Übungen (practicals) - third institute of physics · covering contents parallel to the lectures...

Übungen (Practicals) http://www.physik3.gwdg.de/cns

4 exercise sheets, over three weeks, eachCovering contents parallel to the lectures

Required: C++ programming and gnuploti.e., lecture Computational Physics

Submission of programs +10 min presentation and discussion

Details: First session right after the lecturein the PC pool: Room C.00.110

http://www.physik3.gwdg.de/cns

Learning and Memory

Learning:Learning Types/Classes and Learning Rules (Overview)

Conceptualizing about Learning

Math (Rules, Algorithms and Convergence) together with the

Biological Substrate for different learning rules and

Biological- and some other Applications (Pattern Recogn.,

Robotics, etc.)

Memory:Theories

Biological Substrate

Integrative Models – towards Cognition

Different Types/Classes of Learning

Unsupervised Learning (non-evaluative feedback)• Trial and Error Learning.

• No Error Signal.

• No influence from a Teacher, Correlation evaluation only.

Reinforcement Learning (evaluative feedback)• (Classic. & Instrumental) Conditioning, Reward-based Lng.

• “Good-Bad” Error Signals.

• Teacher defines what is good and what is bad.

Supervised Learning (evaluative error-signal feedback)• Teaching, Coaching, Imitation Learning, Lng. from examples and more.

• Rigorous Error Signals.

• Direct influence from a Teacher/teaching signal.

M achine Learn ing C lass ica l C ondition ing Synaptic P las tic ity

D ynam ic Prog .(Be llm an Eq .)

R EIN FO R C EM EN T LEAR N IN G U N -SU PERVISED LEAR N IN Ge x a m p le b a s e d c o rre la tio n b a s e d

δ -R u le

M onte C arloC on tro l

Q -Learn ing

TD ( )o ften = 0

λλ

TD (1) TD (0 )

R escorla /W agner

N e u r.T D -M o d e ls(“C rit ic ”)

N e u r.T D -fo rm a lism

D iffe ren tia lH ebb-R u le

(”fas t”)

STD P-M ode lsb io p h y s ic a l & n e tw o rk

EVALU ATIVE FEED BAC K (R ew ards )

N O N -EVALU ATIVE FEED BAC K (C orre la tions )

S A R S AC o rre la tio n

b a se d C o n tro l(non -eva lua t ive )

IS O -L e a rn in g

IS O -M o d e lo f S T D P

A cto r /C r iticte c h n ic a l & B a s a l G a n g l.

E lig ibility Tra ce s

H ebb-R u le


(”s low ”)

supe rv ised L .

A n tic ip a to ry C o n tro l o f A c tio n s a n d P re d ic tio n o f Va lu e s C o r re la tio n o f S ig n a ls

=

=

=

N eurona l R ew ard Sys tem s(Basa l G ang lia )

B iophys . o f Syn . P las tic ityD o p a m in e G lu ta m a te

STD P

LTP(LT D = a n ti)

IS O -C on tro l

Overview over different methods

M achine Learn ing C lass ica l C ondition ing Synaptic P las tic ity

D ynam ic Prog .(Be llm an Eq .)

R EIN FO R C EM EN T LEAR N IN G U N -SU PERVISED LEAR N IN Ge x a m p le b a s e d c o rre la tio n b a s e d

δ -R u le

M onte C arloC on tro l

Q -Learn ing

TD ( )o ften = 0

λλ

TD (1) TD (0 )

R escorla /W agner

N e u r.T D -M o d e ls(“C rit ic ”)

N e u r.T D -fo rm a lism


(”fas t”)

STD P-M ode lsb io p h y s ic a l & n e tw o rk

EVALU ATIVE FEED BAC K (R ew ards )

N O N -EVALU ATIVE FEED BAC K (C orre la tions )

S A R S AC o rre la tio n

b a se d C o n tro l(non -eva lua t ive )

IS O -L e a rn in g

IS O -M o d e lo f S T D P

A cto r /C r iticte c h n ic a l & B a s a l G a n g l.

E lig ibility Tra ce s

H ebb-R u le


(”s low ”)

supe rv ised L .

A n tic ip a to ry C o n tro l o f A c tio n s a n d P re d ic tio n o f Va lu e s C o r re la tio n o f S ig n a ls

=

=

=

N eurona l R ew ard Sys tem s(Basa l G ang lia )

B iophys . o f Syn . P las tic ityD o p a m in e G lu ta m a te

STD P

LTP(LT D = a n ti)

IS O -C on tro l

Overview over different methods

Supervised Learning: Manymore methods exist !

What can neurons compute ?

What can networks compute ?

Neurons can compute ONLY correlations!

Networks can compute anything .

What is the biological Substrate for all learning?

The Synapse/synaptic strength (the connection strength between two neurons.)

The Basics and a quick comparison(before the maths really starts)

The Neuroscience Basics asa Six Slide Crash Course

I forgot to make a backup of my brain.

All what I had learned last term is gone now.

Human Brain

Cortical Pyramidal Neuron

At the dendrite the incomingsignals arrive (incoming currents)

At the soma currentare finally integrated.

At the axon hillock action potentialare generated if the potential crosses the membrane threshold

The axon transmits (transports) theaction potential to distant sites

At the synapses are the outgoingsignals transmitted onto the dendrites of the target neurons

Structure of a Neuron:

Schematic Diagram of a Synapse

Receptor ≈ ChannelTransmitter Terms to remember !

Ion channels consist of big (protein) molecules which are inserted into to the membrane and connect intra- and extracellular space.

Ion channels:

)()(1ruheruhe VVgVV

RI mmR −=−= restrest


Channels act as a restistance against the free flow of ions: Electrical resistor R:



If Vm = Vrest (resting potential) there is no current flow. Electrical and chemical gradient are balanced (with opposite signs).




Channels are normally ion-selective and will open and close in dependence on the membrane potential (normal case) but also on (other) ions (e.g. NMDA channels).




Channels are normally ion-selective and will open and close in dependence on the membrane potential (normal case) but also on (other) ions (e.g. NMDA channels).

Channels exists for: K+, Na+, Ca2+, Cl-

What happens at a chemical synapse during signal transmission:

The pre-synaptic action potential depolarises the axon terminals and Ca2+-channels open.Pre-synaptic

action potential

Concentration oftransmitterin the synaptic cleft

Post-synapticaction potential

The pre-synaptic action potential depolarises the axon terminals and Ca2+-channels open.

Ca2+ enters the pre-synaptic cell by which the transmitter vesicles are forced to open and release the transmitter.



Thereby the concentration of transmitter increases in the synaptic cleft and transmitter diffuses to the postsynaptic membrane.



Thereby the concentration of transmitter increases in the synaptic cleft and transmitter diffuses to the postsynaptic membrane.

Transmitter sensitive channels at the postsyaptic membrane open. Na+ and Ca2+ enter, K+ leaves the cell. An excitatory postsynaptic current (EPSC) is thereby generated which leads to an excitatory postsynaptic potential (EPSP).

Information is stored in a Neural Network by the Strengthof its Synaptic Connections

Up to 10000 Synapsesper Neuron

Growth or newgeneration ofcontact points

Contact points(syn. Spines)for otherneurons

Time Scales

Working memory

msec sec min hrs days years

Short-term memory

Long-term memory

Mem

ory

Activity

Short-termplasticity

Long-term plasticity

Structural plasticityPh

ysio

logy

Tetzlaff et al. (2012). Biol. Cybern.

Basic Hebb-Rule: = µ ui v µ << 1dωidt

For Learning: One input, one output

An unsupervised learning rule:

A supervised learning rule (Delta Rule):

No input, No output, one Error Function Derivative,where the error function compares input- with output-examples.

A reinforcement learning rule (TD-learning):

One input, one output, one reward

ωit+1 = ωi

t + µ [rt+1 + γvt+1 - vt] uit

ωit+1 = ωi

t - µ dEt

dωi

…Basic Hebb-Rule:

…correlates inputs with outputs by the…

= µ u1 v µ << 1dω1

dt

vx1ω1

Correlation based (Hebbian) learning…

x

How can correlations be learned?

This rule is temporally symmetrical !

Conventional Hebbian Learning

Symmetrical Weight-change curve

Pre

tPre

Post

tPost

Synaptic change %

Pre

tPre

Post

tPost

The temporal order of input and output does not play any role

= µ u1 v dω1

dt

ω 1

X

x1vΣ

Our Standard Notation

Synapse = Amplifier with variable weight ω1

Neuron (will sum differentinputs, here only one)

Output

Input

= µ u1 x vdω1

dt Correlation between Input andOutputHebbian

Learning

u1

ω

δ

1

X

x1

r

vv ’Σ

E

Σ

Compare to Reinforcement Learning (RL)

SynapseNeuron

Output

Input

Error Term

Reward Derivative

Trace

Correlation

This is Hebb !

u1

ω

δ

1

X

x1

r

vv ’Σ

E

ΣTrace

What is this Eligibility Trace E good for ?

Equation for RLSo-called: Temporal Difference (TD) Learning

u1

ωit+1 = ωi

t + µ [rt+1 + γvt+1 - vt] uit

I. Pawlow

Classical Conditioning

Σω0 = 1

ω1

Unconditioned Stimulus (Food)

Conditioned Stimulus (Bell)

Response

Σ

We start by making a single compartment model of a dog !

X

∆ω1+

The reductionist approachof a theoretician:

Stimulus Trace E

What is this Eligibility Trace E good for ?

The first stimulus needs to be “remembered” in the system

ω

δ

1

X

x1

r

vv ’Σ

E

Σ

TD LearningCondition for convergence: δ=0

Measured at theOutput of the System(Output Control)

u1

δt = rt+1 + γvt+1 - vt

Correlation based learning: No teacher

Reinforcement learning , indirect influence

Reinforcement learning, direct influence

Supervised Learning, Teacher

Programming

Learning Speed Autonomy

Animal

Env.

Animal

Open Loop versus Closed Loop Systems

Output Controlthrough observationof the agent

External Value systems

Input Controlat the agent’sown sensors

True internalValue systems

Evaluative Feedback(Klopf 1988)

Non- Evaluative Feedback

Designer

Agent

Reinforcement

Env.

The Difference between Input and Output Control

Is this a “real” or just an “academic” Problem:Why would we want Input Control ?

Designer

Agent

WrongReinforcement

Output Controlthrough observationof the agent

Input Controlat the agent’sown sensors

The Output control paradigm can and does lead to major problems inreinforcement learning, because the wrong behaviour might be reinforced.

Env.

Agent with own Goals(Me !)

Environment(You !)

My perception of yourattentiveness

Speech

Input Control Loop:Allows me to control my lectureand to learn to improve

Prior knowledgeand shared goalshelp!

Reinforces my running around

“Marsian” observerwith other Sensors and/or

other Goals

Bodyheat

A “funny”example

Relevance for Learning:1) Use output control to get a system that does what YOU want. (engineering

system)

2) Use Input control to get an autonomous (biologically motivated system).

Correlation based learning: No teacher

Reinforcement learning , indirect influence

Reinforcement learning, direct influence

Supervised Learning, Teacher

Programming

Learning Speed AutonomyOther considerations:

• Good ending point

Is this a real or just an academic problem?

Observer ObservableQuantity

Agent thatbehaves(System)

observes

reinforces

What is the desired(most often occurring)output state ?

Zero !

V

0

Observation of V

Control of Lever

ObservedSystem

Observer/Controller

The Situation

Experiment:

V

0

Lever

Here are some valid solutionsfor a V=0 reinforcement.How should the lever be moved?

Assume you have one lever by which you can try to drive V towards zero, whenever it suddenly deviates

Obviously V=0 can be easily obtained when the lever follows V!

Motors& Wheels

Sensor RangeSensors

SR = SL = 0AR

AL

What the Agent wanted to learn was to approach theyellow food blob and eat it.

SensibleStimulus

The System: A Braitenberg VehicleV. Braitenberg, (1984), “Vehicles: Experiments in synthetic Psychology”

Motor Signals A

SR

SL

Sensor Signals S

1:1 conn.

Output signal V=SR - SL AR -AL =Lever signal

SR = SL = 0

What you have reinforced:

Leaving the food blob totally out of sight also gets V=0(only the poor creature never eats and dies…….)

And………….. Things will get worse…….

The observable quantity V was not appropriate !One should have observed AR, AL (but could not).

0

Observer Observer knows:“1 )This is a Down-Neuron”

(for Eye-Muscles)

Synapses=StatesWeights =Values

>1=reward

Enough to triggeran action !

Motor Neuron (Actor)

Assumptions 1,2lead to

Observerinduced

reinforcement

Observer knows: “2) There is evidence that the spatial ordering ofsynapses at a dendrite leads to direction selectivity andthe observer has measured where the synapses are on the dendrite”

Assumptions 1 and 2 correspond to the Observer’s knowledge of this system

This is OutputControl !

Observer “This is a Down-Neuron”(for Eye-Muscles)


>1=reward

Environmenthere also “Optics”


Ret

inal

rece

ptiv

e fie

lds

This Observer did lack the knowledge that the optics of the eye inverts the image

True virtualimage motion

Really this synapse shouldhave been reinforced

The observable quantities were appropriate but the Observer had a lack of knowledge about the inner signal processing in this system.

Observer



Motor Neuron (Actor)R

etin

al re

cept

ive

field

s

True virtualimage motion

A first order fallacy:

A second order fallacy:

0

The observable quantity V was not appropriate !One should have observed AR, AL (but could not).

More realistically !

• Think of an engineer having to control the behavior and learning of a complex Mars-Rover which has many (1000?) simultaneous signals. – How would you know which signal configuration is at the moment

beneficial for behavior and learning. OUTPUT CONTROL WILL NOT WORK

• Ultimately only the Rover can know this.– But how would it maintain stability to begin with (not the be doomed

from starters)

Since observers cannot have complete knowledge of the observed system we find that:

Output Control is fundamentally problematic.

A complex robot-world model required deep understanding on the side of the designer to define the appropriate reinforcement function(s).

This leads to a large degree of interference.

As a consequence the robot has then the world model of the designer (but not its own) – A slave not an autonomous agent.

∆ρ = Ι ∗ ΙΙ ∗S > 0I



Ret

inal

rece

ptiv

e fie

lds

Spont.DriveIII

I

II

S

Input Controlwill always work!

This isInput Control

∆ρ = ΙΙΙ ∗ ΙΙ ∗S = 0III

Input Control

The Chicken-Egg Problem Type I

Which came first: Chicken or Egg?

Control of my Input(I, chook, want to feel an egg under my butt):

I, chook, would like to sit onthis egg as long as requiredto hatch .

Control of its Output:

I, farmer, would like to getas many eggs as possible and takethem away from the chook.

AutonomyControl from inside

ServituteControl from Outside

A fundamental Conflict

Here a Chicken-Egg Problem of Type II

But that’s simple, isn’t it: Teaching will do it (supervised learning) !You tell me, this is good and that is bad…………..

Supervised Learning

Reinforcement Learning – Learning from experience while acting in the world

I tell myself, this is good and that is bad………….

Requires a Value-System in the Animal(Dopaminergic System, Schultz 1998)

Still: How do we get this in the first place ?

a) Bootstrapping Problem: Evolution does not teach (evaluate).b) Viewpoint Problem: Those are the values of the teacher and not of the creature.c) Complexity Problem: SL requires already complex understanding.

Value Systems (in the brain)

Animal

Evolution

World

Fully situatedbut takes long

Robot

Designer

WorldBadly situatedbut can be achieved quickly

Designer’sWorld-view

ValuesValues

The Problem:How to bootstrap a Value System ?

Evolve it ! Design it !

Übungen (practicals) - third institute of physics · covering contents parallel to the lectures...

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