brain-like design of sensory-motor programs for robots g. palm, uni-ulm

Brain-like design of sensory-motor programs

for robots

G. Palm, Uni-Ulm

The cerebral cortex is a huge associative memory,

or rather a large network of associatively connected topographical areas.

Associations between patterns are formed by Hebbian learning.

Even simple tasks require the interaction of many cortical areas.

Modelling Cortical Areas withAssociative Memories

Andreas Knoblauch & Günther PalmDepartment of Neural Information Processing

University of Ulm, Germany

• Introduction• Neural associative memory

• Willshaw model

• Spiking associative memory (SAM)

• Modeling Cortical Areas for the MirrorBot project• Cortical areas for the minimal scenario „Bot show plum!“

• Implementation of the language areas using SAM

• Summary and Discussion

Overview

Associative Memory (AM)

P1 , P

2 , ... , P

M AM

Addressing with one or more noisy patterns P

X = P

i1 + P

i2 + ... + P

im + noise

AM (Pi1

, Pi2

, ... , Pim

)

(1) Learning patterns:

(2) Retrieving patterns

Neural Associative Memory (NAM)

Binary Willshaw model - sparse coding:

pattern P = 1 1 1 {0,1}n

k = O(log n)

n neurons O(n2/log2n) patterns can be storedmemory capacity ln 2 0.7 bit/synapse

- extensions:- iterative retrieval (Schwenker/Sommer/Palm 1996, 1999)

- spiking associative memory (Wennekers/Palm 1997)

(mainly for biological modelling)

(Willshaw 1969, Palm 1980, Hopfield 1982)

k

n

Binary Willshaw -NAM: Learning

Patterns P(k) {0,1}n , k=1,...,M

P(1) = 1 1 1 1 0 0 0 0

Memory matrix

Aij = min ( 1 , P(k) · P(k))

k i j

P(1) 1 1 1 1 0 0 0

1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

i

j

Binary Willshaw -NAM: Learning

Patterns P(k) {0,1}n , k=1,...,M

P(1) = 1 1 1 1 0 0 0 0P(2) = 0 0 1 1 1 1 0 0

Memory matrix

Aij = min ( 1 , P(k) · P(k))

k i j

P(1) 1 1 1 1 0 0 0 P(2) 0 0 1 1 1 1 0

1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0

i

j

Binary Willshaw -NAM: Retrieving

Learned patterns:P(1) = 1 1 1 1 0 0 0 0P(2) = 0 0 1 1 1 1 0 0

Address pattern:PX = 0 1 1 0 0 0 0 0

PX A

0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0




neuron potentials:x = APX

PX A

0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0

x 2 2 2 2 1 1 0




Neuron potentials:x = APX

Retrieval result:PR = x

PX A

0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0

x 2 2 2 2 1 1 0

PR (=2) 1 1 1 1 0 0 0

NAM and Problems with Superpositions: Learning

NAM and Problems with Superpositions: Retrieving (1)

Classical: Addressing with 1/2 pattern (k/2) + noise (f)

NAM and Problems with Superpositions: Retrieving (2)


Superposition: Addressing with2 x 1/2 pattern + noise

NAM and Problems with Superpositions: Solutions?


Superposition: Addressing with2 x 1/2 pattern + noise

Possible Solutions: Spiking neuron models Iterative retrieval? combination?

Working Principle of Spiking Associative Memory

Interpretation of classical potentials x as dx/dt temporal dynamics- the most excited neurons fire first- breaking of symmetry by feedback

- pop-out of one pattern- suppression of others

Problem: How to achieve threshold control?

(e.g. Wennekers/Palm '97)

Counter Model of Spiking Associative Memory

States („counters“) of neuron i : CH

i(t) : # spikes received heteroassociatively until time t

CAi(t) : # spikes “ auto- “ “ “

C(t) : # all spikes

Instantaneous Willshaw-Retrieval-Strategy at time t:

neuron i probably is part of the pattern to be retrieved, if

CAi(t) C(t)

Simple linear example: dx

i / dt = a CH

i + b ( CA

i - C) , b >> a > 0 , 1

Knoblauch/Palm 2001

Overview

A minimal cortical model for a very simple scenario, “Bot show plum!”

Information flow and binding in the model: Hearing and understanding “Bot show plum!” Reacting: Seeking the plum, and pointing to the plum

Minimal model “Bot show plum!” - Overview


- 3 auditory sensory areas


- 3 auditory sensory areas- 2 grammar areas


- 3 auditory sensory areas- 2 grammar areas- 3 visual sensory areas


- 3 auditory sensory areas- 2 grammar areas- 3 visual sensory areas- 1 somatic sensory area


- 3 auditory sensory areas- 2 grammar areas- 3 visual sensory areas- 1 somatic sensory area- 1 visual attention area


- 3 auditory sensory areas- 2 grammar areas- 3 visual sensory areas- 1 somatic sensory area- 1 visual attention area- 4 goal areas


- 3 auditory sensory areas- 2 grammar areas- 3 visual sensory areas- 1 somatic sensory area- 1 visual attention area- 4 goal areas- 3 motor areas



Together 17 cortical areas (incl. 2 sequence areas A4/G1)




+ evaluation fields




+ evaluation fields+ activation fields

Minimal model “Bot show plum!” - Integration

Input fromrobot sensors -

robot software - simulation environment -

Minimal model “Bot show plum!” - Integration

Input fromrobot sensors -

robot software - simulation environment -

Output to - robot actors - robot software - simulation environment

Minimal model “Bot show plum!” - Connectivity

Bot listens to “Bot show plum!”

“Bot show plum!”: Processing of ‘bot’ (1)

“Bot show plum!”: Processing of ‘show’ (1)

“Bot show plum!”: Processing of ‘show’ (8/9)

“Bot show plum!”: Processing of ‘plum’ (1)

After listening to “Bot show plum!”: Bot knows finally what to do (G1/G3)

Bots reaction to “Bot show plum!”

“Bot show plum!”: Seek plum - Activate motor areas (1)

“Bot show plum!”: Seek plum - Activate motor areas (6/7)

“Bot show plum!”: Seek plum - Motor areas are activated!

“Bot show plum!”: Seek plum - Activate visual attention (1)

“Bot show plum!”: Seek plum - Activate visual attention (2)

“Bot show plum!”: Seek plum - Activate vis. attention (3)

“Bot show plum!”: Seek plum - Activate vis. attention (4)

“Bot show plum!”: Seek plum - Attention is active!

“Bot show plum!”: Seek plum - Check if plum is visible (1)

“Bot show plum!”: Seek plum - Wait until plum is visible!

“Bot show plum!”: Seek plum - plum is visible (1)

“Bot show plum!”: Plum is found, now point to plum

“Bot show plum!”: point to plum - activate motor areas (1)

“Bot show plum!”: point to plum - activate motor areas (5/6)

“Bot show plum!”: point to plum - motor areas are activated!

“Bot show plum!”: point to plum - activate hand position control (1)

“Bot show plum!”: point to plum - hand position control is active

“Bot show plum!”: point to plum - hand moves to correct position (1)

“Bot show plum!”: point to plum - hand moves to correct position (2)

“Bot show plum!”: point to plum - hand moves to correct position

“Bot show plum!”: point to plum - hand is in correct position (1)

“Bot show plum!”: point to plum - hand is in correct position (2)

“Bot show plum!”: Bot has completed the task!

Summary:

- We have proposed a minimal model for „Bot show plum!“ - in principle implementable by using

biological neurons and associative memories

Discussion:

- biologically realistic?

- Modell extensions? - complexer scenarios? - learning? - mirror system?

brain-like design of sensory-motor programs for robots g. palm, uni-ulm

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