## 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: 1/19/2021*