Paulo Rauber

Recommended reading

I recommend the following references to students interested in artificial intelligence research.

I am currently interested in unlocking the potential of formalization to accelerate the development of machine learning theory. If you would like to work under my supervision, you should be interested in at least some of the PhD-level references listed below.

PhD-level

• Automated theorem proving:
  • T. Achim, A. Best, et al. "Aristotle: IMO-level Automated Theorem Proving". 2025.
• Lean:
  • K. Buzzard, J. Eugster, et al. "Natural Number Game". Available here.
  • D.T. Christiansen. "Functional Programming in Lean". Available here. [Note: Chapters 1-3.]
  • J. Avigad, L. Moura, S. Kong, S. Ullrich, et al. "Theorem Proving in Lean 4". Available here.
  • K. Buzzard, B. Mehta. "Formalising Mathematics". Available here. [Note: Tactics summary.]
  • E. Karunus. "How to Search for Theorems in Lean 4". Available here.
• Measure-theoretic probability (notes):
  • D. Pollard. "A User's Guide to Measure Theoretic Probability". Cambridge University Press, 2010.
• Machine learning theory (notes and notes):
  • T. Lattimore, C. Szepesvári. "Bandit Algorithms". Cambridge University Press, 2020.
  • A. Agarwal, N. Jiang, S.M. Kakade, W. Sun. "Reinforcement Learning: Theory and Algorithms". 2022.
  • F. Bach. "Learning Theory from First Principles". MIT Press, 2024.
  • M. Hutter, E. Catt, D. Quarel. "An Introduction to Universal Artificial Intelligence". Chapman & Hall, 2024.

[Note: I am not familiar with most of the content of the last two references listed above. However, they are excellent candidates for formalization.]

MSc-level

• Supervised learning and unsupervised learning (notes and notes):
  • C. Bishop. "Pattern Recognition and Machine Learning". Springer-Verlag, 2007.
  • K.P. Murphy. "Probabilistic Machine Learning: An Introduction". MIT Press, 2022.
• Neural networks (notes):
  • S.J.D. Prince. "Understanding Deep Learning". MIT Press, 2023.
• Reinforcement learning and decision making (notes):
  • R.S. Sutton, A.G. Barto. "Reinforcement Learning: An Introduction". MIT Press, 2020.
  • S. Levine. "Deep Reinforcement Learning". Available here.
  • M.J. Kochenderfer, T.A. Wheeler, K.H. Wray. "Algorithms for Decision Making". MIT Press, 2022.

BSc-level

• Programming:
  • E. Matthes. "Python Crash Course". No Starch Press, 2023.
  • K.N. King. "C Programming: A Modern Approach". W. W. Norton & Company, 2008.
• Computer design:
  • D.A. Patterson, J.L. Hennessy. "Computer Organization and Design: RISC-V Edition". Morgan Kaufmann, 2020.
• Mathematical proof:
  • D.J. Velleman. "How to Prove It: A Structured Approach". Cambridge University Press, 2019.
• Calculus (notes):
  • J. Stewart. "Calculus: Early Transcendentals". Brooks/Cole, 2011.
• Algorithms:
  • T.H. Cormen, C.E. Leiserson, R. Rivest, C. Stein. "Introduction to Algorithms". MIT Press, 2022.
• Theory of computation:
  • M. Sipser. "Introduction to the Theory of Computation". Course Technology, 2012.
• Analysis:
  • T. Tao. "Analysis I". Springer, 2022.
• Linear algebra (notes):
  • S. Axler. "Linear Algebra Done Right". Springer, 1997. [Note: Second edition.]
• Probability (notes, Sec. 2):
  • D.P. Bertsekas, J.N. Tsitsiklis. "Introduction to Probability". Athena Scientific, 2008.
• Artificial intelligence:
  • S. Russell, P. Norvig. "Artificial Intelligence: A Modern Approach". Pearson, 2021.