15-386/686 Neural Computation

Carnegie Mellon University

Spring 2025

Course Description

Neural Computation is an area of interdisciplinary study that seeks to understand how the brain learns and computes to achieve intelligence. It seeks to understand the computational principles and mechanisms of intelligent behaviors and mental abilities -- such as perception, language, motor control, decision making and learning -- by building artificial systems and computational models with the same capabilities. This course explores computational principles at multiple levels, from individual neurons to circuits and systems, with a view to bridging brain science and machine learning. It will cover basic models of neurons and circuits, computational models of learning, memories and inference in real and artifical systems. Concrete examples will be drawn mostly from the visual system, with emphasis on relating current deep learning research and the brain research, from hierarchical computation, attention, recurrent neural networks, to reinforcement learning. Students will learn to perform quantitative analysis as well as computational experiments using Matlab. No prior background in biology or machine learning is assumed. Prerequisites: Basic knowledge of matrix, linear algebra, basic calculus (partial differential equations), probability and statistics are required. 15-100, 21-120 or permission of instructor. 21-241 preferred but not required.

Course Information

Instructors	Office (Office hours) Class zoom link	Email (Phone)
Tai Sing Lee (Professor)	Friday 9:00-10:00 a.m. Recitation (class zoom)	taislee@andrew.cmu.edu
Tianqin Li (TA)	Thursday 7-8 p.m (class zoom) + Fri Recitation (alt week)	tianqinl@andrew.cmu.edu
Julia Liu (TA)	Tuesday, Friday 7-8 p.m (class zoom)	juliahul@andrew.cmu.edu
Wesley Zhou (TA)	Wednesday 7-8 p.m. (class zoom)	wesleyzh@andrew.cmu.edu
Zhixin Wang (TA)	Monday 7-8 p.m.(class zoom)	zhixinwa@andrew.cmu.edu

Letures: HH B-131 (in Person). Monday/Wednesday 2:00 p.m - 3:20 p.m.
686 Journal Club location and time: On class zoom (link on CANVAS). Alernate week: Friday 2:00 - 3:20 p.m
Website: http://www.ni.cmu.edu/~tai/nc24.html (course info)
Canvas: Both 386/686 students share the same Canvas for access of course materials and announcements.

Recommended Supplementary Textbook

Reading List (below) and on Canvas.
Trappenberg T.P. (TTP) Fundamentals of computational neuroscience, 2nd edition, Oxford University Press 2009 (highly recommended). Matlab codes associated with the book
Ma, Kording and Goldreich (MKG) Bayesian models of perception and action MIT Press. 2022
Dayan, P and Abbott, L (DP) > Theoretical Neuroscience MIT Press. 2001 (reference)
Hertz J, Krogh A, Palmer RG (HKP) Introduction to the theory of neural computation., Addison Wesley 1991 (reference).

Classroom Etiquette

During in-person session, refrain from doing things unrelated to our class with your laptop and cell phone. However, using laptop to answer in-class questions are allowed.

386 Grading Scheme

Evaluation	% of Grade
Assignments	70
Class Participation (optional)	bonus up to 5 points
Midterm	10
Final Exam	20

Grading scheme: A: > 88% B: > 75%. C: > 65% .

686 Grading Scheme

Evaluation	% of Grade
Assignments	70
Class Participation (optional)	bonus up to 5 points
Midterm	10
Final Exam	20
BiWeekly Journal Club or Term Paper	Required. You can miss one

Grading scheme: A+ > 96%, A: > 88% B: > 75%. C: > 65% .

Assignments

There will be 5 assignments, approximately once every two weeks.
Collaboration in team of two (for 15386 only) is allowed for the first two assignments. Students are encouraged to discuss the problem sets and help each other in Piazza, but not allowed to copy each other's homework. Each student should submit their codes and a write up to CANVAS as well as to Gradescope.

Late Policy

You will have approximately 2 weeks to do each homework assignment. For the semester, you have a total of seven free-late-days (168 hours) allowance to submit homework late without penalty. However, for each homework, no more than four late days can be used. Each day beyond five days after deadline will entail a 5 percent discount on the homework grade you earned. No homework will be accepted one week after the due day.
There will be no exception to the late policy unless an extension is granted to the whole class or you have a legitimate medical excuse with doctor's or academic adviser's letter. You may not submit a problem set once the solution set is released, typically one week after due day.

Examinations

The midterm and final exam will cover materials covered in lectures and the problem sets. Problem set solutions are available to all students one week after due day.

Syllabus

Date	Lecture Topic	Relevant Readings	Assignments
	Part 1: Neurons and Logics
M 1/13	1. Introduction and Overview	NIH Brain Facts (chapter 1)
W 1/15	2. Neurons and Membranes	Trappenberg Ch 1.1-2.2
F 1/17	Journal Club #0 Orientation
W 1/22	3. Spikes and Cables	Trappenberg Ch 2 (C)	HW1 out
F 1/24	Recitation: Problem set 1 and Matlab Tutorial	Trappenberg Math Appendix
M 1/27	4. Axons and Synapse	Trappenberg Ch 3.1, 3.3
W 1/29	5. Dendrites and Logics	Trappenberg 3.1,3.5 McCulloch and Pitts (1943)
F 1/31	Journal Club #1
	Part 2: Learning and Representation
M 2/3	6. Synaptic plasticity	Trappenberg Ch 4 Abbott and Nelson (2000)
W 2/5	7. Hebbian Learning	Trappenberg Ch 4, HPK Ch 8 Oja (1982)	HW1 due. HW2 Out
F 2/7	Recitation: Problem Set 2
M 2/10	8. Sensory Representation
W 2/12	9. Source Separation	Foldiak (1990)
F 2/14	Journal Club #2
M 2/17	10. Sparse Coding	Olshausen and Field (1997) (2004)
	Part 3: Association and Memories
W 2/19	11. Association	Trappenberg Ch 10.3 Hinton and Salahutdinov (2006)	HW2 due. HW3 out.
F 2/21	Recitation: Problem Set 3
M 2/24	12. Attractors	Trappenberg Ch 8. Ch 9.4 Hopfield and Tank (1986)
W 2/26	Midterm
F 2/28	Journal Club #3
3/3-3/7	Midsemester and Spring break.
M 3/10	13. Memory	Kumaran, Hssabis and McClelland (2016)	&nbps;
W 3/12	14. Computational Maps	HPK Ch 9. Trappenberg 7.1-7.2 Kohonen (1982)	Midsemester Grade due
F 3/14	Journal Club #4
	PART 4: Networks and Computation
M 3/17	15. Recurrent Network	Marr and Poggio (1976) Samonds et al. (2013) Wang et al. (2018)
W 3/19	16. Hierarchy	Trappenberg Ch 6, 10.1. Fukushima (1988), Yamins and DiCarlo (2016)	HW 3 in. HW 4 out.
F 3/21	Recitation: Problem Set 4
M 3/24	17. Feedback	Trappenberg 5.1. Van Essen et al (1992) Fellman and Van Essen ( 1991)
W 3/26	18. Hierarchical Inference	Mumford (1992) Rao and Ballard (1998) Lee and Mumford (2003)
F 3/28	Journal Club #5
	PART 5: Prediction and Decision
M 3/31	19. Predictive Coding	Trappenberg Ch 10. Lotter et al (2016), Colah (2015) Rao (2015)
W 4/2	20. Reinforcement Learning	Trappenberg. Ch 9. Niv (2009), Montague et al. (1996)	HW 4 in. HW 5 out.
F 4/4	Spring Carnival No. Class
M 4/7	22. Bayesian Integration	Ernst and Banks (2002). Kording and Wolpert (2004) Weiss et al. (2002).
W 4/9	21. Population Codes	Ma et al. (2006) Kersten and Yuille (2003)
F 4/11	Recitation Problem set 5
M 4/15	23. Probabilistic Inference	Orban et al. (2016). Shivkumar et al. (2019)
W 4/17	24. Attention	Trappenberg Ch 10. Vaswani et al. (2017) Lindsay (2020) Knudsen (2007)	HW 5 due
F 4/19	Journal Club #6
M 4/21	25. Consciousness	Blum and Blum (2018) Koch (2018).
W 4/23	26. Review
F 4/25	Journal Club #7
X 5/X	Final Exam	5:30 pm - 8:30 p.m In Person

Journal Club 2022

Week 1 (1/24): Dynamics and Manifold of Neural Codes

David Wang and Xirui Liu will read a couple of the overview papers below, introducing the concepts of computation by dynamics and manifold of neural population code.
Lea Duncker and Maneesh Sahani (2021) Dynamics on the manifold: Identifying computational dynamical activity from neural population recordings. Current Opinion in Neurobiology 70:163-170
Saurabh Vyas, Matthew D. Golub, David Sussillo, and Krishna V. Shenoy (2020) Computation Through Neural Population Dynamics Annual Review of Neuroscience <\em> 43:249-75

Supplementary Reading List

Questions or comments: contact Tai Sing Lee
Last modified: spring 2025, Tai Sing Lee