Fundamentals of Computational Neuroscience 2e

Transcription

1 Fundamentals of Computational Neuroscience 2e January 1, 2010 Chapter 10: The cognitive brain

2 Hierarchical maps and attentive vision A. Ventral visual pathway B. Layered cortical maps Receptive field size / deg Inferior Temporal cortex Posterior V4 V2 V1 } Cccipital cortex Layer 4 Layer 3 Layer 2 LGN Eccentricity / deg Thalamus Layer 1 Layer 1

3 Attention in visual search and object recognition Visual search WHERE Given : Particular Features features ( Target target object Object )) Function : Scanning ( Attentional attentional window Window scans Scanns the the Entire entire scene Scene ) Given : Particular Spatial spatial location Location ( Target target position) Position) Function : Binding ( Attentional attentional Windo window binds Bind Features features for Identification identification ) WHAT Object Recognition recognition Gustavo Deco

4 Model Inhibitory IT Pool ( Object recognition ) Top-down bias ( Object specific ) Top-down bias ( Location specific ) Locus attentional preferred What Where PP ( Spatial location ) V1 V4 (Feature extraction )... Inhibitory pool... Inhibitory pool Gabor jets Inhibitory pool LGN Visual field

5 Example results A. `Parallel search B. `Serial search E X X Number of items F E F Number of items Activity Activity PP PP Time Time

6 The interconnecting workspace hypothesis Evaluative system (VALUE) Long-term memory (PAST) Global workspace Attentional system (Focusing) Perceptual system (PRESENT) Motor system (FUTURE) Stanislas Dehaene, M. Kergsberg, and J.P. Changeux, PNAS 1998

7 Stroop task modelling REWARD (error signal) VIGILANCE WORKSPACE NEURONS attentional suppression of word attentional amplification of colour SPECIALIZED PROCESSORS INPUTS & OUTPUTS WORD grey COLOUR black NAMING RESPONSE black

8 The anticipating brain 1. The brain can develop a model of the world, which can be used to anticipate or predict the environment. 2. The inverse of the model can be used to recognize causes by evoking internal concepts. 3. Hierarchical representations are essential to capture the richness of the world. 4. Internal concepts are learned through matching the brain s hypotheses with input from the world. 5. An agent can learn actively by testing hypothesis through actions. 6. The temporal domain is an important degree of freedom.

9 Outline Environment Agent PNS Sensation CNS Sensation p ( s c, a ) p ( s s, c ) Internal states External states p ( c a ) p ( c s,c ) p ( c c,c ) p ( a a, s ) p ( a s, c ) PNS Action CNS Action

10 Recurrent networks with hidden nodes The Boltzmann machine: Hidden nodes Visible nodes Energy: H nm = 1 2 ij w ijs n i s m j Probabilistic update: p(s n i = +1) = 1 1+exp( β P j w ij s n j ) Boltzmann-Gibbs distribution: p(s v ; w) = 1 Z m h exp( βhvm )

11 Training Boltzmann machine Kulbach-Leibler divergence KL(p(s v ), p(s v ; w)) = = v s p(s v ) log p(sv ) p(s v ; w) v p(s v ) log p(s v ) s v p(s v ) log p(s v ; w) s Minimizing KL is equivalent to maximizing the average log-likelihood function l(w) = v p(s v ) log p(s v ; w) = log p(s v ; w). s Gradient decent Boltzmann Learning w ij = η l w ij = η β ( ) 2 si s j clamped s i s j free.

12 The restricted Boltzmann machine Hidden nodes Visible nodes Contrastive Hebbian learning: Alternating Gibbs sampling t=1 t=2 t=3 t= 8

13 Deep generative models Concept input Recognition readout and stimulation RBM layers RBM/Helmholtz layers Model retina Image input

14 Adaptive Resonance Theory (ART) Gain control Attentional subsystem F 2 u t Reset Orienting subsystem w t w b g + F 1 v s ρ + + Input

15 Further Readings Edmund T. Rolls and Gustavo Deco (2001), Computational neuroscience of vision, Oxford University Press. Karl Friston (2005), A theory of cortical responses, in Philosophical Transactions of the Royal Society B 360, Jeff Hawkins with Sandra Blakeslee (2004), On intelligence, Henry Holt and Company. Robert Rosen (1985), Anticipatory systems: Philosophical, mathematical and methodological foundations, Pergamon Press. Geoffrey E. Hinton (2007), Learning Multiple Layers of Representation, in Trends in Cognitive Sciences 11: Stephen Grossberg (1976), Adaptive pattern classification and universal recoding: Feedback, expectation, olfaction, and illusions, in Biological Cybernetics 23: Gail Carpenter and Stephen Grossberg (1987), A massively parallel architecture for a self-organizing neural pattern recognition machine in Computer Vision, Graphics and Image Processing 37: Daniel S. Levine (2000), Introduction to neural and cognitive modeling, Lawrence Erlbaum, 2nd edition. James A. Freeman (1994), Simulating neural networks with Mathematica, Addison-Wesley.