About the Course

This course reviews various computational theories of coding, computation and learning in the nervous systems. We focus in particular on how the brain encodes, selects, and represents behaviorally relevant.variables, how it computes function of those variables, and how it modifies  its circuitry as a result of experience. The course involves a fair amount of math but we will review all mathematical methods before applying them to specific topics. This course is meant to be accessible to ANY BCS graduate students and the math level is adjusted accordingly.

Who should take this course?

Any students interested in how the brain works, even if you are not necessarily fascinated by neurobiological details. We will spent a fair amount of time discussing neuronal mechanisms of various functions, but most of the theories we use can be readily applied to other subfields of cognitive science, cognitive neuroscience, linguistics or computer science. For instance, we will look into the neural basis of decision making and statistical inferences. These theoretical concepts are not only relevant, but essential for  anybody interested in statistical learning in the context of language acquisition or any other domains.

If you're interested in this course but still wondering whether this is really for you, do not hesitate to contact me (alex@bcs.rochester.edu).

Prerequisites:

There are no prerequisite although a decent neuroscience background is helpful  (i.e., BCS110 or something equivalent) and it's best if you take BCS512 first (Computational Methods in Cognitive Science).

Office Hours

Alex Pouget will be available regularly on Wednesdays from 4:00 to 5:00 PM in Meliora 402, and at other times by appointment.

Readings

We will be using the book by Dayan and Abbott, Theoretical Neuroscience, MIT press. 2001.

Homework, Exams and Grading

There will be one computer assignment every week, or every other week, but no midterm or final exam. All assignments will have to be performed under matlab and will typically consist in implementing a simplified version of one of the models presented in class. 

Auditing

I strongly discourage BCS students from auditing this course because it is considerably easier to understand the course material if you do the homework.

Schedule

01/17  

Math Primer PPT slides

• Calculus: derivatives, chain rule, gradient descent, taylor expansions

• Bayes Rule

• Fourier Transform

• Linear systems analysis

01/24  

Neural encoding PPT slides PDF slides

• What's a code?

• Population codes

• Noise and signal in the brain

• Theory of neuronal variability

• Quantifying the quality of a neural code: Shannon  information

Readings:   Chap 1, Chap 4 (up to page 9)

Exercises (due 1/31)

01/31  

Neural decoding PPT slides PDF slides

• Estimation theory

• Quantifying the quality of a code: Fisher  information

• Fisher information and ideal observer analysis

• Maximum likelihood

• Optimal linear estimator

• Center of Mass

• Population vector

• Bayesian Estimator

Readings:

• Chap 3. Abbott and Dayan

• Pouget, A., Dayan, P. and Zemel, R.S.. Annual Review Neuroscience. 26:381-410. 2003

Exercises (due 2/14)

02/07  

Spiking networks (Beck)

Readings: Chap 5 & 6

02/14  

Bayesian models of perception and decision making  PPT slides PDF slides

• Bayesian multisensory integration

• Bayesian inference for motion processing

• The role of the prior

• Log likelihood ratio for binary decision making

• Bayesian inference for decision making

Readings:

• Weiss Y, Simoncelli EP, Adelson EH. 2002. Motion illusions as optimal percepts. Nat Neurosci 5: 598-604

• Gold JI, Shadlen MN.Neural computations that underlie decisions about sensory stimuli.Trends Cogn Sci. 2001 Jan 1;5(1):10-16.
   

02/21  

Neural implementations of Bayesian inference PPT slides 

• Various codes for probability distributions: Log probability, Convolution codes, PPCs

• Bayesian inference in networks

• Maximum likelihood estimation and attractor dynamics

Readings:

• Deneve S, Latham PE, Pouget A. Nat Neurosci. 2001 Aug;4(8):826-31. Efficient computation and cue integration with noisy population codes.

• Ma et al. Nature Neuroscience. 2006. Bayesian inference with probabilistic population codes.

Exercises

02/28   Probabilistic approaches to language processing, production and acquisition (Jaeger)

Readings:

• Perfors, A., Tenenbaum, J., Regier, T. (2006) Poverty of the Stimulus? A rational approach. 28th Annual Conference of the Cognitive Science Society. Vancouver, British Columbia.

• Levy, R. and Jaeger, T.F. to appear. Speakers optimize information density through syntactic reduction. Pre-Proceedings of Neural Information Processing Systems (NIPS), Vancouver, BC, December 4-7, 2006.

• John Hale. 2001. A Probabilistic Earley Parser as a Psycholinguistic Model. In Proceedings of the Second Meeting of the North American Chapter of the Asssociation for Computational Linguistics.
   

03/07   Probabilistic approaches to cognition PPT slides

Readings:

03/14  

SPRING BREAK

03/21  

Memory: from single cells to semantic memory PPT slides PDF slides    

• Hopfield network

• Null cline analysis

• Self sustained activity in network of spiking neurons

• Continuous attractor network

• Probabilistic semantic memory

Readings: 

• Durstewitz D, Seamans JK, Sejnowski T. Nature Neuroscience 2000, Suppl:1184-91. Neurocomputational models of working memory.

• Steyvers M, Griffiths TL, Dennis S (2006) Probabilistic inference in human semantic memory. Trends Cogn Sci 10:327-334.

03/28

Unsupervised Learning PPT slides PDF slides       

Readings:          Chap 8 (sections 8.1-3)

Exercise HTML  Exercise PDF  Due 4/4

04/04  

Computational Vision:  PPT slides PDF slides

• Information maximization in the retina

• Energy filters

• Neural networks for object recognition

Readings: Chap 2, Chap 4 (page 11-19)

• Adelson-Bergen. Spatiotemporal energy models for the perception of motion. JOSA A. 1985.

• Models of object recognition M.Riesenhuber, T. Poggio. Nature Neuroscience Volume 3  Page 1199 - 1204 (2000)

Exercise HTML 

04/11

Representational learning/Bayesian networks PPT slides PDF slides

Readings:          Chap10  

04/18

Reinforcement learning  (Jacobs)

Readings:          Chap 9

Exercise pdf due 4/26

4/26 9-10:30am Note new day and time for this lecture only. Same room as usual.

Sensory motor transformations PPT slides PDF slides    

Readings: Chap7, Pouget, A., and Snyder, L. Computational approaches to sensorimotor transformations. Nature Neuroscience. 3:1192-1198. 2000

Exercise due 5/02

• Basis function networks for sensorimotor transformations

• Optimal nonlinear computations

• Forward models

• Learning a jacobian

05/02  

Motor control PPT slides PDF slides

Readings:  Computational principles of movement neuroscience

Daniel M. Wolpert, Zoubin Ghahramani
Nature Neuroscience Volume 3 Number 0 Page 1212 - 1217 (2000)