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 time constantri (t) firing rate of neuron i Ii (t) input current for neuron i Jij synaptic strength between neurons i,j Θ current bias

Firing-Rate Model

0

x if x > 00 if x < 0

Jij = -J0 + J2 cos (2π(i-j)/N)

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 constantly-

updating 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

Supervised learning with lateral interaction and back propagation

within a neural network4/27/11

Sunmee Park, Jing Wang, Rizwan Huq

Computational neuroscience 2011

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

…

- Hand-written digits set from 0~ 9, collected by USPS/NIST database

- 8 bit grayscale images (1100 examples of each class)

Input dataset

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