Courses

Intro to Theory

Computational Neuroscience, Spring 2021

Larry Abbott, Ken Miller, Ashok Litwin Kumar, Stefano Fusi, Sean Escola

TAs: Denis Turcu, Elom Amematsro, Ramin Khajeh, Matteo Alleman

Meetings: Tuesdays 2:00-3:30 & Thursdays 1:30-3:00

Text - Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)

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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)

Class Notes (Larry)

February

(Ken) Linear Algebra I
Assignment 2 Due
(Ken) Linear Algebra II
(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, Class Notes

Class Notes (Ken)
Class Notes (Ashok)

March

Spring Break
Spring Break
(Ashok) Decoding, Fisher Information I
10  Assignment 6 Due
11  (Ashok) Decoding, Fisher Information II
16  (Ashok) Information Theory (Assignment 7)
18  (Ashok) Optimization I
23  (Ashok) Optimization II (Assignment 8)
24  Assignment 7 Due
25  (Stefano) The Perceptron
30  (Stefano) Multilayer Perceptrons and Mixed Selectivity (Assignment 9)
31  Assignment 8 Due

Class Notes (Stefano)

April

(Stefano) Deep Learning I (backpropagation)
(Stefano) Deep Learning II (convolutional networks) (Assignment 10)
Assignment 9 Due
(Sean) 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

 

Introduction to Theoretical Neuroscience (Spring 2020)

Introduction to Theoretical Neuroscience (Spring 2019)

Introduction to Theoretical Neuroscience (Spring 2018)

Mathematical Tools

Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)

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Spring 2021

Lecturer: Dan Tyulmankov (dt2586@columbia.edu)
Faculty contact: Prof. Ken Miller (kdm2103@columbia.edu)*

Time: Tuesdays, Thursdays 11:40a-12:55p
Place: Zoom
Webpage: CourseWorks (announcements, assignments, readings) and Piazza (Q&A, discussion)
Credits: 3 *(Please contact Prof. Miller to sign add/drop forms and other items which require faculty permission)

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. 

Registration:

  • Undergraduate and graduate students: Must register** on SSOL and on Piazza
  • All others: Please fill out this form and register on Piazza

(**If you’re only interested in attending a subset of lectures, register anyways and contact Dan) 

Prerequisites: Basic prior exposure to trigonometry, calculus, and vector/matrix operations at the high school level

 

Mathematical Tools for Theoretical Neuroscience (Spring 2020)

Advanced Theory

Special Virtual Edition, Summer/Fall 2020

Meetings: Wednesdays, 10.00 am 

Location: Zoom, contact re2365@columbia.edu for details

Schedule:

7/15/2020     Time-dependent mean-field theory for mathematical streetfighters (Rainer Engelken)

7/22/2020     Predictive coding in balanced neural networks with noise, chaos, and delays, Article (Everyone) 

7/29/2020     A solution to the learning dilemma for recurrent networks of spiking neurons, Article (Everyone) 

8/5/2020       Canceled             

8/12/2020     Artificial neural networks for neuroscientists: A primer, Article (Robert Yang)

8/19/2020     A mechanism for generating modular activity in the cerebral cortex (Bettina Hein)

8/26/2020     Dynamic representations in networked neural systems, Article (Kaushik Lakshminarasimhan) 

9/2/2020       Network principles predict motor cortex population activity across movement speeds (Shreya Saxena)

9/9/2020       Modeling neurophysiological mechanisms of language production (Serena Di Santo)

9/16/2020     How single rate unit properties shape chaotic dynamics and signal transmission in random neural networks, Article (Samuel Muscinelli)

9/23/2020     Shaping dynamics with multiple populations in low-rank recurrent networks, Article (Laureline Logiaco)

9/30/2020     Deep Graph Pose: a semi-supervised deep graphical model for improved animal pose tracking, Article (Anqi Wu)

10/7/2020     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)

11/4/2020      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)

12/2/2020        Canceled

12/9/2020        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)

 

Advanced Theory Seminar (Spring 2020) website
Advanced Theory Seminar (Spring 2019) website

Page Last Updated: 1/19/2021