Week 6: Competitive Learning model of place cells

Question 1

Sharp model of place cells developed in

Answer 1

1991

Question 2

Sharp model of place cells uses

Answer 2

standard artifical neurons with no dynamics = update everytime step it fires

Question 3

Sharp model of place cells uses interesting learning rule called

Answer 3

competitive learning rule

Question 4

Diagram of competitive learning (5)

Answer 4

1. • We have input pattern
2. • Some neurons active or not
3. • We have output neurons (i.e., receiver neuron)
4. • There is initally random weight between each input and output neuron
5. We have strong inhbition between the output neurons

Question 5

Competitive learning rule has winner take all dynamics

Answer 5

Output neuron with higher activity of 1 compared to others will have strongest inhbition to neighbour and slowly suppress them even though they try to suppress it as well causing it to be lone survivor

Question 6

Competitive learning rule

For each input pattern X, with inital random connections, a particular output neuron (randomly) Oi with be the most

Answer 6

active neuron

Question 7

Competitive learning rule

Assuming output neuron O have )

Answer 7

inhbitory connections among each other (lateral inhbition) but we don’t model them explicility

Question 8

Competitive learning rule first step

We find the maximum Oi, set it to 1 (max activity) and set all other Ok

Answer 8

to 0

Question 9

Competitive learning rule second step

We then do Hebbian learning (2)

Answer 9

Wij –> wij + ε Oi Xj for all x other weights don’t change where Ok = 0

We do this for all other connecitons where output neuron is active (since if activity of O is 0 it does not change weight) and update my weights between neurons

Question 10

epsilon

Answer 10

is a tiny number as want small incremental changes to weights in Hebbian learning

Question 11

Oi is the most active neuron

Answer 11

set to 1

Question 12

Xj is

Answer 12

all the other input neurons

Question 13

Hebbian learning equation in words

Wij –> wij + ε Oi Xj (2)

Answer 13

ε Oi Xj = Activity of given output and input neuron multipled by each other and output of this is made very small by epilson (learn slowly)

This is added to my pre-existing weight (wij)

Question 14

Before updating weights (doing Hebbian learning) in competitive learning rule betwen neurons we need to

Answer 14

normalise synaptic connections first

Question 15

We repeat process of Hebbian learning and normalising synaptic connections in competitive learning rule

Answer 15

with presentation of each input pattern

Question 16

What happens as a result of competitive learnig rule is that outputs whose incoming weights

We have different..

(2)

Answer 16

are most similar to the pattern xn wins and its weight then become more similar as we do learning

Different oututs find their own clusters in input data

Question 17

Normalisation in competitive learning where is

Answer 17

For a given neuron, the total sum of connection (i.e. input) weights to each output neuron stays constant (e.g., sum (wi) = 1)

Question 18

If we did not have normalisation then… (3)

Answer 18

• If we continue learning for a long time, the weight will become very strong in Hebbian learning
• There must be a physiological limit in brain as how strong a synaptic conneciton can be
• Output neuron can only fire at a given maximum rate

Question 19

Diagram of normalisation

Answer 19

Question 20

sum(wi) = ….

Answer 20

can be any random number

Question 21

Diagram of normalisation explained of sum (wi) = 1

Answer 21

The sum of all the input weights going into output neuron O2 have to 1

Question 22

How do we do normalisation and keep track of it since weights increase by learning?

Answer 22

We divide the weights after each learning step by the sum of the total weights (sum[wi]) so sum will always stay 1

Question 23

Example of keeping track of normalisation (2)

Answer 23

E.g., weights after 1 learning step are 2,1,8,3,2

sum(wi) = 2+4+5+3+2 = 16 => update weights to be 2/16, 1/16, 8/16, 3/16, 2/16 so sum of all these magenta weights is still 1

Question 24

Example of keep tracking of normalisation where now one of the weights gets much stronger (3) after example of keeping track

Answer 24

• The strongest weights get stronger : wij –> wij + ε oi xj
• For example, wij = 8/16 grows stronger faster at expense of wij = 1/16
• The weakest weights get weaker

Question 25

Normalisation and tracking it repeats with

Answer 25

presentation of each input pattern

Question 26

Competitive learning rule in a nutshell (4)

Answer 26

* Select output neuron * Update weight * Normalise weights = squash weak input and up strong inputs * Output neuron becomes selective to to the strongest neuron in input pattern

Question 27

Normalisation and keep tracking of it is done for

Answer 27

each output neuron in the network whenever they are active

Question 28

Normalisation over time - (3)

Answer 28

By presenting input 1 over time, over multiple learning steps, some input weights get stronger and some get weaker This is what is meant by selective of input cluster O2 becomes selective to X3 and X5 in this example

Question 29

Model sharp proposes (3)

Answer 29

* Maybe at a given location, certain sensory inputs are very strong and select and map place cells on this * Maybe at different location, different sensory inputs are active and map those onto PC * In this way we get location specific input

Question 30

Diagram of Sharp (1991) palce cell firing model simulation of rat (5)

Answer 30

* Simulation of rat (blue triangle) that moves around circular box * There is cues around the box * At each location, the simulated rat "observes" distance to visual cues and "observes" direction of cues relative to itself * So we progate the neural activity [i.e., updating the value the neuron equation gives for each neuron) and perform learning updates * Then the simulated rat "moves" and explore box and "rotates" a small distance

Question 31

What happens to the neurons as simulated rat moves around and "observes" distance to cue and "observes" direction of cues in Sharp's 1991 place cell firing model? (3)

Answer 31

There is two stages of competitive learning First stage: conjunctions of distance and direction to landmarks is learned Second stage: conjunctions of there first stage output yields place cells

Question 32

First stage: conjunctions of distance and direction to landmarks is learned meaning... (2)

Answer 32

Input pattern is now a representation of distance and direction of all cues There will be a co-occurence of distance and direction input patterns,

Question 33

Output of the Sharps' (1991) model Simulated place cell firing is resistant to cue-removal - - (4)

Answer 33

* At each location , activity of PC output neurons is calculated * Get these place fields for specific locations for cell 3, 9 and 13 * If you remove some cues, the place field is still there (exactly see experimental) as subset of remaining cues is sufficient once learned correct connections to reactive that cell * We also get directionality in linear tracks

Question 34

General results of simulation of Sharp's 1991 place cell firing model (2)

Answer 34

* Simulated place cell firing is resistant to cue-removal * Simulated place cells are omni-directional only after random exploration and not following directed exploration!

Question 35

Output of Sharp's (1991) place cell firing model Simulated place cells are omni-directional only after random exploration and not following directed exploration! (5)

Answer 35

* We also get directionality in linear tracks * This is PC in model recorded its location and direction of "simulated rat" * Fires same locaiton roughly independent of head direction of rat in open field * If simulated linear track, take certain routes * PC cells are directional as some fire when "simulated rat" moving east or northeast but not moving in other directions in starburst maze