Network Models (2)

clangedbivalveAI and Robotics

Oct 19, 2013 (3 years and 7 months ago)

77 views

Network Models (2)

LECTURE 7

I.
Introduction



Basic
concepts of neural networks


II.
Realistic neural networks




Homogeneous excitatory and


inhibitory populations



The olfactory bulb


− Persistent neural activity




Perceptual decision




Discrete versus continuous


attractor


Random
-
dot motion direction discrimination
experiment

Dorsal stream (Where pathway ):


V1


嘲V


䵔M⼠䵓M


灯獴p物潲r灡物整慬p捯牴數e⡌䥐



……

Encoding the motion stimulus

The decision process occurs

and guides saccades

(Shadlen and Newsome 2001)

Network model


(Wang 2002, Neuron 36: 955)

with
N
E

=
1600 and
N
I

=
400

A or B group: 0.15
N
E

Below threshold,

W =1.7 (in A or B)


= 0.88 (excitatory weights)


= 1.0 (others)

Poisson input



All neurons receive a large amount of background


Poisson inputs and fire spontaneously at a few hertz


• During stimulation, both neural groups receive


stochastic Poisson inputs at rates
µ
A

and µ
B

Model reproduces
salient
characteristics of
decision
-
correlated
neural activity in LIP

Input presentation (1 s) is
followed by a delay period (2 s)

(Wang 2002, Neuron 36: 955)

Decision dynamics with
inputs of zero coherence

(Wang 2002, Neuron 36: 955)

Optimal decision
-
making performance requires
sufficiently strong and slow synaptic reverberations

(Wang 2002, Neuron 36: 955)

When W =1.7 (in A or
B)


1.4, attractor
dynamics can no longer
be sustained by intrinsic
network excitation.


With
stronger excitatory reverberations
, persistent


activity level is doubled (from 20 Hz in control to 40


Hz), and the integration time of stimulus is


shortened by a half





If there are
only fast AMPA receptors

( )


at recurrent synapses, the network can still show


attractor dynamics. However, the network cannot


integrate stimuli for more than tens of milliseconds,


and it “latches onto” one

of the two attractors


immediately after the stimulus onset

I.
Introduction



Basic
concepts of neural networks


II.
Realistic neural networks




Homogeneous excitatory and


inhibitory populations



The olfactory bulb


− Persistent neural activity




Perceptual decision




Discrete versus continuous


attractor


1.
Kinds of attractors in network models:


fixed points, line (or ring) attractors,

limit cycles,

and
chaos


2. The network for persistent neural activity

has a
continuous

(vs.
discrete
) line attractor embedded in
the phase space.

Continuous attractor neural
networks

are emerging as promising models for
describing the encoding of continuous stimuli in
neural systems


A point attractor

A line attractor

A cyclic attractor

A chaotic attractor

Discrete versus continuous attractor

This neutral stability allows the system to change status smoothly,
following a fixed path. This property (not shared by discrete attractors) is
crucial for the system to seamlessly track the smooth change of stimulus

Robustness of line attractors to noise

(Brody et al. 2003)

L
:

Imagine that there is a function of the state of the system and that the


dynamics of the system are such that
L

always tends to fall in value as


time progresses

The neutral stability implies the system is sensitive to fluctuations


along the attractor space

Cellular bistability at single neuron level as a
candidate mechanism for robust working
memory performance


In order to
perform a working memory
, the PFC network should
be able to be “switched on” into a persistent firing pattern by
transient

cue stimuli and be “turned off” back to its resting state
of spontaneous activity by a suitable “go” signal

I

f

100 Hz

Physiological

Range

Cellular bistability (or multistable states)

Two stable membrane states correspond to different activation
conditions of various voltage
-
dependent ionic currents.

Typically, neuromodulatory
inhibition of certain potassium
currents (and/or modulation of
calcium and other currents) is
required to unmask the plateau
potential and enable the
bistability behavior.

(Activation function of

medium spiny neurons (MSNs) in the
striatum of the BG)

Homework

1. Develop a neural network
including
the minimal

biophysical mechanisms necessary to reproduce
persistent activity in neural systems. And how
about the stability of network attractors?


2.
The possible computational mechanism underlying
perceptual choice


3.
The differences in dynamics between feedforward
and recurrent neural networks