Fall 2023
Intro to Theory
Computational Neuroscience, Fall 2023
Faculty: Larry Abbott, Stefano Fusi, Ashok Litwin-Kumar, Ken Miller, Kim Stachenfeld
TAs: Ching Fang, Ishani Ganguly, Francisco Sacadura, Erica Shook
Meetings: Tuesdays & Thursdays 2:00-3:30 (JLG L5-084)
Text: Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)
Extra TA sessions:
- Math Review I: Calculus (Francisco)
- Monday, September 11, 6 PM. Location L6-086
- Coding Review 1: (Erica)
- Tuesday, September 12, 6 PM. Location L5-084
- Math Review II: Linear Algebra (Ching)
- Wednesday, September 13, 5 PM. Location L6-086
- Coding Review 2: (Ishani)
- Wednesday, September 13, 6 PM. Location L6-086
September
5 (Larry) Introduction to Course and to Computational Neuroscience
7 (Larry) Electrical Properties of Neurons, Integrate-and-Fire Model
12 (Larry) Numerical Methods, Filtering (Assignment 1)
14 (Larry) The Hodgkin-Huxley Model
19 (Larry) Adaptation, Synapses, Synaptic Plasticity (Assignment 2)
21 (Larry) Types of Neuron Models and Networks
22 Assignment 1 Due
26 (Stefano) Generalized Linear Models
28 (Ken) Linear Algebra I (Assignment 3)
29 Assignment 2 Due
October
3 (Ken) Linear Algebra II
5 (Ken) PCA and Dimensionality Reduction
10 (Ken) Rate Networks/E-I networks I (Assignment 4)
11 Assignment 3 Due
12 (Ken) Rate Networks/E-I networks II
17 (Ken) Unsupervised/Hebbian Learning, Developmental Models (Assignment 5; extra info on ring models; extra info on gaussian distributions)
19 (Ashok) Chaotic Networks
20 Assignment 4 Due
24 (Ashok) Low Rank Networks
26 (Ashok) Introduction to Probability, Encoding, Decoding (Assignment 6)
27 Assignment 5 Due
31 (Ashok) Fisher Information
November
2 (Ashok) Optimization (Assignment 7)
7 Holiday
8 Assignment 6 Due
9 (Stefano) Perceptrons
14 (Stefano) Multilayer Perceptrons and Mixed Selectivity (Assignment 8)
15 Assignment 7 Due
16 (Ashok) Dimensionality and kernel methods
21 (Stefano) Deep Learning (Assignment 9)
22 Assignment 8 Due
23 Holiday
28 (Stefano) Learning in Recurrent Networks
30 (Stefano) Continual Learning and Catastrophic Forgetting
December
5 (Kim) Reinforcement Learning (Assignment 10)
6 Assignment 9 Due
7 Course Wrapup
13 Assignment 10 Due
Spring 2023
Computational Statistics (Stat GR6104), Spring 2023
Time: Th 2:30 - 4.00 pm
Place: Jerome L. Greene Science Center, L3-079
Professor: Liam Paninski; Email: liam at stat dot columbia dot edu. Hours by appointment.
This is a Ph.D.-level course in computational statistics.
Note: instructor permission is required to take this class for students outside of the Statistics Ph.D. program.
See this page for additional course details.
Advanced Theory, Spring 2023
Please register via Courseworks, the course is also open to external guests
Time: Wednesdays, 10.00-11.30 am
Place: Jerome L. Greene Science Center, L4.078 (will eventually be L5.084, but check email announcements)
For the zoom link contact [email protected]
Schedule:
Information theory
Jan 25 Information theory (Jeff Johnston) Material
Feb 01 Fisher information (Jeff Johnston)
Feb 08 Gaussian Information bottleneck (Rainer Engelken)
Learning systems
Feb 15 Expectation Maximization (Ji Xia)
Feb 22 Reinforcement learning I (Kaushik Lakshminarasimhan)
Mar 01 Reinforcement learning II (Kaushik Lakshminarasimhan)
Mar 08 No session (Cosyne)
Mar 15 No session (Spring break)
Mar 22 Feedforward architectures I (Samuel Muscinelli)
29 Mar Feedforward architectures II (Samuel Muscinelli)
Neural dynamics and computations
Apr 05 Oscillations and Wilson-Cowan model (Patricia Cooney)
Apr 12 Mean-field theory and perturbative approaches (Agostina Palmigiano)
Apr 19 Low-rank neural networks I (Manuel Beiran)
Apr 26 Low-rank neural networks II (Manuel Beiran)
May 3 Single-neuron computations (Salomon Muller)
May 10 Student presentations
Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)
Spring 2023: Download schedule
Class Assistants:
Ines Aitsahalia ([email protected])
Elom Amematsro ([email protected])
Ching Fang ([email protected])
Christine Liu ([email protected])
Amol Pasarkar ([email protected])
Faculty contact: Prof. Ken Miller ([email protected])
Time: Tuesdays, Thursdays 12:10 - 1:25pm
Place: L5-084
Webpage: CourseWorks (announcements, assignments, readings)
Credits: 3
Description: An introduction to mathematical concepts used in theoretical neuroscience aimed to give a minimal requisite background for NBHV G4360, Introduction to Theoretical Neuroscience. The target audience is students with limited mathematical background who are interested in rapidly acquiring the vocabulary and basic mathematical skills for studying theoretical neuroscience, or who wish to gain a deeper exposure to mathematical concepts than offered by NBHV G4360. Topics include single- and multivariable calculus, linear algebra, differential equations, signals and systems, and probability. Examples and applications are drawn primarily from theoretical and computational neuroscience.
Prerequisites: Basic prior exposure to trigonometry, calculus, and vector/matrix operations at the high school level.
Registration: Undergraduate and graduate students must register on SSOL. *If you’re only interested in attending a subset of lectures, register Pass/Fail and contact the TAs.
Neuroscience and Philosophy (GU4500), Spring 2023
Time: Thursdays, 2:10-4:00
Place: Jerome L. Greene Science Center, L5-084
Professor: John Morrison, Email: [email protected], office hours
Description: This course is about the philosophical foundations of cognitive neuroscience. Cognitive neuroscientists often describe the brain as representing and inferring. It is their way of describing the overall function of the brain’s activity, an abstraction away from detailed neural recordings. But, because there are no settled definitions of representation and inference, there are often no objective grounds for these descriptions. As a result, they are often treated as casual glosses rather than as rigorous analyses. Philosophers have proposed a number of (somewhat) rigorous definitions, but they rarely say anything about the brain. The goal of this course is to survey the philosophical literature and consider which definitions, if any, might be useful to cognitive neuroscientists. I will begin each class with a description of a different definition from the philosophical literature. We will then rely on our collective expertise to assess its potential applications to the brain. This course is for graduate students in Neurobiology and Behavior. No prior background in philosophy will be assumed.
Format: Each lecture will begin with a summary of the books and articles listed below. But I don’t expect you to read any of them. Many of them are (unnecessarily!) dense and inaccessible. Plus, they total hundreds of pages. It’s my job to distill them into a few basic points. If you want to learn more, reach out and I will recommend particular chapters, papers, etc.
Evaluation: Graduate students in Neurobiology and Behavior should write a 15-page term paper applying one of the philosophical definitions to a particular experiment, preferably an experiment relevant to their own research. Other students should consult with the professor to identify an alternative form of evaluation. Undergraduates will be required to write at least two papers.
Fall 2022
Computational Neuroscience, Fall 2022
Faculty: Larry Abbott, Sean Escola, Stefano Fusi, Ashok Litwin-Kumar, Ken Miller
TAs: Elom Amematsro, Ho Yin Chau, David Clark, Zhenrui Liao
Meetings: Tuesdays & Thursdays 2:00-3:30 (JLG L5-084)
Text: Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)
Download Schedule
September
06 (Larry) Introduction to Course and to Computational Neuroscience
08 (Larry) Electrical Properties of Neurons, Integrate-and-Fire Model
13 (Larry) Numerical Methods, Filtering (Assignment 1)
15 (Larry) The Hodgkin-Huxley Model
20 (Larry) Types of Neuron Models and Networks (Assignment 2)
21 Assignment 1 Due
22 (Stefano) Adaptation, Synapses, Synaptic Plasticity
27 (Sean) Generalized Linear Models
28 Assignment 2 Due
29 (Ken) Linear Algebra I (Assignment 3)
October
04 (Ken) Linear Algebra II
06 (Ken) PCA and Dimensionality Reduction
11 (Ken) Rate Networks/E-I networks I (Assignment 4)
12 Assignment 3 Due
13 (Ken) Rate Networks/E-I networks II
18 (Ken) Unsupervised/Hebbian Learning, Developmental Models (Assignment 5)
19 Assignment 4 Due
20 (Ashok) Introduction to Probability, Encoding, Decoding
25 (Ashok) Decoding, Fisher Information I
26 Assignment 5 Due
27 (Ashok) Decoding, Fisher Information II (Assignment 6)
November
01 (Ashok) Information Theory
03 (Ashok) Optimization I (Assignment 7)
08 Holiday
09 Assignment 6 Due
10 (Ashok) Optimization II
15 (Stefano) The Perceptron (Assignment 8)
16 Assignment 7 Due
17 (Stefano) Multilayer Perceptrons and Mixed Selectivity
22 (Stefano) Deep Learning (Assignment 9)
23 Assignment 8 Due
24 Holiday
29 (Sean) Learning in Recurrent Networks
December
01 (Stefano) Continual Learning and Catastrophic Forgetting
06 (Stefano) Reinforcement Learning (Assignment 10)
07 Assignment 9 Due
08 (Larry) Course Wrap up
14 Assignment 10 Due
Spring 2022
Computational Statistics (Stat GR6104), Spring 2022
Time: Tu 2:10 - 3:40pm
Place: Zoom for a while, then JLG L7-119
Professor: Liam Paninski; Email: liam at stat dot columbia dot edu. Hours by appointment.
This is a Ph.D.-level course in computational statistics.
Note: instructor permission is required to take this class for students outside of the Statistics Ph.D. program.
See this page for additional course details.
Advanced Theory, Spring 2022
Time: Tuesdays, 10.00 am
Place: Jerome L Greene Science Center, L7-119
For the zoom link contact [email protected]
Schedule:
Methods for decoding and interpreting neural data
Feb 01 Methods on calculating receptive fields (Ji Xia) Material
Feb 08 Information theory (Jeff Johnston)
Feb 15 cancelled
Neural representations
Feb 22 Geometry of abstractions (theory session) (Valeria Fascianelli) slides
Mar 01 Geometry of abstractions (hands-on session) (Lorenzo Posani)
Network dynamics
Mar 08 Solving very nonlinear problems with Homotopy Analysis Method (Serena Di Santo) notes notebook
Mar 29 Forgetting in attractor networks (Samuel Muscinelli)
Apr 05 Mean-field models of network dynamics (Alessandro Sanzeni + Mario Dipoppa)
Dynamics of learning
Apr 12 Learning dynamics in feedforward neural networks (Manuel Beiran + Rainer Engelken)
Apr 19 Learning dynamics recurrent neural networks (Manuel Beiran + Rainer Engelken)
Causality
Apr 26 Introduction to some causality issues in neuroscience (Laureline Logiaco)
May 3 Causality and latent variable models (Josh Glaser)
May 10 student presentations
May 17 Bonus session: Many methods, one problem: modern inference techniques as applied to linear regression (Juri Minxha)
Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)
Spring 2022: Download schedule
Teaching Assistants:
Ching Fang [email protected]
Jack Lindsey [email protected]
Zhenrui Liao [email protected]
Amol Pasarkar [email protected]
Dan Tyulmankov [email protected]
Recitation instructor: David Clark [email protected]
Faculty contact: Prof. Ken Miller* [email protected]
(*Please contact Prof. Miller to sign add/drop forms and other items which require faculty permission)
Time:
Lectures: Tues/Thurs 10:10 - 11:25a
Office hours: Thurs 11:30a - 12:30p
Recitations: Alternating Fridays 10 - 11a
Location: Zoom
Webpage: CourseWorks
Credits: 3
Description: An introduction to mathematical concepts used in theoretical neuroscience aimed to give a minimal requisite background for NBHV G4360, Introduction to Theoretical Neuroscience. The target audience is students with limited mathematical background who are interested in rapidly acquiring the vocabulary and basic mathematical skills for studying theoretical neuroscience, or who wish to gain a deeper exposure to mathematical concepts than offered by NBHV G4360. Topics include single- and multivariable calculus, linear algebra, differential equations, signals and systems, and probability. Examples and applications are drawn primarily from theoretical and computational neuroscience.
Prerequisites: Basic prior exposure to trigonometry, calculus, and vector/matrix operations at the high school level.
Fall 2021
Introduction to Theoretical Neuroscience, Fall 2021
Faculty: Larry Abbott, Sean Escola, Stefano Fusi, Ashok Litwin-Kumar, Ken Miller
TAs: Elom Amematsro, Ramin Khajeh, Minni Sun, Denis Turcu
Meetings: Tuesdays & Thursdays 2:00-3:30
Text: Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)
September
09 (Larry) Introduction to Course and to Computational Neuroscience
14 (Larry) Electrical Properties of Neurons, Integrate-and-Fire Model
16 (Stefano) Adaptation, Synapses, Synaptic Plasticity
21 (Larry) The Hodgkin-Huxley Model (Assignment 1)
23 (Larry) Types of Neuron Models and Networks
28 (Larry) Numerical Methods, Filtering (Assignment 2)
29 Assignment 1 Due
30 (Sean) Generalized Linear Models
October
05 (Ken) Linear Algebra (Assignment 3)
06 Assignment 2 Due
07 (Ken) PCA and Dimensionality Reduction
12 (Ken) Rate Networks/E-I networks I (Assignment 4)
13 Assignment 3 Due
14 (Ken) Rate Networks/E-I networks II
19 (Ken) Unsupervised/Hebbian Learning, Developmental Models (Assignment 5)
20 Assignment 4 Due
21 (Ashok) Introduction to Probability, Encoding, Decoding
26 (Ashok) Decoding, Fisher Information I
27 Assignment 5 Due
28 (Ashok) Decoding, Fisher Information II (Assignment 6)
November
02 Holiday
04 (Ashok) Information Theory
09 (Ashok) Optimization I (Assignment 7)
10 Assignment 6 Due
11 (Ashok) Optimization II
16 (Stefano) The Perceptron (Assignment 8)
17 Assignment 7 Due
18 (Stefano) Multilayer Perceptrons and Mixed Selectivity
23 Holiday
25 Holiday
30 (Stefano) Deep Learning (Assignment 8)
December
01 Assignment 8 Due
02 (Sean) Learning in Recurrent Networks
07 (Stefano) Continual Learning and Catastrophic Forgetting (Assignment 10)
08 Assignment 9 Due
09 (Stefano) Reinforcement Learning
15 Assignment 10 Due
Spring 2021
Introduction to Theoretical Neuroscience, Spring 2021
Faculty: Larry Abbott, Stefano Fusi, Ashok Litwin Kumar, Ken Miller
TAs: Matteo Alleman, Elom Amematsro, Ramin Khajeh, Denis Turcu
Meetings: Tuesdays 2:00-3:30 & Thursdays 1:30-3:00
Text: Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)
January
12 (Larry) Introduction to the Course and to Theoretical Neuroscience
14 (Larry) Electrical Properties of Neurons, Integrate-and-Fire Model
19 (Larry) Adaptation, Synapses, Spiking Networks (Assignment 1)
21 (Larry) Numerical Methods, Filtering
26 (Larry) The Hodgkin-Huxley Model (Assignment 2)
27 Assignment 1 Due
28 (Larry) Types of Neuron Models and Networks (Assignment 3)
February
02 (Ken) Linear Algebra I
03 Assignment 2 Due
04 (Ken) Linear Algebra II
09 (Ken) PCA and Dimensionality Reduction (Assignment 4)
10 Assignment 3 Due
11 (Ken) Rate Networks/E-I networks I
16 (Ken) Rate Networks/E-I networks II (Assignment 5)
17 Assignment 4 Due
18 (Ken) Unsupervised/Hebbian Learning, Developmental Models
23 (Ashok) Introduction to Probability, Encoding, Decoding (Assignment 6)
24 Assignment 5 Due
25 (Sean) GLMs
March
02 Spring Break
04 Spring Break
09 (Ashok) Decoding, Fisher Information I
10 Assignment 6 Due
11 (Ashok) Decoding, Fisher Information II
16 (Ashok) Information Theory (Assignment 7)
18 (Ashok) – Optimization
23 (Ashok) – Optimization II (Assignment 8)
24 Assignment 7 Due
25 (Stefano) Perceptron
30 (Stefano) Multilayer Perceptrons and Mixed Selectivity (Assignment 9)
31 Assignment 8 Due
April
01 (Stefano) – Deep Learning I (backpropagation)
06 (Stefano) – Deep Learning II (convolutional networks) (Assignment 10)
07 Assignment 9 Due
08 (Stefano) Learning in Recurrent Networks
13 (Stefano) Continual Learning and Catastrophic Forgetting (Assignment 11)
14 Assignment 10 Due
15 (Stefano) Reinforcement Learning
21 Assignment 11 Due
Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)
Faculty: Ken Miller ([email protected])
Instructor: Dan Tyulmankov ([email protected])
Teaching Assistant: Amin Nejatbakhsh ([email protected]) (Office Hours: Thursdays 1-2pm)
Time: Tuesdays, Thursdays 8:40a-10:00a
Place: JLGSC L5-084 Zoom (https://columbiauniversity.zoom.us/j/489220180)
Webpage: CourseWorks
Credits: 3 credits, pass/fail only (Register on SSOL. Do not register for a grade.)
Description: An introduction to mathematical concepts used in theoretical neuroscience aimed to give a minimal requisite background for NBHV G4360, Introduction to Theoretical Neuroscience. The target audience is students with limited mathematical background who are interested in rapidly acquiring the vocabulary and basic mathematical skills for studying theoretical neuroscience, or who wish to gain a deeper exposure to mathematical concepts than offered by NBHV G4360. Topics include single- and multivariable calculus, linear algebra, differential equations, dynamical systems, and probability. Examples and applications are drawn primarily from theoretical and computational neuroscience.
Prerequisites: Basic prior exposure to trigonometry, calculus, and vector/matrix operations at the high school level
Fall 2020
Special Virtual Edition
Meetings: Wednesdays, 10.00 am
Location: Zoom, contact [email protected] for details
Schedule
07/15/2020 Time-dependent mean-field theory for mathematical streetfighters (Rainer Engelken)
07/22/2020 Predictive coding in balanced neural networks with noise, chaos, and delays, Article (Everyone)
07/29/2020 A solution to the learning dilemma for recurrent networks of spiking neurons, Article (Everyone)
08/05/2020 Canceled
08/12/2020 Artificial neural networks for neuroscientists: A primer, Article (Robert Yang)
08/19/2020 A mechanism for generating modular activity in the cerebral cortex (Bettina Hein)
08/26/2020 Dynamic representations in networked neural systems, Article (Kaushik Lakshminarasimhan)
09/02/2020 Network principles predict motor cortex population activity across movement speeds (Shreya Saxena)
09/09/2020 Modeling neurophysiological mechanisms of language production (Serena Di Santo)
09/16/2020 How single rate unit properties shape chaotic dynamics and signal transmission in random neural networks, Article (Samuel Muscinelli)
09/23/2020 Shaping dynamics with multiple populations in low-rank recurrent networks, Article (Laureline Logiaco)
09/30/2020 Deep Graph Pose: a semi-supervised deep graphical model for improved animal pose tracking, Article (Anqi Wu)
10/07/2020 Decoding and mixed selectivity, Article, Article, Article (Fabio Stefanini)
10/14/2020 Theory of gating in recurrent neural networks, Article, Article (Kamesh Krishnamurthy)
10/21/2020 Decentralized motion inference and registration of neuropixel data (Erdem Varol)
10/28/2020 Decision, interrupted (NaYoung So)
11/04/2020 Abstract rules implemented via neural dynamics (Kenny Kay)
11/11/2020 Canceled for Holiday
11/18/2020 "Rodent paradigms for the study of volition (free will)" (Cat Mitelut)
11/25/2020 Gaussian process inference (Geoff Pleiss)
12/02/2020 Canceled
12/09/2020 Structure and variability of optogenetic responses in multiple cell-type cortical circuits (Agostina Palmigiano)
12/16/2020 Manifold GPLVMs for discovering non-Euclidean latent structure in neural data, Article (Josh Glaser)
Page Last Updated: 08/31/2023