The Art of Scientific Research

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The Art of Scientific Research

This is a preparatory course for the main part of m1p.

The student's response-based syllabus

  1. We start
  2. Prepare your tools
  3. Check the foundations
  4. How to measure impact?
  5. Describe your system
  6. Write the abstract
  7. Write the intro
  8. Review the paper
  9. Deliver a message
  10. Your one-slide talk
  11. Blind management game
  12. List your ideas
  13. List the foundations
  14. Suggest an impactful theorem
  15. Review for your topic
  16. Good, bad, ugly: tell the difference
  17. Tell about a scientific society
  18. Reproducible computational experiment
  19. Computer-supported brainstorming
  20. Conferences and journals, review, and schedules
  21. Writing a grant proposal

The theory to discuss

  1. Machine learning at one go
  2. Linear models (and processes) with time (regression, SVD, PCA, NN)
  3. Tensor indexing and decomposition, Tucker, HOSVD, TT (getting rid of time by constructing a state space)
  4. Types of optimization (what is the gradient and Jacoby matrix)
  5. Convolution is a linear operator, Fourier is a linear operator
  6. Graph convolution, metric spaces (if possible)
  7. Kernel methods and RKHS
  8. Canonical correlation analysis and autoencoders
  9. Bayesian inference and regularization, optimization
  10. Model selection
  11. Multimodeling (privilege, distilling, domain transfer)
  12. Introduction to sampling and generative models
  • Goals for the next year are CaТ, NODE, SDE, Diffusion, Riemannian, Tensors as tensors, Advanced calculus, Clifford algebra, Homology

Scoring

  1. Tests at the beginning of a seminar
  2. Talks at the end of a seminar
  3. Downloads of the homework
  4. The coursework

Similar courses

  1. Around

Main references

  1. (long reading 2196 pages) Algebra, Topology, Differential Calculus, and Optimization Theory for Computer Science and Machine Learning by Jean Gallier and Jocelyn Quaintance, 2024. pdf, github
  2. (fun reading) The Art of Scientific Investigation by W. I. B. Beveridge, 1957 pdf
  3. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems. and Control by S.L. Brunton and J. N. Kutz, 2019.
  4. Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges by M.M. Bronstein, J. Bruna, T. Cohen, P. Veličković, 2021. arxiv
  5. Deep Learning: Foundations and Concepts by C.M. Bishop, H. Bishop, 2024 version'06
  6. Mathematics for Physicists: Introductory Concepts and Methods by A. Altland. J. von Delf, 2017 pdf
  7. Mathematics for Machine Learning by M.P. Deisenroth, A.A. Faisal, C.S. Ong pdf

Cath-up

Check and develop your typing skills

Dates

Sat 9:30 – 10:50 zoom | Sept 7 14 21 28 | Now 5 12 19 26 | Oct 2 9 16 23 30 | Dec 7 14 21 28

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