1. Derek Harter University of Memphis May 17, 2004
Aperiodic Dynamics and the Self-Organization of Cognitive Maps in Autonomous Agents
Derek Harter
University of Memphis
May 17, 2004
FLAIRS 2004

2. Discrete difference eq.
ANN KA K
Discrete difference eq.
Continuous
Feed-Forward
Recurrent
Back-Propogation
Hebbian

3. Table 1: Characterization of the hierarchy of K-sets
KA – Set Hierarchy
Table 1: Characterization of the hierarchy of K-sets
Type
Structure
Inhrt Dynamics
Exs. in brain*
KA-0
Single Unit
Nonlinear I/O function
All higher level K sets are composed of K0 units
KA-I
Populations of excitatory or inhibitory units
Fixed point convergence to zero or nonzero value
PG, DG, BG, BS
KA-II
Interacting populations of excitatory and inhibitory units
Periodic, limit cycle oscillations; frequency in the gamma band
OB, AON, PC, CA1, CA3, CA2, HT, BG, BS, Amygdala
KA-III
Several interacting KII and KI sets
Aperiodic, chaotic oscillations
Cortex, Hippocamp, Midline Forebrain
KA-IV
Interacting KIII sets
Spatio-temporal dynamics with global phase transitions (itinerancy)
Hemisphere cooperation of cortical, HF and MF by the Amygdala
* Notations: PG – periglomerular; OB - olfactory bulb; AON - anterior olfactory nucleus; PC- prepyriform cortex; HF - hippocampal formation; DG - dentate gyrus; CA1, CA2, CA3 - curnu ammonis sections of the hippocampus; MF - midline forebrain; BG - basal ganglia; HT - hypothalamus; DB - diagonal band; SP - septum
KA-0 Unit Difference Equation:
Transfer function:
KA-III
KA-Ie/i E1 E2 I1 I2
Layer 1 d
receptors
Layer 2
Layer 3 E1 E2
Named in honor of Katchalsky, a famous and influential neuroscientist)
Maximal slope of transfer function is displaced to the excitatory side of the resting level. An excitatory input to the population raises the activity level of its neurons, and also increases their sensitivity to input from each other, so that they interact more strongly.
The asymmetry of the sigmoid function means that the OB is destabilized by input. I1 I2
KA-II E1 E2 I1 I2 + -

4. KA-III =0.058 =0.-044 =0.0109 =0.152 E1 E2 I1 I2 Layer 1 d
receptors
Layer 2
Layer 3

5. KA, K-Set and Rat Power Spectra
KA-III model – Layer 1

6. Evolution of Intentional & Deliberative Behavior in Complete Biological Organisms
3.5 billion years: single-cell entities
550 million years: fish & vertebrates
430 million years: insects
370 million years: reptiles
330 million years: dinosaurs
250 million years: mammals
120 million years: primates
18 million years: great apes
2.5 million years: man
5000 years: writing
Basic Limbic System
Primitive Hippocampus
Long-term memory
Beyond stimulus/response
Episodic Memory
Cognitive Maps
Intentional Behavior & Deliberative Actions

7. Limbic System: Simplest Complete Intentional System
Far from equilibrium, therodynamic systems
Mechanisms of self-organization
competition
cooperation
autocatalytic loops
hierarchy & mesh
Aperiodic dynamics
Expectation or reafference
Embodiment
environment/organism coupling
Small worlds type divergent-convergent systems connections
(Kozma, Freeman & Erdi, 2002)

9. Architecture of Hippocampal Simulation

10. Formation of AM Pats in KA-IIIc d b
(Loc 1) (Loc 2) (Loc 3) (Loc 4) (Loc 5) (Loc 6) (Loc 7) (Loc 8)
(Test d) (Test c) (Test b) (Test a)

11. Comparison of Closest AM Pattern
Target
Loc-Test
Closest
1-a 1-b
1-b 1-a
1-c 1-b
1-d 1-a
2-a 2-d
2-b 2-c
2-c 2-b
2-d 2-b
3-a 3-b
3-b 3-a
3-c 3-b
3-d 3-a
4-a 4-c
4-b 4-d
4-c 4-a
4-d 4-b
5-a 5-b
5-b 5-a
5-c 5-d
5-d 5-c
6-a 6-b
6-b 6-d
6-c 6-b
6-d 6-b
7-a 7-d
7-b 7-d
7-c 7-d
7-d 7-a
8-a 8-c
8-b 8-d
8-c 8-a
8-d 8-c a c d b b d c a

12. Conclusion The K/KA neural population model
highly recurrent
multi-layer
biologically grounded model
aperiodic neurodynamics
The Limbic system model with the primitive hippocampus represents an enormous leap in behavioral complexity in biological organisms
Intentional behavior
Deliberative behavior
KA-III can develop representations of the environment using aperiodic dynamics.