (A) Scatter plot showing the reference frame response characteristics of all neurons in the output layer. (B) Scatter plot showing the combination of head centered receptive field size and head-centered receptive field location of all head-centered output neurons.
Table 4.
Results for experiment without competition in output layer.
Figure 9.
Simulations exploring the effects of varying the length of the activation time constants and the trace time constant
in the hebbian learning rule 16 and trace learning rule 5, respectively. The top row shows the series of simulations where a hebbian learning rule was used and the activation time constant was varied. The bottom row shows the series of simulations where a trace rule was used and the trace time constant was varied. The left plots show the fraction
of output neurons that were deemed to be head centered (blue curve), and the coverage of the head centered training locations by the output neuron population (green curve). The right plots present the average size of the head centered receptive field among head-centered neurons (black curve), and the average head-centeredness value among all head-centered neurons (red curve). The error bars on these last two curves represent the standard deviations. The dashed line in each plot shows the corresponding quanitity in the untrained model, and since there was no coverage in the untrained model this line is absent.
Figure 10.
Varying fixation sequence length .
Simulations exploring the effects of varying the number, , of eye fixation positions for each fixed head centered location of the visual target during training. Results are presented showing the response characteristics of the output neurons after 20 epochs of training. The dashed lines represent the corresponding values for the untrained network.