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 V2 MT / MST posterior parietal cortex (LIP ) ……

Encoding the motion stimulus

The decision process occurs and guides saccades

(Shadlen and Newsome 2001)

Network modelNetwork model

(Wang 2002, Neuron 36: 955)

with NE =1600 and NI =400A or B group: 0.15NE

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 µA and µB

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 progressesThe 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 HzPhysiological

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 ofmedium 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