![3
Experiment One – introduction
• Inspired by the article:
• A back-propagation programmed network that simulates response
properties of a subset of posterior parietal neurons. David Zipser,
Richard A. Andersen (Nature, 1988) [http://dx.doi.org/10.1038/331679a0]
• Excerpt:
• Experiments in macaque monkeys (proposed that
area 7a contains visual and eye-position neurons)
• Experimental results from area 7a:
eye-position neurons (15%),
visual neurons (21%), combination (57%)
• Interaction between eye-position and visual
responses ( gain fields) Image source:
http://en.wikipedia.org/wiki/Brodmann_area_7](https://image.slidesharecdn.com/cnc-121205090151-phpapp01/85/Short-presentation-about-my-thesis-3-320.jpg)
Short presentation about my thesis
- 1. Representation of object position in various frames of reference using robotic simulator Gain Modulation CNC seminar 5.12.2012 Student: Marcel Švec Supervisor: doc. Ing. Igor Farkaš, PhD.
- 2. 2 Annotation • Humans use several egocentric frames of reference for effective sensomotoric coordination (eye-hand): eye-centered, head-centered, body-centered location… • How does brain carry out computations such as coordinate transformation? How are sensory inputs translated to motor outputs? • Our aim is to implement and evaluate neural network model capable of coordinate translation • Goal of the design is to create inner representation of the surrounding space in simulated agent • We use robotic simulator iCub for experiments • Study of area 7a (visual and eye-position neurons), most likely this area preforms spatial transformations
- 3. 3 Experiment One – introduction • Inspired by the article: • A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons. David Zipser, Richard A. Andersen (Nature, 1988) [http://dx.doi.org/10.1038/331679a0] • Excerpt: • Experiments in macaque monkeys (proposed that area 7a contains visual and eye-position neurons) • Experimental results from area 7a: eye-position neurons (15%), visual neurons (21%), combination (57%) • Interaction between eye-position and visual responses ( gain fields) Image source: http://en.wikipedia.org/wiki/Brodmann_area_7
- 4. 4 Experiment One – spatial gain fields • Determining the effect of eye position on receptive fields • visual stimulus always present at the same retinal location • monkey has had fixed and fixates on a point f (Zipser, Andersen 1988)
- 5. 5 Experiment One – neural network model Proposed neural network model: • Three layer, back-propagation • Input: visual stimulus and eye position • Output: head-centered coordinates Model and experimental retinal receptive fields were remarkably similar (Zipser, Andersen 1988)
- 6. 6 Experiment One – dataset • Input: • eye position – vertical and horizontal orientation (angle) • visual stimulus – images from the left and right eye (processed) • Output: • Body-referenced target position expressed by horizontal and vertical slope • iCub generator: • controlling iCub (eyes limits) • where to put an object (camera properties) • eyes rotation (keeping object in FOV) • what size (scaling) • processing (color filter)
- 7. 7 Experiment One – training, testing, results • FANN – Fast Artificial Neural Network Library • C, multilayer neural networks, back-propagation training (incremental, RPROP, Quickprop, batch), cross-platform, bindings to >15 languages… • Network model: • Input layer = eye_tilt + eye_version + left_eye_image + right_eye_image = 11 + 21 + 64*48 + 64*48 = 6176 neurons • Hidden layer = 250 neurons • Output layer = x-slope + y-slope = 10 + 10 = 20 neurons (every 20 degrees) • So far best results: • Sigmoids, steepness hidden = 0.05 (1/20), output = 0.0715 (1/14) • Algorithm – RPROP (batch, doesn’t use learning rate) • 93 epochs on 1000 patterns, MSE < 0.0001, training took less than 15 minutes, comparing to incremental training – 200 epochs, MSE < 0.0017, 53 minutes • Average error: x < 4, y < 3.3 degrees, standard deviations: x = 3.6, y = 3.2
- 8. 8 Experiment One – results sorted errors on testing data • Possible cause of inaccuracies is the character of patterns – objects of different size, shape and orientation may appear at the same location, which means that inputs that differ in visual stimulus (size, shading) may require the same output. • Solutions (open): another hidden layer, different network model? Comparing real and desired values of output neurons
- 9. 9 Gain fields Mapping the receptive field of parietal neuron Stimulus is present at the same retinal location (head turned left) Neural response of the neuron when the head is turned right and left: • location and shape remains • amplitude (gain) changes Salinas et al. (2001)
- 10. 10 Gain fields – computing • Gain fields of parietal neurons depend on eye position, head position… note: although single neurons are modulated, several neurons have to be combined to get the whole information (population code) • r = f(x – a) g(y) // single parietal neuron • x – retinal location of the stimulus • y – gaze angle • f – function for the response to the visual stimulus • a – location of the peak of function f • r – amplitude of the response • g – gain field • R = F(c1x + c2y) // downstream response • F – peaked function that represent receptive field • Set of downstream neurons may represent quantity (x + y), while another (x-y), both sets being driven by the same population of gain-modulated neurons. • Very general mechanism. Salinas et al. (2001)
- 11. 11 Gain modulation and coordinate transformations • Gain modulated neurons are suited to add, subtract and performs operations essential for coordinate transformations. • Figure: • 3 eyes positions • left columns – responses of 4 idealized gain-modulated neurons • right column – responses of a downstream neuron (weighted sum) Salinas et al. (2001)
- 12. 12 Gain modulation • it is an extremely widespread mechanism • non-linear combination of information from several sources • affected is sensitivity (amplitude, gain), not selectivity (sensitivity or receptive field properties) • indications that it serves as a basis for computations (coordinate transformations, invariant responses) • related also to • Object recognition (invariance) • Focusing attention • Motion processing
- 13. 13 http://masterthesis.itbrutus.com Thanks for your attention Cited sources: • Salinas, E. and T. J. Sejnowski (2001). Gain modulation in the central nervous system: Where behavior, neurophysiology, and computation meet. The Neuroscientist 7, pp. 430440. • Zipser, D. and R. A. Andersen (1988). A backpropagation programmed network that simulates response properties of a subset of posterior parietal neurons. Nature 331, pp. 679684.