15-386/686 Neural Computation

Carnegie Mellon University

Spring 2026

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. (class zoom)	taislee@andrew.cmu.edu
Zhangyang Geng (Head TA)	Thursday 8-9 p.m.	zgeng2@andrew.cmu.edu
Jinyi Ye (TA)	Tuesday 7-8 p.m.	ye3@andrew.cmu.edu
David Wang (TA)	Monday 7-8 p.m.	davidwa3@andrew.cmu.edu
Xirui Liu (TA)	Wednesday 7-8 p.m.	xiruil@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
Office Hours: TA will have office hour Monday-Thursday, Professor will have office hour Friday. TA will rotate to hold office hours on the Friday that assignment is due. Most office hours are on class Zoom. Some office hours will be held in person at the discretion of the TA.
Website: http://www.ni.cmu.edu/~tai/nc26.html (course info)
Canvas: Both 386/686 students share the same Canvas for access of course materials and announcements.
Piazza: Student-student, student-TA communication. Piazza questions will be answered daily except Sat. Sat questions will be answered Sunday.
Gradescope: Homework should be submitted to both Gradescope and CANVAS.

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.

386 Grading Scheme

Evaluation	% of Grade
Assignments	70
Midterm	10
Final Exam	20

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

686 Grading Scheme

Evaluation	% of Grade
Assignments	70
Midterm	10
Final Exam	20
Weekly Journal Club or Term Project	Required.

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 grace days (counted as 168 hours) allowance to submit homework late without penalty. Students eligible for Flexiblity Accommodation is entitled to an additional 7 grace days. 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 should be available to all students one week after due day.

Syllabus

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

Journal Club

Possible topic 1: Dynamics and Manifold of Neural Codes

Neural Manifold and Dynamic computation is an important topic in current neuroscience and deep learning. We will explore these concepts.
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 43:249-75

Supplementary Reading List

Questions or comments: contact Tai Sing Lee
Last modified: spring 2026, Tai Sing Lee