Week 2: How to Model the Brain = CHECKED

Question 1

McCulluch Pits Model of Neurons 1943 has X1,X2,X3 having synaptic connecitons

Answer 1

to a receiver neuron Y

Question 2

Simmplest approximation we can make of McCulluch Pits Model of Neurons is

Answer 2

Add inputs of X neurons (X1+X2+X3) which gives output activity of Y neuron

Question 3

Making MCP model more realistic by saying more inputs more important than others by adding

Answer 3

synaptic weights

Question 4

Although hardly used, The MCP is the grand father

Answer 4

of all neuron models

Question 5

Disadvantage of MCP model is that it ignores

Answer 5

properties of ion channels, different types of synapses etc..

Question 6

We can calculate the output of Y in McCulloh Pits weighted model of neurons by

Answer 6

w1X1 + w2X2 +w3X3 = Y

Question 7

McCulloh Pits Formula means the large w

Answer 7

influence Y more

Question 8

Some synapses are more stronger than others due to

Answer 8

learning

Question 9

We can write w1X1 +w2X2 + w3X3 in McCulloh Pits Model more concisely as realistically there are more than 3 neurons giving input to receiver neuron Y

Answer 9

Writing sigma formula with N = arbitary number of neurons

Question 10

Transfer function is introducing

Answer 10

one more step between Y and the final output of the neuron

Question 11

McCulloh Pits Model of Neurons (1943) Transfer function G is… (4)

Answer 11

Define a threshold value Θ
if Y ≥ Θ then Y = 1 (neuron active)
if Y < Θ then Y = 0 (neuron silent)

also called ‘step function’

Question 12

Final output from McCulloh Pits Model of Neuron is

Answer 12

Y activation of neuron
G(Y) = r = 1 or 0

Question 13

McCulloh Pits Final Neuronal Model, Y is referred to as

Answer 13

activation of neuron which is fairly abstract notion

Question 14

McCulloh Pits Final Neuronal Model, Y could be thought of as the internal state of the neuron

Answer 14

in a state that leads to action potentials or does not (neuron is silent)

Question 15

McCulloh Pits Final Neuronal Model, output is r

Answer 15

it is some measure of output of the neuron given its activation

Question 16

McCulloh Pits Final Neuronal Model,
We tentatively (not definitely) identify r (the output) with

Answer 16

firing rate (number of action potentials fired per second)

Question 17

In Linear Neuron Model they do not use a step function as transfer function since

Answer 17

real neurons have a lot of variability in their firing (not just firing just at 0 or 1)

Question 18

Diagram of Linear Neuron Model Trasnfer Function

Answer 18

Question 19

Linear Neuron Model’s Transfer function is

Answer 19

piece-wise linear

Question 20

Linear Neuron Model’s Final Output is (2)

Answer 20

G(Y) = r = Y

r can have values between 0 and infinity (what???)

Question 21

In Linear Neuron Model transfer function

Y < 0 then neuron is silent because

Answer 21

there can be no negative firing rates so it is off limits

Question 22

In Linear Neuron Model, it seems unreasonable to have - (2)

Answer 22

firing rate grow without a bound as input increase

We can not have neurons for instance to fire million spikes per second

Question 23

In Linear Neuron Model, it seems unreasonable to have firing rate grow without a bound as input increase as…

Therefore, in Sigmoid Neuron Model

(2)

Answer 23

Their firing rate can not go faster than a given frequency

We should introduce a saturating transfer function

Question 24

In Sigmoid Neuron model, (3)

Answer 24

As G(Y) = r grow, Y grows

As G(Y) = r grows more, we hit the threshold where we saturate the output of Y

This transfer function our output does not grow to infinity with infinite inputs

Question 25

The McCulloh Pits, Linear Neuron and Sigmoid Neuron have different ways in which concept of mapping summed inputs to firing rate due to

Answer 25

having different transfer functions (G)

Question 26

McCulloch Pitts , Linear and Sigmoid Neuron have same equation of (2)

Answer 26

w1X1 +w2X2+ w3X3 = Y

General form of sigma formala

Question 27

The McCulloh Pitts, linear neuron and sigmoid neuron models have something in common is that

Answer 27

they have no dynamics

Question 28

These models have no dynamics

According to these models..

This means… - (3)

Answer 28

According to these models, once Y met threshold value to fire (e.g., Y = 1 in some cases),

This means Y neuron is constantly in a state which it fires action potential

There is no internal mechanisms in these models that changes values of Y to 0 or another value

Question 29

It costs a lot of metabolic energy to

Answer 29

fire action potentials so it is not possible for neurons to fire action potentials constantly

Question 30

Since there is no dynamics in these models (McCulloch-Pitts Neuron, Linear Neuron, Sigmoid Neuron) we will have to perform

Answer 30

w1X1 + w2X2 + w3X3 again with different inputs to obtain a new value

Question 31

These models (McCulloch-Pitts neuron, linear neuron and sigmoid neuron) is still radially different from how

Answer 31

real neurons behave

Question 32

These models (McCulloch-Pitts neuron, linear neuron and sigmoid neuron) are called

Answer 32

connectionist type models

Question 33

Connectionist networks are

Answer 33

networks produced with neural models with no dynamics

Question 34

Dyanmic change in membrane potential integrate and fire model wants to model - (2)

Answer 34

When we raise the membrane potential of a real neuron (below the firing threshold), it will decay back to -70mV over time’

This property is not captured by connectionist models

Question 35

Integrate and fire model does not mdoel the action potentials as its equation tell us how the MP evolves

Answer 35

with time, given some synaptic inputs and any externally injected currents

Question 36

Integrate and fire model models the change in membrane potential (dyanmic change) by adding

Answer 36

factors that increase or decrease variable u (membrane potential)

Question 37

At rest at integrate and fire model, u is

Answer 37

-70 mV (millivolts)

Question 38

Adding dynamics to integrate and fire model

Factors that increase u is (3)

Answer 38

excitatory synaptic inputs,

injected current
These are positive terms in model’s equation of du/dt

Question 39

Adding dynamics to integrate and fire model

Factors that decrease u is (3)

We assume this…

Answer 39

at a high u, ion-channels open that bring u back down,

these are negative term — in model’s du/dt equation

We assume this effect is proportional to u. The further away we are from rest (-70mV) the stronger we are pushed back down.

Question 40

Integrate and fire model equation means:

Answer 40

Change in u over time is equal to –u + the synaptic inputs + any external currents into our neuron

Question 41

Integrate and fire model adds time constant t, and other variables (urest = resting potential and u is current MP) to make units work out to look like this:

Answer 41

Question 42

When will tdu/dt (rate of change) be 0? (when will membrane potential have no change - resting membrane potential) - in integrate and fire model

Answer 42

urest - u = 0

Question 43

To calculate integrate and fire model equation’s we - (3)

Answer 43

spilt the derivative which makes dt not infinitely small but merely very small which makes no more derivative

We can now calculate u2 (u at time t2)from u1 (u at time t1) and all the inputs

Repeat for every neuron in your network given certain connectivity pattern (i.e., specificed by weights) and other inputs

Question 44

In the integrate and fire model, if the membrane potential hits a threshold value of action potential (e.g., -40 mV) we say that

Answer 44

spike has been fired and then the membrane potential is reset to -70 mV

Question 45

In integrate and fire model it has dynamics meaning that

Answer 45

once it hits threshold to fire, the membrane potential will eventually decay back to resting membrane potential value (-70mV)

Question 46

The (leaky) integrate and fire model is also called

Answer 46

‘formal’ spiking neuron model

Question 47

In the integrate and fire model gives us spike times but the

Answer 47

spike wave-forms are not calculated in this model

Question 48

The non-spiking relative of IF model (firing rate model)

making changes to IF model (4)

Answer 48

We remove the spiking threshold, the post-spike reset, and u_rest

We re-interpret what u stands for, and (if we want to) we rename it, say to a (activation)

We substitute synaptic action (as an effect on the membrane potential) with the familiar (from connectionist models) summation of incoming inputs

We add a transfer function (from connectionist model), for instance a sigmoid such that negative a values get mapped to 0 and positive values saturate

Question 49

Firing rate model schematic:

Answer 49

Question 50

IF and connectionist models

Answer 50

IF and connectionist models

Question 51

Firing rate model , a is

Answer 51

interpreted as activation of neuron

Question 52

Firing rate model transfer function turns a into

Answer 52

firing rate

Question 53

Firing rate model transfer function decays the membrane potential just like the

Answer 53

IF model

Question 54

Firing rate model captures the

Answer 54

dynamics and does not give spike times

Question 55

Firing rate model transfer function decays the membrane potential just like the IF model, but we think of it as

Answer 55

firing rate than membrane potential

Question 56

Am I interested in spike times?
What model?

Answer 56

IF

Question 57

Am I interested in only care of spikes per second
What model?

Answer 57

firing rate model

Question 58

Firing rate model has the assumption that the average rate of firing action potentials for a neuron (in response to inputs) adequately

Answer 58

captures the fundamental properties of a neural network

Question 59

Firing rate model is a non-spiking model meaning (2)

Answer 59

does not model spike

Any phenomena that depends on accurate spike timing can not be modelled with it

Question 60

Although firing rate model is not spiking,

Firing rate model is a non-spiking model and captures the (2)

Answer 60

dynamic changes in activity (i.e., average rate spikes over time)

Many neural phenomena can be modelled just in terms of rates

Question 61

The Hodgkin and Huxley model models ion channels and outlines the mechanisms that underline

Answer 61

the propagation and initation of action potentials based on work they did with a squid giant axon

Question 62

Taxonomy of models

Answer 62

Question 63

The Hodgkin-Huxley model have an equation

Answer 63

of how each ion channel changes and plug into equation of MP.

Question 64

General Form Table of Connectionist Neuron Models

Answer 64