Faculty: Larry Abbott, Stefano Fusi, Ashok Litwin Kumar, Ken Miller
TAs: Matteo Alleman, Dan Biderman, Salomon Muller, Amin Nejatbakhshesfahani, Marjorie Xie
Meetings: Tuesdays & Thursdays, JLGSC L5-084, Lecture 2.00 - 3.30pm
Text: Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)
January
21 (Larry) Introduction to the Course and to Theoretical Neuroscience
23 (Larry) Mathematics Review: Notes
28 (Larry) Electrical Properties of Neurons, Integrate-and-Fire Model (Assignment 1, neuron models)
30 (Larry) Adaptation, Synapses, Spiking Networks (Numerical methods)
February
4 (Larry) Numerical Methods, Filtering (Assignment 2)
5 Assignment 1 Due
6 (Larry) The Hodgkin-Huxley Model (I&F Model, White Noise, Synapses-Networks)
11 (Larry) Types of Neuron Models and Networks (Assignment 3, Poisson Spiking, Networks)
12 Assignment 2 Due
13 (Ashok) Linear Algebra I (Notes)
18 (Ashok) Linear Algebra II (Notes, Assignment 4)
19 Assignment 3 Due
20 (Ashok) Introduction to Probability, Encoding, Decoding (Notes)
25 (Ashok) GLMs (Notes, Assignment 5)
26 Assignment 4 Due
27 COSYNE
March
3 COSYNE
5 (Ashok) Decoding, Fisher Information I
10 (Ashok) Decoding, Fisher Information II (Assignment 6)
11 Assignment 5 Due
12 (Ashok) Information Theory
17 Spring Break
19 Spring Break
24 (Ken) – PCA and Dimensionality Reduction I
25 Assignment 6 Due
26 (Ken) – PCA and Dimensionality Reduction II
31 (Ken) – Rate Networks/E-I networks I (Assignment 7)
April
1 Assignment 6 Due
2 (Ken) – Rate Networks/E-I networks II
7 (Ken) – Unsupervised/Hebbian Learning, Developmental Models (Assignment 8)
8 Assignment 7 Due
9 (Ken) – Optimization
14 (Ken) – Optimization II (Assignment 9)
15 Assignment 8 Due
16 Research Topic
21 (Stefano) Perceptron (Assignment 10)
22 Assignment 9 Due
23 (Stefano) Multilayer Perceptrons and Mixed Selectivity
28 (Stefano) – Deep Learning I (backpropagation) (Assignment 11)
29 Assignment 10 Due
30 (Stefano) – Deep Learning II (convolutional networks)
May
5 (Stefano) Learning in Recurrent Networks (Assignment 12)
6 Assignment 11 Due
7 (Stefano) Continual Learning and Catastrophic Forgetting
12 (Stefano) Reinforcement Learning
13 Assignment 12 Due
14 Research Topic
Meetings: Wednesdays, 10.15 - 11.45am
Location – Jerome L Greene Science Center, L6-087
See course website for updated schedule
Control Theory and Reinforcement Learning
Jan 29 Examples of control theory in neuroscience (Bettina Hein, Laureline Logiaco)
Feb 5 Methods in control theory (Bettina Hein, Laureline Logiaco)
Feb 12 Reinforcement learning (James Murray)
Feb 19 From optimal control theory to reinforcement learning (Samuel Muscinelli)
Feb 26 Cosyne break
Mar 4 Cosyne break
Latent Variable Models
Mar 11 Hidden Markov Models (Matt Whiteway)
Mar 18 Latent Dynamical Systems (Josh Glaser)
Mar 25 Gaussian Processes (Rainer Engelken)
Apr 1 Modeling of Behavior (Juri Minxha)
Apr 8 Hackathon on Latent Variable Models
Miscellaneous
Apr 15 Phenomenological Renormalization Group (Serena Di Santo)
Apr 22 Additional and diverse perspectives in neuroscience (Laureline Logiaco, Matt Whiteway, Juri Minxha)
Apr 29 Introduction to replica theory (SueYeon Chung)
May 6 Classification and Geometry of General Perceptual Manifolds (SueYeon Chung)
Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)
Faculty: Ken Miller (kdm2103@columbia.edu)
Instructor: Dan Tyulmankov (dt2586@columbia.edu)
Teaching Assistant: Amin Nejatbakhsh (mn2822@columbia.edu)
Time: Tuesdays, Thursdays 8:40a-10:00a
Place: JLGSC L5-084
Webpage: https://ctn.zuckermaninstitute.columbia.edu/courses
Credits: 3 credits, pass/fail only
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
Grading: 100% attendance-based
Readings and exercises: Lecture notes and optional practice exercises will be provided for each lecture, and supplementary readings will be assigned from various textbooks.