Courses

Spring 2024

Mathematical Tools for Theoretical Neuroscience

Spring 2024: Download schedule

Lecturers: 

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: Tuesdays and Thursdays 12:10pm – 1:25pm
  • Office hours: TBD
  • Recitations: TBD

Location: Jerome L Greene Science Center, room L5-084

Webpage: CourseWorks

Credits: 3 

Call Num: 18535

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.

Audit Interest Form/Courseworks Access Request: Link 

Grading: 

  • 50% homeworks (approximately bi-weekly)
  • 50% participation (attendance, asking/answering questions, office hours, comments on notes, etc.)

Extra credit: +1% on your next homework assignment for finding a typo and +10% for finding an error in the typed lecture notes. (Please add comments directly to the posted files.)

Computational Statistics (Stat GR6104)

Spring 2024: Schedule


This is a Ph.D.-level course in computational statistics. A link to the most recent previous iteration of this course is here.

Note: instructor permission is required to take this class for students outside of the Statistics Ph.D. program.

Time: Tu 2:10
Place: Jerome L Greene Science Center, room L5-084
Professor: Liam Paninski; Email: liam at stat dot columbia dot edu. Hours by appointment.

Course goals: (partially adapted from the preface of Givens' and Hoeting's book): Computation plays a central role in modern statistics and machine learning. This course aims to cover topics needed to develop a broad working knowledge of modern computational statistics. We seek to develop a practical understanding of how and why existing methods work, enabling effective use of modern statistical methods. Achieving these goals requires familiarity with diverse topics in statistical computing, computational statistics, computer science, and numerical analysis. Our choice of topics reflects our view of what is central to this evolving field, and what will be interesting and useful. A key theme is scalability to problems of high dimensionality, which are of most interest to many recent applications.
Some important topics will be omitted because high-quality solutions are already available in most software. For example, the generation of pseudo-random numbers is a classic topic, but existing methods built in to standard software packages will suffice for our needs. On the other hand, we will spend a bit of time on some classical numerical linear algebra ideas, because choosing the right method for solving a linear equation (for example) can have a huge impact on the time it takes to solve a problem in practice, particularly if there is some special structure that we can exploit.

Audience: The course will be aimed at first- and second-year students in the Statistics Ph.D. program. Students from other departments or programs are welcome, space permitting; instructor permission required.

Background: The level of mathematics expected does not extend much beyond standard calculus and linear algebra. Breadth of mathematical training is more helpful than depth; we prefer to focus on the big picture of how algorithms work and to sweep under the rug some of the nitty-gritty numerical details. The expected level of statistics is equivalent to that obtained by a graduate student in his or her first year of study of the theory of statistics and probability. An understanding of maximum likelihood methods, Bayesian methods, elementary asymptotic theory, Markov chains, and linear models is most important.

Programming: With respect to computer programming, good students can learn as they go. We'll forgo much language-specific examples, algorithms, or coding; I won't be teaching much programming per se, but rather will focus on the overarching ideas and techniques. For the projects, I recommend you choose a high-level, interactive package that permits the flexible design of graphical displays and includes supporting statistics and probability functions, e.g., R, Python, or MATLAB.

Evaluation: Final grades will be based on class participation and a student project.


Topics:
Deterministic optimization
- Newton-Raphson, conjugate gradients, preconditioning, quasi-Newton methods, Fisher scoring, EM and its various derivatives
- Numerical recipes for linear algebra: matrix inverse, LU, Cholesky decompositions, low-rank updates, SVD, banded matrices, Toeplitz matrices and the FFT, Kronecker products (separable matrices), sparse matrix solvers
- Convex analysis: convex functions, duality, KKT conditions, interior point methods, projected gradients, augmented Lagrangian methods, convex relaxations
- Applications: support vector machines, splines, Gaussian processes, isotonic regression, LASSO and LARS regression

Graphical models: dynamic programming, hidden Markov models, forward-backward algorithm, Kalman filter, Markov random fields

Stochastic optimization: Robbins-Monro and Kiefer-Wolfowitz algorithms, simulated annealing, stochastic gradient methods

Deterministic integration: Gaussian quadrature, quasi-Monte Carlo. Application: expectation propagation

Monte Carlo methods
- Rejection sampling, importance sampling, variance reduction methods (Rao-Blackwellization, stratified sampling)
- MCMC methods: Gibbs sampling, Metropolis-Hastings, Langevin methods, Hamiltonian Monte Carlo, slice sampling. Implementation issues: burnin, monitoring convergence
- Sequential Monte Carlo (particle filtering)
- Variational and stochastic variational inference

References:
Givens and Hoeting (2005) Computational statistics
Robert and Casella (2004) Monte Carlo Statistical Methods
Boyd and Vandenberghe (2004), Convex Optimization.
Press et al, Numerical Recipes
Sun and Yuan (2006), Optimization theory and methods
Fletcher (2000) Practical methods of optimization
Searle (2006) Matrix Algebra Useful for Statistics
Spall (2003), Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control
Shewchuk (1994), An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Boyd et al (2011), Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

 Advanced Topics in Theoretical Neuroscience (Spring 2024)

Led by: Rainer Engelken ([email protected]) & Manuel Beiran ( [email protected])

 You may register via Courseworks, or contact us if you do not have a Columbia ID.

The classes will take place in person every Wednesday, 10:00-11:30 AM, location: L5-084 at Jerome L. Greene building. The course will begin next Wednesday January 24th and will continue on a weekly basis until May 1st, except for the winter break and the weeks overlapping with the Cosyne conference. The full schedule will be shared shortly. 

The course is taught by postdocs, and is intended to be interactive and oriented towards recent research advances. The topics will include: deep learning models for neuroscience, recurrent neural networks -dynamics and computation-, synaptic plasticity rules, and information theory.

Schedule: 

Neural chaos

Jan 24th - JLG L5-084

Rainer Engelken: Lyapunov exponents in spiking networks

 

Learning in neural networks

Jan 31st - JLG L5-084

Kaushik Lakshminarasimhan: Reinforcement learning in recurrent neural networks

Feb 7th - JLG L5-084

Owen Marschall: Algorithms for training recurrent neural networks

 

Neural processing in feed-forward networks

Feb 14th - JLG L5-084: 

W Jeffrey Johnston: Information theory for sensory processing

Feb 21st - JLG L5-084:

Samuel Muscinelli: Random expansion in biological neural networks

 

Feb 28st - JLG L5-084: no class (CoSyNe)

Mar 6th - JLG L5-084: no class (CoSyNe)

Mar 13th - JLG L5-084: no class (spring break)

 

Control theory

Mar 20th - JLG L5-084: 

Bin Wang: Predictive Coding and its Network Models 

 

Computations in recurrent networks

Mar 27th - JLG L5-084:

Ji Xia: Non-normal dynamics

Apr 3rd - JLG L5-084: 

Manuel Beiran: Ring attractor models

 

Neural representations

Apr 10th - JLG L5-084:

Tahereh Toosi: Deep neural networks as models in neuroscience

Apr 17rd - JLG L5-084:

Valeria Fascianelli & Lorenzo Posani: Geometry of neural representations

 

Student presentations

Apr 24th - JLG L5-084

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

Download Schedule  

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)
7  Course Wrapup
13 Assignment 9 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.

View Course Schedule

 

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

Download schedule

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