Week 5: Hopfield Network = CHECKED

Question 1

Why associative memory models? - (4)

Answer 1

1. Introduce learning
2. Introduce fundamental ideas about associating patterns of neural activity
3. Associating patterns or sequences of patterns is needed for episodic memory
4. The hippocampal anatomy maps very well onto these ideas

Question 2

The Hopfield Network uses neurons that are very simple which are the

Answer 2

standard artificial neurons with no dynamics

Question 3

Representation of the Hopfield (1982) Associative Memory Network:

Answer 3

Question 4

Representation of the Hopfield (1982) Associative Memory Network shows (2)

Answer 4

all the neurons are connected with each other

Neuron Si is connected to Sj with weight of wij

Question 5

Assumption of the Hopfield Associative Memory Network

Answer 5

Assume a fully connected network with symmetric connections (Wij = Wji)

Question 6

Properties of the Hopfield (1982) Associative Memory Network (5)

Answer 6

1. Simple connectionist neurons
2. No dynamics
3. We impose the update schelude
4. Sign function as a transfer function
5. Units can be active (Si = 1) or inactive (Si = -1)

Question 7

In Hopfield network, the sign function as transfer function meaning: (2)

Answer 7

If a value is below 0 then it is set to -1

If a value is above 0 then set it to 1

Question 8

Equation of activity of neuron in Hopfield Associative Memory Network

Answer 8

Question 9

What do we mean by symmetric connections in Hopfield Associative Memory Network?

Answer 9

We mean that weight in one direction is the same as the weight in other direction

Question 10

In Hebbian learning it proposes that

Answer 10

neurons that “fire together wire together”

Question 11

Hebbian learning proposes that:

neurons that “fire together, wire together” which in other words

meaning, if sender and receiver are both active (3)

Answer 11

• Sender likely contributed to making the receiver fire!
• Thus, it strengthens the connection between sender and receiver
• That is the weight increases

Question 12

In Hebbian learning,

changing the weights of synaptic connections between neurons mathematically in Hopfield Network by

Answer 12

We take one of the weight (Wij) and add to it the product of activity of pre and post synaptic neurons (if both active) times this very tiny number (epilson)

Question 13

The symbol ε in weight equation means: (2)

Answer 13

1. A tiny number as we don’t want to change the the weights in the network too quickly
2. Most cases you want to incrementally learn something new (so have multiple presentations of two stimuli to associate them together)

Question 14

The first step of the Hopfield network learning

Answer 14

impose a pattern we want to learn then let the learning rule act

Question 15

What do we mean by imposing a pattern?

Answer 15

To impose a pattern, we clamp the activity of a subset of neurons for one pattern and let the learning rule act to change those synaptic weight connections in the network

Question 16

Diagram of example of imposing a pattern for instance Pattern 1 - (6)

Answer 16

Pattern 1 a given number of neurons are active (orange) and keep them active

By saying these activity (i.e., firing state) of neurons can not be updated

Then we let the learning rule act between all these neurons

Connection between blue and orange neurons not going to be strengthened (-1 [non-active] * 1 [active] = -1)

Connections between orange and orange neurons connection is strengthed (1 * 1 = 1) so that in future we don’t force these neurons to be active as one neuron makes the other one fire.

Connection between two neurons that are silent (two blue = -1 * - 1 = -1) so weight increases meaning that neuron silences the other one.

Question 17

Learnign rule table act when imposing a pattern table:

neurons (3)

Answer 17

1. Both -1, weight goes up = connec strengthened
2. Both 1, weight goes up = connec strengthened
3. Mixed, weight goes down, may lead to pruning of connections.

Question 18

With more neurons in Hopfield network (imposing pattern letting learning rule act)

Answer 18

We can have many more patterns

Question 19

In the hopfield network, patterns of activations are (2)

Answer 19

learned as ‘stable states’ under the rule for updating activations

If we clamp activity of neurons for one pattern, (some active some silent) and let learning rule act the weights will change until there is no more change in set of active neurons

Question 20

Stable states mean

Answer 20

update rule produces no more changes in active neurons

Question 21

When pattern of activation does not change anymore we say…

Answer 21

we say a stable state has been reached

Question 22

We can update learning rule for units in Hopfield network model in two ways: 2)

Answer 22

Asynchronously: One unit is updated at a time, picked at random or a pre-defined order

Synchronously: All units are updated at the same time.

Question 23

In update rule, many different

Answer 23

patterns can be learned in the same network, but the memory capacity is limited to ~ 0.14N (N is the number of neurons) in Hopfield network

Question 24

Memory in the Hopfield network is

Answer 24

“content addressable”, performing “pattern completion of a partial cue”

Question 25

What does it mean by memory in the Hopfield network is content addressable?

Answer 25

Content addressable simply means part of the content of the memory is sufficient to address to find the complete memory

Question 26

What does it mean in memory in Hopfield network, performing a ‘pattern completion of partial cue?’ - (3)

Answer 26

Say we learned this pattern of three active neurons and give partial cue where neuron on top left is active.

Then update the network which will cause neuron on top middle to be active because of learning connections as well as the other active neuron

we complete the pattern at time of learning from a partial input.

Question 27

The memory capacity is limited in Hopfield network meaning we may form

Answer 27

overlapping memories which can cause spurious memories (a fake memory via combinations of real memories) to be formed

Question 28

The Hopfield network does not work

Answer 28

in isolation

Question 29

Memory of what…? = HF network does not exist in isolation - (3) = toy model

Answer 29

Say we have a memory of “I saw a magenta turtle that was squeaking”

That should trigger the activity of neurons in visual cortex that represented magenta turtle as well as neurons in auditory cortex that represent the squeak sound

Direct connections of neurons in Hopfield network to other neurons

Question 30

Pattern completion will continue in associative memory store in HF network but also

Answer 30

extend to reactive the neurons in the sensory cortices that were first active when you first memorised the thing (“e.g., the magenta turtle squeaking”)

Question 31

Why this toy model (3)

Answer 31

The hippocampus has extensive connections to virtually ‘all association areas (polymodal) in neocortex

But no necessarily direct connections to early (unimodal) sensory cortices

So sketch below is a severe simplification

Question 32

Continuous vs discrete attractors diagram

Answer 32

Question 33

Hopfield memories are discrete attractors! - (2)

Answer 33

Don’t want a continuous attractor as too easy to get interference between different patterns

We want to separate our memories

Question 34

Once learning is done we can perform recall in which involves:

Answer 34

Start from a pattern similar a memorized pattern of activation, change activation according to sign of input (update until no changes occur) to recover original pattern

Question 35

Once learning is done, we perform recall example - (3)

Answer 35

Original pattern we have all three neurons active, two of them are now active (via moo! via auditory cortex)

and pattern completion and these neurons will drive via synaptic connections for other neuron to be active (visual representation of a cow)

then we recall a nearby (i.e., similar) pattern that “I saw a purple cow that was mooing”

Question 36

To support a pattern of activation, connectionist should be

Answer 36

positive between units in the same state (i.e., 1/1 or -1/-1) and negative between units in different units (1/-1 or -1/1) i.e., si sj wij > 0.

Question 37

The learning rule sets the weights so that

Answer 37

to-be-remembered patterns of activity are stable or attractor states.