The computational brain (or why studying the brain with math is cool )
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1 The computational brain (or why studying the brain with math is cool ) +&'&'&+&'&+&+&+&'& Jonathan Pillow PNI, Psychology, & CSML Math Tools for Neuroscience (NEU 314) Fall 2016
2 What is computational neuroscience? 1. Use of mathematical/computational tools to study the brain. Estimate biological properties from noisy data build models that replicate behavior of neurons 2. Study how the brain behaves as a computer Brain is a machine for processing information & computing relevant outputs What algorithms / routines does it use?
3 Mind-Brain Problem What is the relationship of the mind to the brain?
4 The brain as a computer: The brain computes! This is accepted as a truism by the majority of neuroscientists engaged in discovering the principles employed in the design and operation of nervous systems. What is meant here is that any brain takes the incoming sensory data, encodes them into various biophysical variables, such as the membrane potential or neuronal firing rates, and subsequently performs a very large number of ill-specified operations, frequently termed computations, on these variables to extract relevant features from the input. The outcome of some of these computations can be stored for later access and will, ultimately, control the motor output of the animal in appropriate ways. - Christof Koch, Biophysics of Computation
5 Short history of brain metaphors: hydraulic device (Descartes, 17th C.) mill (Leibniz, 17 th C.) telegraph (Sherrington, early 20 th C.) telephone switchboard (20 th C.) digital computer (late 20th C.) quantum computer? (Penrose, 1989) convolutional neural network? (21st C.)
6 What does it mean to claim the brain is a computer? Sensory Input Brain Motor Output The physical parts of the brain are important only insofar as they represent steps in a formal calculation. Any physical device implementing the same formal system would have the same mind properties as a brain.
7 What does it mean to claim the brain is a computer? Sensory Input Brain Motor Output Claim: Most neuroscientists take it for granted that the brain is a computer. They are devoted to finding out which computer (i.e., what formal structure? what algorithms does the brain implement?).
8 What is (some of) the evidence that the brain is a computer?
9 Mathematical model of sensory neurons the retina photoreceptors detect light bipolar cells retinal ganglion cells output cells (send all visual information to the brain) to brain!
10 Mathematical model of sensory neurons the retina photoreceptors bipolar cells retinal ganglion cells what mathematical operation? Difference of light in center and light in the surround
11 Mathematical model of sensory neurons stimulus photoreceptors bipolar cells retinal ganglion cells Difference of light in center and light in the surround lots of spikes!
12 Mathematical model of sensory neurons stimulus photoreceptors bipolar cells retinal ganglion cells Difference of light in center and light in the surround few spikes
13 Mathematical model of sensory neurons stimulus photoreceptors bipolar cells retinal ganglion cells Difference of light in center and light in the surround more spikes
14 Mach Bands Each stripe has constant luminance Then why does it look like there s a gradient?
15 Mach Bands Each stripe has constant luminance Cell on left edge Cell on right edge Then why does it look like there s a gradient?
16 The Neural Coding Problem stimulus encoding function spikes How does the brain take stimuli and code them with sequences of spikes?
17 Lightness Illusion
18 Hermann illusion
19 This magical slide can track where you re looking
20 Color Computations Beau Lotto
21 Color Computations Beau Lotto
22
23
24 color after-images neurons adjust their response properties after prolonged exposure to an image we can compute (and predict) these changes! red > green after-image blue > yellow after-image black > white after-image
25 Neural prostheses: Neurons can be replaced by other entities (silicon chips) that have different physical structure but carry out the same (or similar) mathematical operations, allowing the organism to produce ( compute ) the same behavior.
26 Cochlear implants (using a different computer to encode auditory signals) transmitter receiver microphone cochlea to brain electrode array
27 Interchangeability: replacing neurons with silicon Sensory Input Brain Motor Output If we understand the mathematical operations carried out by different parts of the brain, we could (in theory) replace them with new parts that perform the same computations!
28 There are about 10 billion cubes of this size in your brain! 10 microns
29 And this is a great time to study neuroscience. Why? We are about to get incredible data. Computers are getting extremely fast. Advances in statistical/mathematical techniques are allowing us to gain a deep understanding of neural data and neural information processing capabilities
30 some of the kinds of math involved linear algebra probability & statistics dynamical systems / differential equations (including chaos theory) signal processing information theory / coding theory
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