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
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