CNS 187 Neural Computation

Course Description

Prerequisites: introductory neuroscience (Bi 150 or equivalent), mathematical methods (Bi 195 or equivalent), and scientific programming.

This course aims at a quantitative understanding of how the nervous system computes. The goal is to link phenomena across scales from membrane proteins to cells, circuits, brain systems, and behavior. Students learn how to formulate these connections in mathematical models, test these models experimentally, and interpret experimental data quantitatively.

Concepts are developed with motivation from animal behavior, including aerobatic control of insect flight, precise sound localization, sensing of single photons, reliable navigation and homing, rapid escape decision-making, one-shot learning, and large-capacity recognition memory.

Learning Goals

• Neurobiology: learn new facts about the brain and behavior while building on basic neuroscience background.
• Modeling skills: translate messy brain phenomena into mathematical relationships and learn how to choose among possible models.
• Mathematical methods: use linear algebra and probability as ingredients for understanding neural computation.
• Scientific programming: practice modeling and numerical simulation exercises based on Python.

Scientific Scope

The course treats instances of modeling and mathematical understanding at all levels of phenomena, from molecular events to cellular integration, circuit function, and animal behavior.

Format

• All materials and communications are handled on Canvas.
• Course meetings are Tuesday and Thursday, 10:30-12:00, in BBB 180B.
• The first 30 minutes of each meeting after the first is a student-led Q&A session about the preceding meeting, followed by one hour of lecture on new material.
• Each student prepares at least one question about the preceding lecture and submits it to Canvas.
• Questions for Tuesday lectures are due Wednesday at 7 pm; questions for Thursday lectures are due Sunday at midnight.
• Weekly assignments are issued on Thursday and due Thursday at midnight.
• During the last four weeks, students complete a final research project due at the end of the term, with topic options suggested by the instructors, consultation allowed, and independent reports required.

Grading

Grading is based on attendance and discussion (20%), weekly assignments (50%), and the final project (30%).

• Attendance: question submissions to all 17 lectures count for 17%, with 3% free points from grace days.
• Assignments: total points from all assignments are scaled to 50%. Bonus problems can add points, but the assignment score is capped at 50%.
• Grace days: students have two cumulative grace days for assignments across the term.
• Late submissions beyond grace days are subject to penalty, and grace days do not apply to the final project.
• Final project: graded by the instructors.

Missing Lectures and Course Questions

For missing lectures or homework extensions, students should email the full instruction team at least one day ahead with their reasons.

For homework, lecture, or logistics questions, students should email both teaching assistants at the same time. Homework questions should be directed to office hours and the Canvas discussion platform, where they can be answered faster than by email.

Lecture Topics

• Sensory and motor transduction.
• Cellular processing.
• Networks.
• Neural coding.
• Memory.
• Navigation.
• Decision-making.
• Motor control.
• Optimality theories.

Useful Books

• Dayan, P., and Abbott, L.F. (2001). Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. MIT Press.
• Gerstner, W., Kistler, W.M., Naud, R., and Paninski, L. (2014). Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge University Press.

Collaboration Policy

Collaboration on homework assignments and the final project is encouraged. Students may consult outside reference materials, other students, the teaching assistants, or the instructors, but may not consult homework solutions from prior years, whether developed at Caltech or elsewhere.

Students must cite any use of outside reference material. All submitted work must be written individually and should reflect the student's own understanding at the time of writing. Code and code results are considered part of the write-up and must be done individually.