Figure 1.
Overview of plasticity rules used for ICA-like learning.
Synapse weights are modified by nearest-neighbor STDP and synaptic scaling. Additionally, intrinsic plasticity changes the neuron's transfer function by adjusting three parameters
,
, and
. Different transfer functions show the effects of changing each of the three parameters individually relative to the default case depicted in blue. Namely,
gives the slope of the curve,
shifts the entire curve left or right, while
can be used for rescaling the membrane potential axis. Here,
is increased by a factor of 1.5,
by
,
by a factor of
.
Figure 2.
A demixing problem: two rotated Laplace directions.
(A) Evolution of the weights ( in blue,
in red) for different initial conditions, with
, and
weight normalization. (B) Evolution of the instantaneous firing rate
, sampled each 1000 ms, for the initial weights
,
. (C) Corresponding changes in transfer function parameters, with
in Hz and
and
in mV. (D) Final weight vector for different rotation angles
(in red). In the first example, normalization was done by
(the estimated rotation angle is
, instead of the actual value 0.5236); for the others
was used. In all cases the final weight vector was scaled by a factor of 5, to improve visibility.
Figure 3.
The demixing problem with inputs encoded as spike trains.
(A) Evolution of the weights for a rotation angle . (B) Final corresponding weight vector in the original two-dimensional space. The final weight vector is scaled by a factor of 100, to improve visibility.
Figure 4.
Learning a single independent component for the bars problem.
(A) A set of randomly generated samples from the input distribution, (B) Evolution of the neuron's receptive field as the IP rule converges and instantaneous firing rate of the neuron. Each dot corresponds to the instantaneous firing rate () sampled each 500 ms.
Figure 5.
Bars in a correlation-based encoding.
(A) Example of 20 spike trains with . (B) A sample containing two 2-pixel wide bars and the corresponding covariance matrix used for its encoding. (C) Evolution of the weights during learning. (D) Final receptive field and corresponding weights histogram.
Figure 6.
Learning a Gabor-like receptive field.
(A) Evolution of the neuronal activity during learning, (B) Learned weights corresponding to the inputs from the on and off populations, (C) The receptive field learned by the neuron, and its l.m.s. Gabor fit.
Figure 7.
(A) Overview of the network structure: all neurons receive signals from the input layer and are recurrently connected by all-to-all inhibitory synapses, (B) A set of receptive fields learned for the bars problem, (C) Evolution of the mean correlation coefficient and mutual information in time, both computed by dividing the neuron output in bins of width 1000 s and estimating and
for each bin, (D) Learned inhibitory lateral connections, (E) A set of receptive fields learned for natural image patches.
Figure 8.
Evolution of the receptive field for a neuron with a fixed gain function, given by the final parameters obtained after learning in the previous bars experiment. A bar cannot be learned in this case.
Figure 9.
Mean firing constraint is not sufficient for reliable learning.
(A) Evolution of neuron activation for a neuron with a gain function regulated by a simplified IP rule, which adjusts to maintain the same mean average firing
.
or
, in the first and second row, respectively. Inset illustrates final receptive field for each case. (B) Corresponding evolution of weights and (C) their final distribution.