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Biological Modeling of Neural Networks: Week 12 – Decision models: Competitive dynamics Wulfram Gerstner EPFL, Lausanne, Switzerland 12.1 Review: Population.

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Presentation on theme: "Biological Modeling of Neural Networks: Week 12 – Decision models: Competitive dynamics Wulfram Gerstner EPFL, Lausanne, Switzerland 12.1 Review: Population."— Presentation transcript:

1 Biological Modeling of Neural Networks: Week 12 – Decision models: Competitive dynamics Wulfram Gerstner EPFL, Lausanne, Switzerland 12.1 Review: Population dynamics - competition 12.2 Perceptual decision making - V5/MT - Decision dynamics: Area LIP 12.3 Theory of decision dynamics - shared inhibition - effective 2-dim model 12.4. Decisions in connected pops. - unbiased case - biased input 12.5. Decisions, actions, volition - the problem of free will Week 12 – Decision models

2 Week 12-part 1: How do YOU decide?

3 Week 12-part 1: Decision making turn Left? Right?

4 noise model A I(t) h(t) (escape noise/fast noise) high noise slow transient Population activity Membrane potential caused by input Attention: - valid for high noise only, else transients might be wrong - valid for high noise only, else spontaneous oscillations may arise Week 12-part 1: Review: High-noise activity equation

5 I(t) Week 12-part 1: Review: microscopic vs. macroscopic

6 Input indicating ‘left’ Input indicating ‘right’ Week 12-part 1: Competition between two populations

7 Week 12-part 1: How do YOU decide?

8 Biological Modeling of Neural Networks: Week 12 – Decision models: Competitive dynamics Wulfram Gerstner EPFL, Lausanne, Switzerland 12.1 Review: Population dynamics - competition 12.2 Perceptual decision making - V5/MT - Decision dynamics: Area LIP 12.3 Theory of decision dynamics - shared inhibition - effective 2-dim model 12.4. Decisions in connected pops. - unbiased case - biased input 12.5. Decisions, actions, volition - the problem of free will Week 12 – Decision models

9 ‘ Is the middle bar shifted to the left or to the right? ’ Week 12-part 2: Perceptual decision making?

10 2) Neighboring cells in visual cortex MT/V5 respond to motion in similar direction cortical columns visual cortex 1) Cells in visual cortex MT/V5 respond to motion stimuli Week 12-part 2: Detour: receptive fields in V5/MT Albright, Desimone,Gross, J. Neurophysiol, 1985 IMAGE

11 Recordings from a single neuron in V5/MT Receptive Fields depend on direction of motion Week 12-part 2: Detour: receptive fields in V5/MT Random moving dot stimuli: e.g.Salzman, Britten, Newsome, 1990 Roitman and Shadlen, 2002 Gold and Shadlen 2007

12 Receptive Fields depend on direction of motion:  = preferred direction = P Week 12-part 2: Detour: receptive fields in V5/MT

13 coherence 0.8=80% coherence 0.5 = 50% coherence 0.0 Image: Salzman, Britten, Newsome, 1990 Eye movement coherence -1.0 opposite direction Week 12-part 2: Experiment of Salzman et al. 1990

14 Monkey behavior w. or w/o Stimulation of neurons in V5/MT X = coherent motion to bottom right 0.5 No bias, each point moves in random direction 0.5 1.0 Monkey chooses right fixation Visual stim. LED Blackboard: Motion detection/stimulation Salzman, Britten, Newsome, 1990 P N Week 12-part 2: Experiment of Salzman et al. 1990

15 excites this group of neurons coherence 0.8=80% coherence 0.5 = 50% coherence 0.0 coherence -1.0 Week 12-part 2: Experiment of Salzman et al. 1990

16 Behavior: psychophysics With stimulation Week 12-part 2: Experiment of Salzman et al. 1990

17 Biological Modeling of Neural Networks: Week 12 – Decision models: Competitive dynamics Wulfram Gerstner EPFL, Lausanne, Switzerland 12.1 Review: Population dynamics - competition 12.2 Perceptual decision making - V5/MT - Decision dynamics: Area LIP 12.3 Theory of decision dynamics - shared inhibition - effective 2-dim model 12.4. Decisions in connected pops. - unbiased case - biased input 12.5. Decisions, actions, volition - the problem of free will Week 12 – Decision models

18 coherence 85% coherence 50% coherence 0% RF of Neuron in LIP: -selective to target of saccade -increases faster if signal is stronger - activity is noisy LIP is somewhere between MT (movement detection) and Frontal Eye Field (saccade control) Roitman and Shadlen 2002 Week 12-part 2: Experiment of Roitman and Shadlen in LIP (2002)

19 Neurons in LIP: -selective to target of saccade -increases faster if signal is stronger - activity is noisy LIP is somewhere between MT (movement detection) and Frontal Eye Field (saccade control) Week 12-part 2: Experiment of Roitman and Shadlen in LIP (2002)

20 Quiz 1, now Receptive field in LIP [ ] related to the target of a saccade [ ] depends on movement of random dots

21 Biological Modeling of Neural Networks: Week 12 – Decision models: Competitive dynamics Wulfram Gerstner EPFL, Lausanne, Switzerland 12.1 Review: Population dynamics - competition 12.2 Perceptual decision making - V5/MT - Decision dynamics: Area LIP 12.3 Theory of decision dynamics - shared inhibition - effective 2-dim model 12.4. Decisions in connected pops. - unbiased case - biased input 12.5. Decisions, actions, volition - the problem of free will Week 12– Decision models, part 3

22 activity equations population activity Membrane potential caused by input Input indicating left movement Input indicating right movement Week 12-part 3: Theory of decision dynamics Blackboard: reduction from 3 to 2 equations

23 activity equations Population activity Inhibitory Population Blackboard: Linearized inhibition

24 activity equations Membrane potential caused by input population activity Input indicating left movement Input indicating right movement Week 12-part 3: Effective 2-dim. model

25 Exercise 1 now: draw nullclines and flow arrows 1.0 0.8 0.2 0.0 1.0 0.8 0.2 0.0 1.0 h Next Lecture at 10:36

26 Phase plane, strong external input Week 12-part 3: Theory of decision dynamics

27 Phase plane – biased input: Population activity Week 12-part 3: Theory of decision dynamics: biased input

28 Phase plane – symmetric but small input Weak external input: Stable fixed point Week 12-part 3: Theory of decision dynamics: unbiased weak

29 Phase plane Symmetric, but strong input Week 12-part 3: decision dynamics: unbiased strong to biased

30 Phase plane Population activity Biased input = stable fixed point  decision reflects bias Week 12-part 3: Theory of decision dynamics: biased strong

31 Phase plane Homogeneous solution = saddle point  decision must be taken Week 12-part 3: Theory of decision dynamics: unbiased strong

32 Biological Modeling of Neural Networks: Week 12 – Decision models: Competitive dynamics Wulfram Gerstner EPFL, Lausanne, Switzerland 12.1 Review: Population dynamics - competition 12.2 Perceptual decision making - V5/MT - Decision dynamics: Area LIP 12.3 Theory of decision dynamics - shared inhibition - effective 2-dim model 12.4. Decisions in connected pops. - unbiased case - biased input 12.5. Decisions, actions, volition - the problem of free will Week 12– Decision models, part 3

33 Phase plane Homogeneous solution = saddle point  decision must be taken Week 12-part 4: Review: unbiased strong

34 Phase plane – symmetric but small input Weak external input: Stable fixed point  no decision Week 12-4: Review: unbiased weak

35 Simulation of 3 populations of spiking neurons, unbiased strong input X.J. Wang, 2002 NEURON Popul.1 Popul. 2 stimulus

36 Roitman and Shadlen 2002 Stimulus onset saccade onset

37 Biological Modeling of Neural Networks: Week 12 – Decision models: Competitive dynamics Wulfram Gerstner EPFL, Lausanne, Switzerland 12.1 Review: Population dynamics - competition 12.2 Perceptual decision making - V5/MT - Decision dynamics: Area LIP 12.3 Theory of decision dynamics - shared inhibition - effective 2-dim model 12.4. Decisions in connected pops. - unbiased case - biased input 12.5. Decisions, actions, volition - the problem of free will Week 12– Decision models, part 3

38 goal How would you decide? Week 12-5: Decision: risky vs. safe

39 goal Start How would you decide?

40 fMRI variant of Libet experiment Decision and Movement Preparation -Subject decides spontaneously to move left or right hand - report when they made their decision Libet, Behav. Brain Sci., 1985 Soon et al., Nat. Neurosci., 2008

41 goal What decides? Who decides? goal Start -Your experiences are memorized in your brain -Your values are memorized in your brain -Your decisions are reflected in brain activities ‘Your brain decides what you want or what you prefer … ’ ‘ … but your brain – this is you!!!’ ‘We don’t do what we want, but we want what we do’ (W. Prinz) The problem of Free Will (see e.g. Wikipedia article)

42 Wulfram Gerstner EPFL Suggested Reading: - Salzman et al. Nature 1990 - Roitman and Shadlen, J. Neurosci. 2002 - Abbott, Fusi, Miller: Theoretical Approaches to Neurosci. - X.-J. Wang, Neuron 2002 - Libet, Behav. Brain Sci., 1985 - Soon et al., Nat. Neurosci., 2008 - free will, Wikipedia Chapter 16, Neuronal Dynamics, Gerstner et al. Cambridge 2014 Decision, Perception and Competition in Connected Populations

43 Exam: - written exam 17. 06. 2013 from 12:15-15:00 - miniprojects counts 1/3 towards final grade For written exam: -bring 1 page A5 of own notes/summary -HANDWRITTEN! The end Last Lecture in 2 Weeks: (holiday next week) - prepare questions for discussion section

44 Nearly the end : what can I improve for the students next year? Integrated exercises? Miniproject? Overall workload ? (4 credit course = 6hrs per week) Background/Prerequisites? -Physics students -SV students -Math students Comments: slides/notes

45 now QUESTION SESSION! Questions to Assistants possible until June 4 The end … and good luck for the exam!

46 Exercise 2.1 now: stability of homogeneous solution Membrane potential caused by input Assume: a) Calculate homogeneous fixed point b) Analyze stability of the fixed point h(b) as a function of b Next Lecture at 11:15

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