A Neural Model for the Adaptive Control of Saccadic Eye Movements Sohrab Saeb, Cornelius Weber and Jochen Triesch International Joint Conference on Neural Networks (IJCNN)‏ June 2009

Ballistic Movements Ballistic movement. A movement that cannot be controlled once it has been initiated and that is thought to be programmed by the cerebellum.

Saccadic Eye Movements Saccadic eye movements: Quick, simultaneous movements of both eyes in the same direction. During normal saccades, the eye jumps from one fixation point to another. The peak angular speed of the eye during a saccade reaches up to 1000°/sec in monkeys (somewhat less in humans).

Saccadic Eye Movement: Definitions Duration Amplitude Peak Velocity Enderle & Wolfe (1987)‏ Visual Error:

Saccade Characteristics: The Main Sequence, Velocity Profiles Harwood et al. (1999)‏Collewijn et al. (1988)‏ Amplitude (deg)‏

Biological Basis of Saccades Hopp & Fuchs (2004)‏ Superior Colliculus Brainstem Eye Muscles Cerebellum

Biological Basis of Saccades Enderle et al. (1984)‏ Hopp & Fuchs (2004)‏

The Oculomotor Plant: A Computational Model

The Neural Control Signal: Optimization  What is the neural control signal that underlies such kind of behavior?  What is the cost function that underlies this optimization process?  How is this neural control signal optimized?

The Cost Function: Ideas  Minimizing the time (Enderle & Wolfe, 1987)‏  Signal-dependent Noise (Harris & Wolpert, 1998; Chen-Herris et al., 2008)‏

The Cost Function: How to implement adaptation? Numerous experimental results indicate that the saccadic eye movements are constantly adapted (Hopp & Fuchs, 2004). Cost function: signal dependent noise idea Optimization process: stochastic optimal control boundary conditions re-optimization for every saccadic duration Chen-Herris et al. (2008)‏

The Open-Loop Neural Controller Idea Delay Activities Retinal Position Target Position

The gaze should reach the target as soon as possible and then stand still on the target position. The Cost Function 2. The power of the neural command signal should be constrained

Adaptation: The Gradient Descent Approach Adaptive learning rate: Similar to RPROP (Riedmiller & Braun, 1993)‏

Delay Activities Retinal Position Calculating Cost Function Gradients

Retinotopic Position Delay Activities Calculating Cost Function Gradients

Results #1 Optimized neural command signals as the difference between agonist and antagonist neural signals. Eye position (eccentricity) in head coordinates. Model parameters: σ = 0.002, k reg = 0.016, p=4.

Results #2 Comparing simulation results to experimental data. Model parameters: σ = 0.002, k reg = 0.016, p=4 Experimental data from Harwood et al. (1999)‏

Results #3 (a) Adapted velocity profiles for target positions from 5 ◦ to 80 ◦. (b) Experimental data taken from Collewijn et al. (1988). In both plots the symmetry degrades gradually as the saccadic amplitude increases.

Conclusion  Simple open-loop neural controller  Penalizing the total visual error instead of just the movement period  Local learning rule Retinotopic Position Delay Activities

Future Work  Generalizing to two spatial axes  Forward model learning  Liquid State Machine (LSM) instead of delay lines  Other ballistic motor control tasks

Acknowledgements Collaborators: Cornelius Weber FIAS Goethe University Frankfurt Jochen Triesch FIAS Goethe University Frankfurt

Possible Biological Substrates