This course provides an introduction to the theory of neural computation. The goal is to familiarize students with the major theoretical frameworks and models used in neuroscience and psychology, and to provide hands-on experience in using these models. Topics include neural network models, supervised and unsupervised learning, associative memory models, recurrent networks, probabilistic/graphical models, and models of neural coding in the brain.

**Instructor**: Bruno Olshausen, 570 Evans, office hours immediately after class

**GSI**: Shariq Mobin, 560 Evans, office hours 2:30 – 4:00 pm on Mondays.

**Lectures**: Tuesdays & Thursdays 3:30-5, 170 Barrows.

**Grading**: based on weekly assignments (60%) and final project (40%)

- Late homework will not be accepted but your lowest homework score will be dropped at the end of the semester
- Each homework will be graded holistically out of 3 points:
- 3 – problems were done correctly aside from minor errors
- 2 – problems were attempted but some portions or concepts were missed
- 1 – something relevant was done but no clear direction or mostly incomplete
- 0 – problems were not attempted

- You have 1 week to dispute your grade from the time they are released on bCourses

**Textbooks**:

- [
**HKP**] Hertz, J. and Krogh, A. and Palmer, R.G.*Introduction to the theory of neural computation.*Amazon - [
**DJCM**] MacKay, D.J.C.*Information Theory, Inference and Learning Algorithms.*Available online or Amazon - [
**DA**] Dayan, P. and Abbott, L.F.*Theoretical neuroscience: computational and mathematical modeling of neural systems.*Amazon

**Discussion forum**: We have established a Piazza site where students can ask questions or propose topics for discussion.

**Syllabus**

**Aug. 23: Introduction**

- Theory and modeling in neuroscience
- Goals of AI/machine learning vs. theoretical neuroscience
- Lecture slides
- Reading:
**HKP**chapter 1- Dreyfus, H.L. and Dreyfus, S.E. Making a Mind vs. Modeling the Brain: Artificial Intelligence Back at a Branchpoint.
- Bell, A.J. Levels and Loops: the future of artificial intelligence and neuroscience.
- 1973 Lighthill debate on future of AI

- Homework 0:
- Python Installation
- Lab 0 tutorial (start with lab0_1-Introduction-to-Python-for-Scientific-Computing.html, then once in jupyter proceed to lab0_2 and lab0_3)

**Aug. 28, 30: Neuron models**

- Membrane equation, compartmental model of a neuron
- Physics of computation, Analog VLSI
- Reading
- Mead, C. Chapter 1: Introduction and Chapter 4: Neurons from
*Analog VLSI and Neural Systems*. - Carandini M, Heeger D (1994) Summation and division by neurons in primate visual cortex.
- Background on dynamics, linear time-invariant systems and convolution, and differential equations:
- Background on transistor physics and analog VLSI circuits:
- Mead, C., Chapters 2 & 3 from
*Analog VLSI and Neural Systems*. - Mead, C., Chapter 5: Transconductance amplifier from
*Analog VLSI and Neural Systems*. - Mead, C., Chapter 15: Silicon retina from
*Analog VLSI and Neural Systems*.

- Mead, C., Chapters 2 & 3 from
- Extra background on neuroscience:
- Cognitive Consilience, by Solari & Stoner (nice overview of brain architecture and circuits)
- From Neuron to Brain, by Nicholls, et al. (good intro to neuroscience)
- Principles of Neural Science, by Kandel and Schwartz et al. (basic neuroscience textbook)
- Synaptic organization of the Brain, by Gordon Shepard (good overview of neural circuits)
- Ion Channels of Excitable Membranes, by Bertil Hille (focuses on ion channel dynamics)

- Mead, C. Chapter 1: Introduction and Chapter 4: Neurons from
- Lecture slides
- Lab1 Neuron Models (v2) (due Tuesday Sept. 4 before class) (old version)
- To complete the lab you need to fill in text, latex, and code in the indicated spaces (Your TEXT/LATEX/CODE here) of lab1.ipynb. Please indicate your name and anyone you work with at the top of the file. To submit the lab rezipthe folder lab1-neuron_models and upload it to bcourses.
- Solutions

**Sept. 4, 6: Supervised learning**

- Perceptron model and learning rule
- Adaptation in linear neurons, Widrow-Hoff rule
- Objective functions and gradient descent
- Multilayer networks and back propagation
- Reading
**HKP**chapter 5,**DJCM**chapters 38-40, 44,**DA**chapter 8 (sec. 4-6)**HKP**chapter 6- Linear Neuron Models
- Supervised learning in single-stage feedforward networks
- Supervised learning in multi-layer feedforward networks – “back propagation”
- Background on linear algebra
- Linear algebra primer
- Jordan, M.I. An Introduction to Linear Algebra in Parallel Distributed Processing in McClelland and Rumelhart,
*Parallel Distributed Processing*, MIT Press, 1985.

- Further reading:
- Y. LeCun, L. Bottou, G. Orr, and K. Muller (1998) “Efficient BackProp,” in Neural Networks: Tricks of the trade, (G. Orr and Muller K., eds.).

- Lecture slides
- NetTalk demo
- Lab 2 Supervised Learning (due Thursday Sept. 13th before class) (Solutions)
- Please include your group members names in your lab2.ipynb file.

**Sept. 11, 13, 18: Unsupervised learning**

- Linear Hebbian learning and PCA, decorrelation
- Winner-take-all networks and clustering
- Lecture slides
- Reading
**HKP**Chapters 8 and 9,**DJCM**chapter 36,**DA**chapter 8, 10- Hebbian learning and PCA

- Further reading on neuroscience implications:
- Atick & Redlich (1992). What does the retina know about natural scenes?
- Dan, Atick & Reid (1996). Efficient Coding of Natural Scenes in the Lateral Geniculate Nucleus: Experimental Test of a Computational Theory.

- Lab 3 – Unsupervised Learning (Due Thursday Sept. 20th before class)
- lab3_2.ipynb is optional (same algorithms but with pictures of faces instead of 2-dimensional points)
- There is also a file that makes clear our matrix conventions in this class, it is also optional.

**Sept. 20, 25, 27: Sparse, distributed coding**

- Autoencoders
- Natural image statistics, projection pursuit
- Sparse coding model
- Locally competitive algorithms (LCA)
- Lecture slides
- Reading:
- Barlow, HB (1972) Single units and sensation: A neuron doctrine for perceptual psychology?
- Foldiak, P. (1990) Forming sparse representations by local anti-hebbian learning
- Olshausen BA, Field DJ (1996) Emergence of simple-cell receptive field properties by learning a sparse code for natural images.

- Lab 4 – Sparse Coding
- Additional readings:
- Rozell, Johnson, Baraniuk, Olshausen. (2008) Sparse Coding via Thresholding and Local Competition in Neural Circuits.
- Zylberberg, Murphy, DeWeese, (2011) A sparse coding model with synaptically local plasticity and spiking neurons can account for the diverse shapes of V1 simple cell receptive fields.
- Olshausen Sparse coding of time-varying natural images, ICIP 2003. (convolution sparse coding of video)
- Olshausen Highly Overcomplete Sparse Coding, SPIE 2013
- Smith E, Lewicki MS. Efficient auditory coding, Nature Vol 439 (2006). (convolution sparse coding of sound)
- Olshausen & Lewicki.What Natural Scene Statistics Can Tell Us About Cortical Representation. TNVN 2014

**Oct. 2, 4: Self-organizing maps**

- Plasticity and cortical maps
- Self-organizing maps, Kohonen nets
- Models of experience dependent learning and cortical reorganization

**Oct. 9: Manifold learning (Chen)**

- Local linear embedding, Isomap
- The sparse manifold transform

**Oct. 11: Reinforcement learning (Mobin)**

- Reward-based learning
- Predicting future rewards via temporal-difference learning

**Oct. 16, 18: Recurrent networks**

- Hopfield networks, memories as ‘basis of attraction’
- Line attractors and `bump circuits’

**Oct. 23, 25: Probabilistic models and inference**

- Probability theory and Bayes’ rule
- Learning and inference in generative models
- The mixture of Gaussians model (Charles Frye)

**Oct. 30, Nov. 1: Boltzmann machines**

- Sampling, inference and learning rules
- Restricted Boltzmann machines and Energy-based models

**Nov. 6, 8: Independent Components Analysis (ICA)**

- Relation between sparse coding and ‘ICA’
- Applications

**Nov. 13, 15, 20: Dynamical models**

- Hidden Markov models
- Kalman filter model
- Recurrent neural networks

**Nov. 27, 29: Neural coding**

- Integrate-and-fire model
- Neural encoding and decoding
- Limits of precision in neurons
- GLMs

**Dec. 4, 6: High-dimensional (HD) computing**

- Holographic reduced representation; Vector symbolic architectures
- Computing with 10,000 bits
- Sparse, distributed memory