Room: CCSB 1.0202

Instructor: Vladik Kreinovich, email vladik at utep.edu, office CCSB 3.0404,
office phone (915) 747-6951.

• The instructor's office hours are Tuesdays and Thursdays 1:30-2:50 pm, or by appointment.
• If you want to contact the instructor during the scheduled office hours, there is no need to schedule an appointment.
• If you cannot contact the instructor during the instructor's scheduled office hours, please schedule an appointment in the following way:
  • use the instructor's appointments page https://www.cs.utep.edu/vladik/appointments.html to find the time when the instructor is not busy (i.e., when he has no other appointments), and
  • send him an email, to vladik at utep.edu, indicating the day and time that you would like to meet.
  He will then send a reply email, usually confirming that he is available at this time, and he will place the meeting with you on his schedule.

Main Objective: to teach the foundations of deep learning in AI.

Contents

Current deep learning has had many spectacular successes, and many new successes appear all the time. Naive readers of the media reports may be under the false impression that all you need to succeed is to apply the available the current tools to new problems – and then rush to publish the results. This happens but very rarely.

In reality, many ideas have been and are being proposed, some of these ideas lead to empirical successes, but many don't. It is therefore desirable to have some theoretical guidance that would help researchers and practitioners to make their ideas more focused on successful directions, to better avoid blind alleys.

A natural way to come with such a guidance is to analyze the existing empirical successes. This will be the main focus of this course.

In this course, students will learn possible theoretical explanations for many successful features of deep learning:

• starting with the explanation of why neural networks are so successful in the first place,
• then explaining why deep learning is better,
• why the most frequently used activation functions – ReLU, sigmoid, softmax -- work so well,
• why linear combination and max are prevalent in convolutional neural networks,
• where attention formulas come from,
• why Shapley value is useful, etc. –
• all the way to explaining specific features of new promising directions such as Kolmogorov-Arnold networks and combining deep learning with fuzzy techniques.

• learn the general – mostly physics-motivated -- techniques behind these explanations, and
• learn how these techniques can solve the corresponding optimization problems.

As part of the class, students will work on projects. Possible projects range:

• from relatively simpler one – such as reviewing a relevant published paper,
• to more research-oriented such as attempting to analyze why some other properties of deep learning – whose success has not yet been convincingly explained – are empirically successful and/or using newly learned techniques to try to predict which alternatives will work better in new situations.

Since this course is focused on theoretical explanations, it will use some mathematics. Not to worry: we will review the needed mathematics in the class.

Sources: On this topic, there is no up-to-date textbook yet, we will use several papers. For topic for which there are no easy-to-read papers, we will try to post easier-to-summaries of the not-so-easy-to-read papers on the class website.

Projects: An important part of the class is a project. There are three possible types of projects:

• For students who already have a research advisor, an ideal class project is if you do something related to uncertainty of AI which is useful for your research project and/or for your future thesis or dissertation. Please check with your advisor about it, maybe he or she wants you to read and report on some related paper, maybe you need to do some related research, whatever your advisor recommends will be a very good project for this class, just let the class instructor know what exactly you plan to do.
• If you do not have an advisor, find an interesting paper that is related to uncertainty in AI and that you would like to review, and send it to the instructor -- so that he will check that this paper is relevant and reviewing it is a doable task.
• You can also select one of the projects proposed by the instructor.

Assignments: Reading and homework assignments will be announced on the class website. You should expect to spend at least 10 hours/week outside of class on reading and homework.

Homework Assignments: Each topic means home assignments. Howeworks will be due by the day of the next class. To submit a homework, send it to me by email. If it is not electronic, scan it and send him/her the scanned version.

One week after the homework was assigned, I will post correct solutions. I will be glad to answer questions if needed.

If you have a legitimate reason to be late, let me know, you can then submit it until the homeworks are posted. If you were simply late, you can still submit until the homeworks are posted, but then points will be taken off points for submitting late.

Since I will be posting correct solutions to homeworks, it does not make any sense to accept very late assignments: once the solution is posted, it make no sense for you to copy it in your own handwriting, this does not indicate any understanding. So, please try to submit your assignments on time.

Things happen. If there is an emergency situation and you cannot submit it on time, let me know, you will then not be penalized -- and I will come up with a similar but different assignment that you can submit to me when you become available again.

Homework must be done individually. While you may discuss the problem in general terms with other people, your answers and your code should be written and tested by you alone. If you need help, consult the instructor.

Exams: There will be two tests and the final exam.

Similar to homeworks, I will post solution, send you the grades, and answer questions if something is not clear.

As usual, if you are unable to attend the test, let me know, I will organize a different version of the test at a time convenient for you.

Grades: Each topic means home assignments (mainly on the sheets of paper, but some on the real computer). Maximum number of points:

• first test: 15
• second test: 20
• home assignments: 10
• final exam: 35
• project: 20

A good project can help but it cannot completely cover possible deficiencies of knowledge as shown on the test and on the homeworks. In general, up to 80 points come from tests and home assignments. So:

• to get an A, you must gain, on all the tests and home assignments, at least 90% of the possible amount of points (i.e., at least 72), and also at least 90 points overall;
• to get a B, you must gain, on all the tests and home assignments, at least 80% of the possible amount of points (i.e., at least 64), and also at least 80 points overall;
• to get a C, you must gain, on all the tests and home assignments, at least 70% of the possible amount of points (i.e., at least 56), and also at least 70 points overall.

Special Accommodations: If you have a disability and need classroom accommodations, please contact the Center for Accommodations and Support Services (CASS) at 747-5148 or by email to cass@utep.edu, or visit their office located in UTEP Union East, Room 106. For additional information, please visit the CASS website at http://www.sa.utep.edu/cass. CASS's staff are the only individuals who can validate and if need be, authorize accommodations for students.

Scholastic Dishonesty: Any student who commits an act of scholastic dishonesty is subject to discipline. Scholastic dishonesty includes, but not limited to cheating, plagiarism, collusion, submission for credit of any work or materials that are attributable to another person.

Cheating is:

• copying from the test paper of another student;
• communicating with another student during a test to be taken individually;
• giving or seeking aid from another student during a test to be taken individually;
• possession and/or use of unauthorized materials during tests (i.e. crib notes, class notes, books, etc.);
• substituting for another person to take a test;
• falsifying research data, reports, academic work offered for credit.

• using someone's work in your assignments without the proper citations;
• submitting the same paper or assignment from a different course, without direct permission of instructors.

Collusion is unauthorized collaboration with another person in preparing academic assignments.

Instructors are required to -- and will -- report academic dishonesty and any other violation of the Standards of Conduct to the Dean of Students.

NOTE: When in doubt on any of the above, please contact your instructor to check if you are following authorized procedure.

Daily schedule (tentative and subject to change)

August 24: topics to cover:

• why do we need machine learning; see [31], Section 1;
• what is deep learning; see [31], Section 2; [28], Section 1; [30], Section 1;
• what are its successful properties; see [28], Section 1; [30], Section 1;
• why do we need to explain these properties; see [28], Section 1; [30], Section 1.

August 26: topics to cover:

• why do we need neural networks in the first place: an explanation; see [31], Section 2;
• why deep neural networks: an explanation; [31], Sections 3-6;
• discussion of possible projects.

August 31: topics to cover:

• why ReLU: individual study of the material; see [31], Sections 7-10;
• work on your project.

September 2: topics to cover:

• why ReLU: individual study of the material (continued); see [31], Sections 7-10
• work on your project.

September 7: topics to cover -- why ReLU?

• an explanation based on invariance; see [31], Sections 7-10;
• relation between optimality and invariance; see [30], Section 2 and proof of Proposition 1 in Section 7; [28], Section 8.2.

September 9: topics to cover -- why ReLU?

• it is optimal; see [30], Section 2 and proof in Section 7;
• it leads to the most adequate description of the physical world; see [28], Section 3.

September 14: topics to cover -- why ReLU?

• because it does not lose information and does not process irrelevant information; see [28], Section 4.

September 16: topics to cover -- why ReLU?

• because it is the fastest to compute; see [28], Section 5.

September 21: topics to cover -- why ReLU?

• because it is the most appropriate for decision making; see [28], Section 6.

September 23: topics to cover -- why ReLU?

• because it leads to the most understandable results; see [28], Section 7.

[1] Kevin Alvarez, Julio C. Urenda, Orsolya Csiszar, Gabor Csiszar,
  Jozsef Dombi, Gyorgy Eigner, and Vladik Kreinovich, "Towards Fast
  and Understandable Computations: Which `And'- and `Or'-Operations
  Can Be Represented by the Fastest (i.e., 1-Layer) Neural Networks?
  Which Activations Functions Allow Such Representations?", Acta
  Polytechnica Hungarica, 2021, Vol. 18, No. 2, pp. 27-45.
pdf file

[2] Kittawit Autchariyapanikul, Olga Kosheleva, and Vladik Kreinovich,
  "Shapley Value under Interval Uncertainty and Partial Information",
  In: Vladik Kreinovich, Woraphon Yamaka, and Supanika Leurcharusmee
  (eds.), Data Science for Econometrics and Related Topics, Springer,
  Cham, Switzerland, to appear.
pdf file

[3] Chitta Baral and Vladik Kreinovich, "Why Sigmoid Transformation
  Helps Incorporate Logic Into Deep Learning: A Theoretical
  Explanation", In: Martine Ceberio and Vladik Kreinovich (eds.),
  Uncertainty, Constraints, AI, and Decision Making, Springer, Cham,
  Switzerland, to appear.
pdf file

[4] Chitta Baral and Vladik Kreinovich, "How to Make a Neural Network
  Learn from a Small Number of Examples -- and Learn Fast: An Idea",
  Proceedings of the 9th World Conference on Soft Computing, Baku,
  Azerbaijan, September 24-27, 2024.
pdf file

[5] Barnabas Bede, Olga Kosheleva, and Vladik Kreinovich, "Every
  ReLU-Based Neural Network Can Be Described by a System of
  Takagi-Sugeno Fuzzy Rules: A Theorem", In: Hung T. Nguyen,
  Janusz Kacprzyk, and Vladik Kreinovich (eds.), Contributions of
  Fuzzy Techniques to Systems and Control: A Tribute to Michio Sugeno,
  Springer, Cham, Switzerland, to appear.
pdf file

[6] Barnabas Bede, Olga Kosheleva, and Vladik Kreinovich, "For Which
  Activation Functions, Any Neural Network Is Equivalent to a
  Takagi-Sugeno Fuzzy System with Constant or Linear Outputs?", In:
  Marek Z. Reformat, Sabrina Senatore, Yusuke Nojima, and Vladik
  Kreinovich (eds.), Fuzzy Systems 60 Years Later: Past, Present, and
  Future. Proceedings of the Joint 2025 World Congress on the
  International Fuzzy Systems Association and the 2025 Annual
  Conference of the North American Fuzzy Information Processing
  Society IFSA-NAFIPS 2025, Banff, Canada, August 16-19, 2025,
  Springer, Cham, Switzerland.
pdf file

[7] Barnabas Bede, Vladik Kreinovich, and Uyen Pham, "Why Rectified
  Linear Unit is Efficient in Machine Learning: One More
  Explanation", In: Vladik Kreinovich, Songsak Sriboonchitta, and
  Woraphon Yamaka (eds.), Machine Learning for Econometrics and
  Related Topics, Springer, Cham, Switzerland, 2024, pp. 161-167.
pdf file

[8] Barnabas Bede, Vladik Kreinovich, and Peter Toth, "On equivalence
  between Takagi-Sugeno-Kang fuzzy systems with triangular membership
  functions and Neural Networks with ReLU activation in two or more
  dimensions", International Journal of Computers Communications &
  Control, 2025, Vol. 20. No. 4, Paper 7127,
pdf file

[9] Michael Beer, Julio Urenda, Olga Kosheleva, and Vladik Kreinovich,
  "Why Spiking Neural Networks Are Efficient: A Theorem", In:
  Marie-Jeanne Lesot, Susana Vieira, Marek Z. Reformat,
  Joao Paulo Carvalho, Anna Wilbik, Bernadette Bouchon-Meunier, and
  Ronald R. Yager (eds.), Proceedings of the 18th International
  Conference on Information Processing and Management of Uncertainty
  in Knowledge-Based Systems IPMU'2020, Lisbon, Portugal,
  June 15-19, 2020, pp. 59-69.
pdf file

[10] Laxman Bokati, Olga Kosheleva, Vladik Kreinovich, and Anibal Sosa,
  "Why Deep Learning Is More Efficient than Support Vector Machines,
  and How It Is Related to Sparsity Techniques in Signal Processing",
  Proceedings of the 2020 4th International Conference on Intelligent
  Systems, Metaheuristics & Swarm Intelligence ISMSI'2020, Thimpu,
  Bhutan, April 18-19, 2020.
pdf file

[11] Laxman Bokati, Olga Kosheleva, Vladik Kreinovich, and Nguyen Ngoc
  Thach, "Why Shapley Value and Its Variants Are Useful in Machine
  Learning (and in Other Applications)", In: Vladik Kreinovich,
  Songsak Sriboonchitta, and Woraphon Yamaka (eds.), Machine
  Learning for Econometrics and Related Topics, Springer, Cham,
  Switzerland, 2024, pp. 169-174.
pdf file

[12] Laxman Bokati, Vladik Kreinovich, Joseph Baca, and Natasha Rovelli,
  "Why Rectified Power (RePU) Activation Functions Are Efficient in
  Deep Learning: A Theoretical Explanation", In: Martine Ceberio and
  Vladik Kreinovich (eds.), Uncertainty, Constraints, and Decision
  Making, Springer, Cham, Switzerland, 2023, pp. 7-13.
pdf file

[13] Kelly Cohen, Laxman Bokati, Martine Ceberio, Olga Kosheleva, and
  Vladik Kreinovich, "Why Fuzzy Techniques in Explainable AI? Which
  Fuzzy Techniques in Explainable AI?", In: Julia Rayz, Victor Raskin,
  Scott Dick, and Vladik Kreinovich (eds.), "Explainable AI and Other
  Applications of Fuzzy Techniques, Proceedings of the Annual
  Conference of the North American Fuzzy Information Processing
  Society NAFIPS'2021, West Lafayette, Indiana, June 7-9, 2021",
  Springer, Cham, Switzerland, 2022, pp. 74-78.
pdf file

[14] Jonatan Contreras, Martine Ceberio, Olga Kosheleva, and Vladik
  Kreinovich, "Why neural networks in the first place: a theoretical
  explanation", Journal of Intelligent and Fuzzy Systems, 2022,
  Vol. 43, No. 6, pp. 6947-6951.
pdf file

[15] Jonatan Contreras, Martine Ceberio, Olga Kosheleva, and Vladik
  Kreinovich, "Why Gradient Descent -- Not the Best Optimization
  Technique -- Works Best in Neural Networks: Qualitative Explanation",
  Journal of Combinatorics, Information, and System Sciences JCISS,
  2021, Vol. 45, No. 1-4, pp. 1-10.
pdf file

[16] Jonatan Contreras, Martine Ceberio, Olga Kosheleva, Vladik
  Kreinovich, and Nguyen Hoang Phuong, "Computational Paradox of
  Deep Learning: A Qualitative Explanation", In: Nguyen Hoang Phuong
  and Vladik Kreinovich (eds.), Deep Learning and Other Soft
  Computing Techniques: Biomedical and Related Applications,
  Springer, Cham, Switzerland, 2023, pp. 245-252.
pdf file

[17] Jonatan Contreras, Martine Ceberio, Olga Kosheleva,
  Vladik Kreinovich, and Nguyen Hoang Phuong, "Why Rectified
  Linear Neurons: Two Convexity-Related Explanations", In:
  Nguyen Hoang Phuong and Vladik Kreinovich (eds.), "Biomedical
  and Other Applications of Soft Computing", Springer, Cham,
  Switzerland, 2023, pp. 41-47.
pdf file

[18] Jonatan Contreras, Martine Ceberio, and Vladik Kreinovich, "Why
  rectified linear neurons: a possible interval-based explanation",
  In: Nguyen Ngoc Thach, Nguyen Duc Trung, Doan Thanh Ha, and Vladik
  Kreinovich, Artificial Intelligence and Machine Learning for
  Econometrics: Applications and Regulation (and Related Topics),
  Springer, Cham, Switzerland, to appear.
pdf file

[19] Jonatan Contreras, Martine Ceberio, and Vladik Kreinovich, "Why
  Dilated Convolutional Neural Networks: A Proof of Their Optimality",
  Entropy, 2021, Vol. 23, Paper 767.
pdf file

[20] Jonatan Contreras, Martine Ceberio, and Vladik Kreinovich, "One
  More Physics-Based Explanation for Rectified Linear Neurons", In:
  Martine Ceberio and Vladik Kreinovich (eds.), Uncertainty,
  Constraints, and Decision Making, Springer, Cham, Switzerland,
  2023, pp. 195-198.
pdf file

[21] Daniel Cruz, Ricardo Godoy, and Vladik Kreinovich,
  "Why, in Deep Learning, Non-Smooth Activation Function Works
  Better Than Smooth Ones", In: Martine Ceberio and
  Vladik Kreinovich (eds.), "Decision Making under Uncertainty
  and Constraints: A Why-Book", Springer, Cham, Switzerland,
  2023, pp. 111-115.
pdf file

[22] Lehel Denes-Fazakas, Laszlo Szilagyi, Gyorgy Eigner, Olga Kosheleva,
  Martine Ceberio, and Vladik Kreinovich, "Which Activation Function
  Works Best for Training Artificial Pancreas: Empirical Fact and Its
  Theoretical Explanation", Proceedings of the  IEEE Series of
  Symposia on Computational Intelligence SSCI 2023, Mexico City,
  Mexico, December 6-8, 2023.
pdf file

[23] Lehel Denes-Fazakas, Laszlo Szilagyi, and Vladik Kreinovich, "Why
  Linear and Sigmoid Last Layers Work Better in Classification", In:
  Martine Ceberio and Vladik Kreinovich (eds.), Uncertainty,
  Constraints, AI, and Decision Making, Springer, Cham, Switzerland,
  to appear.
pdf file

[24] Damian Lorenzo Gallegas Espinosa, Olga Kosheleva, and Vladik
  Kreinovich, "Why Skew-Normal Distributions and How They Are
  Related to ReLU Activation Function in Deep Learning", In: Hien
  Thi Thu Nguyen, Hai Hong Phan, and Van Nam Huynh (eds.), Data
  Science in Finance and Accounting, Springer, Cham, Switzerland, to
  appear.
pdf file

[25] Sofia Holguin and Vladik Kreinovich, "Why Residual Neural
  Networks", In: Martine Ceberio and Vladik Kreinovich (eds.),
  "Decision Making under Uncertainty and Constraints: A Why-Book",
  Springer, Cham, Switzerland, 2023, pp. 117-120.
pdf file

[26] Olga Kosheleva and Vladik Kreinovich, "Why Semi-Supervised
  Learning Makes Sense: A Pedagogical Note", In: Martine Ceberio
  and Vladik Kreinovich (eds.), "Decision Making under
  Uncertainty and Constraints: A Why-Book", Springer, Cham,
  Switzerland, 2023, pp. 121-124.
pdf file

[27] Olga Kosheleva, Vladik Kreinovich, Victor Timchenko, and Yuriy
  Kondratenko, "Two Is Enough, but Three (or More) Is Better: in AI
  and Beyond", In: A. I. Shevchenko and Yuriy P. Kondratenko (eds.),
  Artificial Intelligence: Achievements and Recent Developments,
  River Publishers, Aalborg, Denmark, 2025, pp. 343-356.
pdf file

[28] Vladik Kreinovich, "Which AI/ML Techniques to Select for
  Applications to Decision Making: Towards Theoretical Explanations
  of Empirical Discoveries", In: Nicholas Daras, Antonios
  Fytopoulos, and Panos Pardalos (eds.), Handbook of Artificial
  Intelligence and Machine Learning in Decision Making, Springer,
  Cham, Switzerland, 2026, to appear.
pdf file

[29] Vladik Kreinovich and Olga Kosheleva, "Fuzzy Or Neural,
  Type-1 Or Type-2 -- When Each Is Better: First-Approximation
  Analysis", In: Yuriy P. Kondratenko, Vladik Kreinovich, Witold
  Pedrycz, Arkadiy A. Chikrii, Anna M. Gil Lafuente (eds.),
  Artificial Intelligence in Control and Decision-Making Systems,
  Springer, 2023, pp. 67-74.
pdf file

[30] Vladik Kreinovich and Olga Kosheleva, "Optimization under
  uncertainty explains empirical success of deep learning heuristics",
  In: Panos Pardalos, Varvara Rasskazova, and Michael N. Vrahatis
  (eds.), Black Box Optimization, Machine Learning and No-Free Lunch
  Theorems, Springer, Cham, Switzerland, 2021, pp. 195-220.
pdf file

[31] Vladik Kreinovich and Olga Kosheleva, "Deep Learning (Partly)
  Demystified", Proceedings of the 2020 4th International Conference
  on Intelligent Systems, Metaheuristics & Swarm Intelligence
  ISMSI'2020, Thimpu, Bhutan, April 18-19, 2020.
pdf file

[32] Vladik Kreinovich and Chon Van Le, "Predicting (Economic)
  Trends: Why Signature Method in Machine Learning", In:
  Songsak Sriboonchitta, Vladik Kreinovich, Woraphon Yamaka
  (eds.), "Credible Asset Allocation, Optimal Transport Methods,
  and Related Topics", Springer, Cham, Switzerland, 2022,
  pp. 185-193.
pdf file

[33] Vladik Kreinovich, Olga Kosheleva, and Andres Ortiz-Munoz,
  "Need for Simplicity and Everything Is a Matter of Degree:
  How Zadeh's Philosophy is Related to Kolmogorov Complexity,
  Quantum Physics, and Deep Learning", In: Shahnaz N. Shahbazova,
  Ali M. Abbasov, Vladik Kreinovich, Janusz Kacprzyk, and Ildar
  Batyrshin (eds.), "Recent Developments and the New Directions of
  Research, Foundations, and Applications", Springer, Cham,
  Switzerland, 2023, Vol. 1, pp. 203-215.
pdf file

[34] Anatole Lokshin, Olga Kosheleva, and Vladik Kreinovich, "Why
  Softmax? Because It Is the Only Consistent Approach to
  Probability-Based Classification", In: Martine Ceberio and Vladik
  Kreinovich (eds.), Uncertainty, Constraints, AI, and Decision
  Making, Springer, Cham, Switzerland, to appear.
pdf file

[35] Ricardo Lozano, Ivan Montoya Sanchez, and Vladik Kreinovich, "Why
  Deep Neural Networks: Yet Another Explanation", In: Martine
  Ceberio and Vladik Kreinovich (eds.), Uncertainty, Constraints,
  and Decision Making, Springer, Cham, Switzerland, 2023, pp. 199-202.
pdf file

[36] Dinh Tuan Nguyen, Vladik Kreinovich, Olga Koshevela, and Nguyen
  Hoang Phuong, "How to Generalize Softmax to the Case When an
  Object May Not Belong to Any Given Class", In: Nguyen Hoang Phuong,
  Nguyen Thi Huyen Chau, and Vladik Kreinovich (eds.), AI and
  Computational Intelligence, Springer, Cham, Switzerland, to
  appear.
pdf file

[37] Hung T. Nguyen, Vladik Kreinovich, and Olga Kosheleva, "Why
  Kolmogorov-Arnold Networks (KAN) Work So Well: A Qualitative
  Explanation", In: Nguyen Hoang Phuong, Nguyen Thi Huyen Chau, and
  Vladik Kreinovich (eds.), Explainable Artificial Intelligence and
  Other Soft Computing Techniques: Biomedical and Related
  Applications, Springer, Cham, Switzerland, to appear.
pdf file

[38] Salvador Robles Herrera, Martine Ceberio, and Vladik Kreinovich,
  "Foundations of Neural Networks Explain the Empirical Success of
  the "Surrogate" Approach to Ordinal Regression -- and Recommend
  What Next", In: Martine Ceberio and Vladik Kreinovich (eds.),
  Uncertainty, Constraints, AI, and Decision Making, Springer, Cham,
  Switzerland, to appear.
pdf file

[39] Salvador Robles Herrera, Martine Ceberio, and
  Vladik Kreinovich, "When Is Deep Learning Better and When Is
  Shallow Learning Better: Qualitative Analysis",
  International Journal of Parallel, Emergent and Distributed
  Systems, 2022, DOI: 10.1080/17445760.2022.2070748.
pdf file

[40] Christian Servin, Olga Kosheleva, and Vladik Kreinovich, "From
  Aristotle to Newton, from Sets to Fuzzy Sets, and from Sigmoid to
  ReLU: What Do All These Transitions Have in Common?", Proceedings
  of the NAFIPS International Conference on Fuzzy Systems, Soft
  Computing, and Explainable AI NAFIPS'2024, South Padre Island,
  Texas, May 27-29, 2024.
pdf file

[41] Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, "Education in
  the Era of Google, Wikipedia, and Deep Learning: Are We Humans
  Still Needed and If Yes for What?", In: Evgeny Dantsin and Vladik
  Kreinovich (eds.), Uncertainty Quantification and Uncertainty
  Propagation under Traditional and AI-Based Data Processing (and
  Related Topics): Legacy of Grigory Tseytin, Springer, Cham,
  Switzerland, to appear.
pdf file

[42] Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, and Nguyen
  Hoang Phuong, "Why embedding-decoder arrangement helps machine
  learning", In: Nguyen Hoang Phuong, Nguyen Thi Huyen Chau, and
  Vladik Kreinovich (eds.), AI and Computational Intelligence,
  Springer, Cham, Switzerland, to appear.
pdf file

[43] Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, and Nguyen
  Hoang Phuong, "Bohr's Observation about Deep Truths, Quantum
  Computing, Multiple-Valued Logic, Neural Networks, LLMs, Hegel's
  Negation of Negation (and Maybe Even Laws of Sexual Attraction)",
  In: Nguyen Hoang Phuong, Nguyen Thi Huyen Chau, and Vladik
  Kreinovich (eds.), AI and Computational Intelligence, Springer,
  Cham, Switzerland, to appear.
pdf file

[44] Miroslav Svitek, Niklas Winnewisser, Michael Beer, Olga Kosheleva,
  and Vladik Kreinovich, "Why Shapley Value and Its Generalizations
  Are Effective in Economics and Finance, Machine Learning, and
  Systems Engineering", In: Hien Thi Thu Nguyen, Hai Hong Phan, and
  Van Nam Huynh (eds.), Data Science in Finance and Accounting,
  Springer, Cham, Switzerland, to appear.
pdf file

[45] Tho M. Nguyen, Saeid Tizpaz-Niari, and Vladik Kreinovich, "How to
  Make Machine Learning Financial Recommendations More Fair:
  Theoretical Explanation of Empirical Results", In: Nguyen Ngoc
  Thach, Nguyen Duc Trung, Doan Thanh Ha, and Vladik Kreinovich
  (eds.), Partial Identification in Econometrics and Related Topics,
  Springer, Cham, Switzerland, 2024, pp. 147-152.
pdf file

[46] Saeid Tizpaz-Niari and Vladik Kreinovich, "How to Best Retrain a
  Neural Network If We Added One More Input Variable",
  In: Nguyen Hoang Phuong, Nguyen Thi Huyen Chau, and Vladik
  Kreinovich (eds.), Machine Learning and Other Soft Computing
  Techniques: Biomedical and Related Applications, Springer, Cham,
  Switzerland, 2024, pp. 23-38.
pdf file

[47] Julio C. Urenda, Orsolya Csiszar, Gabor Csiszar, Jozsef Dombi,
  Olga Kosheleva, Vladik Kreinovich, and Gyorgy Eigner, "Why
  Squashing Functions in Multi-Layer Neural Networks", Proceedings of
  the 2020 IEEE International Conference on Systems, Man, and
  Cybernetics SMC'2020, Toronto, Canada, October 11-14, 2020,
  pp. 296-300.
pdf file

[48] Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich, "Why Deep
  Learning Is Under-Determined? Why Usual Numerical Methods for
  Solving Partial Differential Equations Do Not Preserve Energy? The
  Answers May Be Related to Chevalley-Warning Theorem (and Thus to
  Fermat Last Theorem)", In: Martine Ceberio and Vladik Kreinovich
  (eds.), Uncertainty, Constraints, AI, and Decision Making,
  Springer, Cham, Switzerland, to appear.
pdf file

[49] Julio C. Urenda, Olga Kosheleva, and Vladik Kreinovich, "Fuzzy
  Techniques Explain the Effectiveness of ReLU Activation Function
  in Deep Learning", In: Patricia Melin and Oscar Castillo (eds.),
  Proceedings of the International Seminar on Computational
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[50] Julio C. Urenda and Vladik Kreinovich, "Why Rectified Linear
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[51] Min Xian, Olga Kosheleva, Martine Ceberio, and Vladik Kreinovich,
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[52] Sobita Alam, Arman Hossain, Samin Islam, Arin Rahman, and Vladik
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