CS4540/CS8803: (Is there) A(n Algorithmic) Theory of (Artificial) Intelligence(?)
Fall 2023. MW: 9:30-10:45, Mason 5134
Santosh Vempala, Klaus 2222, Office hour: Mon 1:30-3pm (or by appt)
TAs: Xinyuan Cao OH: Tue 2-4pm, Klaus 3100. Mirabel Reid OH: Wed 12-2pm, Klaus 2100
What is the basis of intelligence? How can neural networks, artificial or natural, provably lead to perception, learning and cognition? We'll begin by studying a few classics, highlight the gaps and challenges posed by modern artificial models and the brain, and then discuss more recent rigorous proposals. Note that this is a mathematically rigorous course and the focus is on what is provably true related to this topic. Students interested in the latest developments in empirical AI should take other courses.
Prerequisites: algorithms, linear algebra.
Grading:
HW (40%): 4-6 Problem sets.
Exams (40%): Two in-class exams. No final. No exams for 8803 students.
Project (20%): Each team can choose one of the following options: (a) read a paper and provide an insightful explanation/simpler proof/ generalization (b) prove a conjecture (c) formulate a precise conjecture supported by experimental or theoretical evidence. A list of candidate projects will be provided.
Candidate Project topics are available here.
Readings (under construction!)
- The McCulloch-Pitts Neuron
- PAC Learning
- Winnow and Weighted Majority
- VC dimension
- Support Vector Machines
- Random Projection for Learning
- Boosting
- Random Graphs
- The Regularity Lemma
- Dynamics and Equilibria: the Brouwer-Kakutani Fixed Point Theorems
- Learning Finite Automata
- Cell Assemblies: Hebb, D. O. The organization of behavior: A neuropsychological theory. Psychology press.
- The Assembly Hypothesis
- Generalization in Deep Learning
- Recurrent Neural Networks
- LLMs??!
Schedule
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Aug 21, 23. Course overview. The Perceptron Algorithm Notes.
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Aug 28, 30. Weighted Majority and Winnow Notes.
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Sep 6, 11, 13. PAC learning, Sample Complexity, VC dimension Notes.
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Sep 18, 20. Support Vector Machines Notes. Random Projection for Learning Notes.
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Sep 25, 27. Boosting, Concentration Inequalities Notes.
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Oct 2, 11. Random Graphs Notes, Notes.
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Oct 4. Midterm I.
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Oct 16, 18. Fixed Point Iterations and Nash Equilibrium Notes.
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Oct 23. Regularity Lemmas Notes.
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Oct 25, 30. Assemblies of Neurons. slides, simulations: small and large.
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Nov 1. Angluin's algorithm for learning a Finite Automaton Notes.
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Nov 6, 8. Neural Networks: Architecture, Optimization, Generalization Notes.
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Nov 13. Rademacher Complexity Notes.
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Nov 15. Midterm II
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Nov 20. The Complexity of Human Cognitive Processing.
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Nov 27, 29. Language
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Dec 4. Language models and Next-word Prediction