Download Bump attractors and the homogeneity assumption

Bump attractors and the
homogeneity assumption
Kevin Rio
NEUR 1680
28 April 2011
Bump attractors
• Can explain sustained (but bounded)
activity in populations of neurons.
• A useful description of working memory by
combining self-sustained activity with
sensitivity to external inputs.
Firing-Rate Model
τr
ri (t)
Ii (t)
Jij
Θ
time constant
firing rate of neuron i
input current for neuron i
synaptic strength between neurons i,j
current bias
Firing-Rate Model
0
Jij = -J0 + J2 cos (2π(i-j)/N)
x if x > 0
0 if x < 0
Homogeneity
• Homogeneity is required to create a
continuum of bump attractors.
– Even a small amount of heterogeneity
destroys continuum, leaving only a few
discrete attractors.
• Biologically implausible: number and
strength of synaptic connections is
variable.
Solutions
• Fine tuning properties of each neuron.
• Network learns to tune itself through an
activity-dependent mechanism.
– “Activity-dependent scaling of synaptic
weights, which up- or downregulates
excitatory inputs so that the long term
average firing rate is similar for each neuron”
(Renart, Song, Wang 2003).
Synaptic Scaling
(Renart, Song, Wang 2003)
τg
time constant [large]
g(θ) factor that multiplies excitatory synaptic
conductances to neuron θ
r(θ) instantaneous firing rate of neuron θ
rtg(θ) target firing rate of neuron θ
Project Outline
1. Simulate network of firing-rate neurons.
2. Observe bump attractors.
3. Show how loss of symmetry destroys
continuum of bump attractors.
4. Restore symmetry by activity-dependent
scaling of synaptic weights.
Sequential Modeling in the
Auditory System
By Rohan Ramesh and Srihari
Sritharan
Recurrent Networks
• Three layer network with feedback: input
layer, intermediate layer, and output layer
• Intermediate layer in this instance are
SAM cells
Spike Accumulation Model
(SAM)
• Variable of importance – the accumulated
potential of SAM cells in intermediate layer
– The accumulated potential = a constantlyupdating characterization of a constant
stream of sensory input
Membrane Time Constant
• Sequential memory dependent on
membrane time constant (τ) of SAM cells
– Different response to stimuli 1  2 than 2  1
due to difference in neuronal response
– Activity of the entire population of SAM cells
important
Output
• Sequential learning decoded due to input
from SAM cells AND efferent copy of
activity of output layer to intermediate
layer
– How do we decode this? How does the
efferent feedback loop aid decoding?
– Activation of output cell:
Learning
• How will the network learn a series of
tones?
• The input to the SAM cells are determined
by a comparison of the output of the
output cells to the output of the input cells
Encode Specificity and Timing
• Specificity – tone 1 vs. tone 2
– Auditory tuning within SAM cells could
determine the frequency of the input
• Timing - tone 1  tone 2 OR tone 2 
tone 1
– The membrane time constant and the efferent
copy of the output will help determine the
order of the tones
Auditory Input
Auditory Tuning Curves
Computational neuroscience 2011
Supervised learning with lateral
interaction and back propagation
within a neural network
4/27/11
Sunmee Park, Jing Wang, Rizwan
Huq
Motivation
• Natural vision can differentiate various
handwritten digits
• Can we mimic the vision system?
(Of course, in a simpler way)
• Supervised learning: given input/output
– Traditional backpropagation neural
network(NN)
– Biophysically appropriate inter-layer
communications
Network diagram
Methods
Input dataset
…
- Hand-written digits set from 0~ 9, collected by
USPS/NIST database
- 8 bit grayscale images (1100 examples of each class)
Preprocessing
Applying Gabor filter
Deliverables
• A simulated neural system capable of
decoding handwritten image data and
identifying the input digit.
• System performance curves, for which we
will reserve training examples.
• Analysis of the impact inter-layer
communications.
Kuhn, et al. 2004: Neuronal
Integration of Synaptic Input in
the Fluctuation-Driven Regime
Project Team: Tommy Tea and Christina
Hahn
Paper Recap
• Visual synaptic bombardment leads to
changes in conductance. This in turn
increases fluctuations in membrane
potential and these fluctuations modify the
firing rate.
• Firing rate decreases because of shunted
membrane potential fluctuations, and
increases because of shorter membrane
time constants, allowing for faster
membrane potential fluctuations.
Methods
• Transient current-based model:
• Transient conductance-based model:
• Firing Rate model:
Figures of model with current input increasing
monotonically
Figures of model with non-monotonic conductance
input:
Physiological Significance
• In the conductance-based model, the
fluctuations are expected to reach a
maximum standard deviation of ~3 mV,
which is within the range of values
observed in vivo