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)
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
2 (Ken) Linear Algebra I
3 Assignment 2 Due
4 (Ken) Linear Algebra II
9 (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
2 Spring Break
4 Spring Break
9 (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
1 (Stefano) Deep Learning I (backpropagation)
6 (Stefano) Deep Learning II (convolutional networks) (Assignment 10)
7 Assignment 9 Due
8 (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)
Mathematical Tools
Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)
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: 2/17/2021