Oleksii Kuchaiev

Artificial Intelligence and Math

Tue, 08 Sep 2026 00:00:06 -0700

On August 26, 2026, I had the pleasure of giving a talk at the Mathematics for the Real World 2026 conference, jointly organized by the International Centre for Mathematics in Ukraine (ICMU) and the Centre for Quantum Mathematics (QM) at the University of Southern Denmark.

The talk was about artificial intelligence and math, and how both fields help and enable each other. I really enjoyed the conversations with mathematicians at the conference afterwards.

Artificial Intelligence and Math

Modern frontier AI systems are, at their core, large mathematical objects brought to life by engineering — and the mathematics behind them is readily accessible to a mathematical audience. This talk consists of two parts. In the first, I will give a high-level overview of the mathematics underlying today’s frontier AI systems: the linear algebra and probability at the heart of transformer architectures, the optimization theory behind training at scale, and the statistical ideas driving techniques such as reinforcement learning from human feedback and from verifiable rewards. In the second part, I will survey recent milestones of AI in mathematics — from performance on olympiad problems and formal proof assistants to first contributions to research-level questions — and discuss where these systems still fail and why. I will conclude with practical thoughts on how mathematicians can use AI productively today: as a collaborator for exploration, literature search, and formalization, while remaining fully in control.

My slides:

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Banning open-source AI would be a historic mistake

Sun, 19 Jul 2026 00:00:06 -0700

Banning open-source AI would be a historic mistake — and a self-inflicted wound to U.S. AI leadership. I’ve been in this field long enough to remember when GPT-2 was called “too dangerous to release.” That didn’t age well — and it drew heavy criticism from researchers even at the time.

Today, we are seeing a repeat of that same impulse. While “better safe than sorry” is a fine mantra, the mechanics of safety matter. The logical conclusion is this: Open AI is safer AI.

“Why hand everyone frontier capabilities?”

The risk from bad actors is real. But we don’t secure systems by hiding how they work. The field that’s lived with this tension longest — cybersecurity — runs on open source. Openness is what makes systems auditable, and auditable is what makes them defensible. Furthermore, the most recent security incident at Huggingface demonstrates the dangers of not having access to the models with frontier capabilities, the ones that you can deploy within your own infrastructure.

“Open-source AI will let terrorists build bioweapons.”

We’ve had the playbook since 1975. At Asilomar Conference, scientists facing the same fear over recombinant DNA didn’t ban the knowledge — they built containment tiers and paused only the riskiest work. Governing use always beats restricting knowledge. The hard chokepoints — DNA synthesis, materials, wet-lab skill — still gate any AI-designed threat.

“Open-source AI isn’t really open.”

Openness is a spectrum. With Nemotron we push toward the far end: open weights, code, and data. For a small lab or university, access to open weights beats API-only access. And weights + code + data beat weights alone and enable entirely new research routes. Particularly around safety and cybersecurity. Openness is also what lets outsiders audit and red team these models. That’s a safety feature, not a bug.

“The biggest real danger in AI?”

In my opinion, it is one or two companies controlling all of it. We’ve already watched providers quietly clip capabilities and bake in censorship that shifts by country of origin. Variety and choice are the fix. Over-restriction is already rampant. Case in point: Fable 5 refused to proofread this a twitter-friendly variant of this post and fell back to Opus 4.8.

A New paradigm shift: From Scalable Imitation Learning to Scalable Exploration Learning

Sun, 13 Apr 2025 00:00:06 -0700

We are likely at the start of a significant paradigm shift in artificial intelligence (AI), comparable to how AlexNet marked the transformative arrival of deep learning in 2012 [1].

To frame this shift, consider that aside from supervised and unsupervised learning, AI research can can be broadly divided into two additional categories, which often overlap in contemporary AI systems:

Imitation Learning (IL): A technique in AI where an agent learns to perform tasks by observing and mimicking the actions of an expert or human demonstrator.
Exploration learning (EL): A learning strategy in AI where an agent independently discovers knowledge or skills by actively experimenting, interacting, and gathering information from its environment, rather than relying on provided demonstrations.

Both imitation learning and exploration learning existed well before 2012. However, the switch to deep learning, significantly accelerated by Transformers in 2017 [2], provided a scalable, generalizable approach for solving IL problems. This generality is demonstrated impressively in modern large language models (LLMs) such as GPT-4 and GPT-4.5 [3], which have been trained on vast portions of the Internet and fine-tuned to imitate an imaginary “assistant”.

Today, we are witnessing the emergence of a similar scalable framework for exploration learning. This new approach combines strong foundation models with extensive multi-stage reinforcement learning (RL), where feedback comes directly from the environment or “reality” itself—examples include mathematical verifiers, code unit-tests, and empirical validation in scientific problem-solving. Models such as OpenAI’s O1/O3/O4, DeepSeek-R1 [4], and Llama-Nemotron-Ultra [5] are examples of this emerging trend.

The reason this is huge is that unlike IL, EL is likely to lead to a (general) super-human intelligence. This potential has already been demonstrated within specific domains such as chess, Go [6], complex computer games [7], protein folding [8], and certain areas of geometry [9]. In each of these areas, success followed a remarkably consistent recipe: deep neural network heuristics combined with exploration (search or self-play) and precise, non-human-derived feedback. When applied to reasoning-capable large language models (LLMs), this recipe is becoming increasingly generalizable, opening pathways to breakthroughs across numerous domains.

Like in 2012 with DL, the exact recipe will surely evolve many times, and many ideas and methods are yet to be discovered/published. However, I believe the general approach will rapidly scale from here. These models essentially have solved math today to a level above 99.99% of humans, coding will “fall” next (this year). Then areas where reward acquisition is not instantaneous but still within minutes, then areas where getting reward takes longer, etc.

References

[1] Krizhevsky, Alex, Ilya Sutskever, and Geoffrey E. Hinton. “Imagenet classification with deep convolutional neural networks.” Advances in neural information processing systems 25 (2012).

[2] Vaswani, Ashish, et al. “Attention is all you need.” Advances in neural information processing systems 30 (2017).

[3] Ouyang, Long, et al. “Training language models to follow instructions with human feedback.” Advances in neural information processing systems 35 (2022): 27730-27744.

[4] Guo, Daya, et al. “Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning.” arXiv preprint arXiv:2501.12948 (2025).

[5] https://huggingface.co/nvidia/Llama-3_1-Nemotron-Ultra-253B-v1

[6] Silver, David, et al. “Mastering the game of go without human knowledge.” nature 550.7676 (2017): 354-359.

[7] Berner, Christopher, et al. “Dota 2 with large scale deep reinforcement learning.” arXiv preprint arXiv:1912.06680 (2019).

[8] Jumper, John, et al. “Highly accurate protein structure prediction with AlphaFold.” nature 596.7873 (2021): 583-589

[9] Chervonyi, Yuri, et al. “Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2.” arXiv preprint arXiv:2502.03544 (2025).

How to get a machine learning internship

Sat, 29 Feb 2020 23:00:06 -0800

I am frequently asked this question - “How to get a machine learning / deep learning internship?” Because the answer I give is somewhat standard and rather long I’ve decided to write this post. I hope that it will help someone I don’t know to get an internship in this exciting field.

Why you might find my advice helpful?

I have been working in machine learning related roles for several years at Microsoft, Apple and, currently, NVIDIA. At Apple and NVIDIA combined, I have interviewed hundreds of candidates and have mentored several interns. Some students I know even got ML internships by following the advice below :)

Why you might find my advice not so useful?

Like I mentioned above, my experience is at the large tech companies. If you are looking for a startup experience, I guess, some things will be different. However, I’m pretty sure that the fundamentals remain the same. Also, I am writing this in 2020 - so if you are reading this several years later some things likely have changed.

Fundamentals

The fundamental qualifications you will need are:

Being a strong engineer/programmer
Understanding of machine learning / deep learning

Point number (1) above is super important and must not be overlooked. You must have strong computer science fundamentals and hands-on experience with Python and, preferably, C++ as well.

Formally, internships (not just ML/DL) will typically have some requirements such that you should be a university student before and after the internship.

How to prepare

You should make yourself a stronger programmer and improve your understanding of deep learning.

Start by making the best use of the courses and resources offered at your school/university. For example, does your program offer the following fundamentals: linear algebra, calculus, optimization, algorithms/data structures, probability, statistics, math logic, programming languages, etc.? If yes - do take those courses and make sure you are learning a lot from them. If you are luckier, and your program has deep learning courses, of course, take them as well. On our team (applied research), for example, we look for people who took at least 2+ deep learning specific university courses (typically fundamentals plus some more focused courses, such as NLP).

An incredibly useful resource these days are MOOCs. When I look at someone’s resume I actually don’t care where they took their deep learning courses: at Stanford/CMU/MIT or on Coursera/Udacity. A lot of my colleagues have similar opinion.

Here is a tiny sample list of MOOC courses which will make you a stronger candidate for ML/DL internship:

You have to take those courses/specializations “for real” - do all the homework and, ideally, earn their certifications.

There are a lot of great blogpost by various people and teams which are can be very useful while preparing for the interview. For example, have a look at Sebatian Ruder’s blogposts on Optimization and NLP ImageNet Moment.

Like I mentioned above, you also have to be a good programmer. If you don’t have strong CS background - MOOCs can help you there as well! There are plenty of courses on algorithms, data structure and programming languages (take Python). However, the most important thing you should do is practice solving programming interview questions. Practice solving problems on sites like GeeksForGeek and LeetCode. You should understand what time and space complexity is and when and how to use particular data structures. You will almost certainly get a coding question during your interview. So make sure you are prepared. I think nowadays “puzzle” or “trick” questions are asked less often and the question you’ll get will most likely test if you understand how and when to use certain data-structures and/or some algorithmic techniques (greedy method, sorting, dynamic programming). A former colleague of mine, Chip Huyen is working on a book about machine learning interviews - check it out.

It is very important to practice. Pick a deep learning framework - I recommend PyTorch but Tensorflow 2.x might be a good option as well and start training and implementing models. To train anything more serious than a tiny toy model, you will need access to the specialized hardware (consumer CPU’s aren’t great at deep learning in general).

Google Colaboratory is an excellent resource. It lets you play with GPUs and TPUs right from your browser! It is free and they recently started offering a paid version which gives you more reliable access to GPUs.
The most flexible option for development is to have a NVIDIA GPU in your desktop (disclaimer: I work at NVIDIA). A good gaming card (Pascal or, better, Turing-based) will get you pretty far.
AWS or Azure with GPU instances is another option. But those are not very convenient for hacking around - those are great choices to train already debugged model and for production.

How to apply

Three best routes (by far) are:

To be recommended by someone who already works there.
Have your advisor recommend you to an industry lab with which he has some kind of collaboration.
Apply at the company’s booth during one of the top deep learning conference.

If you are lucky to be a student at one of the top US universities, another good route is to attend and apply during a career fair at your school (this is how I got into Microsoft). A lot of companies attend career fairs of top universities every year, if not every quarter.

Another option is to simply find a job posting on company’s website and apply there. Obviously, this is the route with the lowest probability of getting an interview. It is still realistic but do have a look at the “How to stand out from the crowd” section below.

How to stand out from the crowd

There are several great ways to stand out from the crowd:

Share your projects on GitHub. Something as simple as re-implementing common models/algorithms or class projects you did is already good. A personal hobby project is better. Try contributing to bigger open-source projects as well. We had interns whom we contacted first after seeing their PRs to one of our projects. When I see someone’s resume, I always look for a GitHub profile link and visit it.
Participate in programming and data science competitions. When you are a university student it is a great time to try yourself at some programming, math or machine learning contests. ICPC, TopCoder Open, Kaggle, ImagineCup, etc. There might be some specific to your school or field of research - do check them out! You don’t have to be the best in the world in any of them. Any achievement is worth mentioning on your resume. Olympiads in Math and Physics are also a good way to stand out. Also, as a former Imagine Cup competitor, I’d like to add that preparation and experience of competition itself is very much worth the effort.
Publications. This is more of a requirement if you are a Ph.D. student. Having published a deep learning related paper is certainly a plus. Especially, at top venues such as NeurIPS, ICLR, ICML, CVPR, etc. Even if it is a workshop poster - it is certainly a plus, especially if it is related to the area of research of the lab you are applying to.

The process

The process for internship is pretty simple (with small variations from company to company). After you applied, a recruiter may contact you for an “exploratory” call. After that, there are typically two technical phone screens during which you will code and answer machine learning related questions. The process may vary a little if you’ve applied at a conference or career fair in which case an engineer might do a technical screen with you sooner and/or in person. If you are a Ph.D. student, you might be asked to come in and do a presentation about your research.

Some myths about getting ML/DL internships

One has to be a Ph.D. student to get a deep learning internship

In many cases being a graduate student is preferable and, for some roles (especially at research labs), being a Ph.D. student can be a requirement. However, this is not a requirement across the field and there are many (even research) teams who will be happy to welcome a strong undergrad for an internship. On our team we had undergrad interns who during their internship produced and published research at top conferences.

You have to be a student at a top CS university

This certainly helps, but it is absolutely not a requirement. Many (myself included) will accept MOOC-based deep learning courses in lieu of similar courses at top school.

You have to be in US to apply to US-based internship

This is a very common misconception. You typically can apply for internships in top companies like NVIDIA, Apple, Google, Microsoft, etc. from anywhere in the world, even if the job description doesn’t explicitly mentions that international candidates can apply. Also, keep in mind, that big companies might have offices with interesting internship positions outside US as well.

Your interviewer wants you to fail

This is a weird one. On the contrary - your interviewer wants you to succeed. And it is quite disappointing when the candidate is unable to answer questions.

TL;DR;

Take Deep Learning and Machine Learning courses at your school and MOOCs such as Coursera. Have a GitHub presence and contribute to (or create) open-source projects. Participate in programming and machine learning competitions. Practice solving coding problems (nothing too fancy). Apply!

My interview on mentorstudents.org

Thu, 20 Feb 2020 23:00:06 -0800

There is a very interesting project - “mentorstudents.org”. It tries to help students get started on their career paths by connecting them with and interviewing different people who are already in the industry and is willing to share some advice.

I’m happy to have been interviewed by them as well and here is a link to my interview. Btw, the results of automatic speech recognition (ASR) on my interview are hilarious :). I especially like that “my major was a brightness magics”. This is just a reminder that ASR still have a long way to go especially for heavily accented speech (like mine).

NeMo talk at MLSys@NeurIPS Workshop

Thu, 12 Dec 2019 23:00:06 -0800

Recently, I gave a short talk about NeMo at MLSys workshop at NeurIPS 2019 in Vancouver, Canada. NeMo is the project I actively work on at NVIDIA. It is open-source and we welcome external contributors.

Get it from github.
Slides Live link