'Science Combines Work, Social Connection, and a Spirit of Adventure'

Marina Sheshukova chose research in mathematical statistics and probability theory over a career in music. In this interview with the HSE Young Scientists project, she discusses Markov chains, multi-armed bandits, and her dog named after the mathematician Camille Jordan.

How I Started in Science

It all began before I even started school. My grandmother was a mathematics teacher, and whenever I visited her, she would give me logic puzzles to solve—which I absolutely loved. At school, this interest grew into a more serious hobby: I began practicing olympiad mathematics and attending online math clubs. My school in the city of Volzhsky, Volgograd Region, offered rigorous training, and nearly all of my classmates went on to study in Moscow or St Petersburg. I chose HSE University and was admitted based on my olympiad results. In my second year, Sergey Samsonov, who taught our mathematical analysis seminars, invited me to join his HDI Lab and try doing research. I decided to give it a go—and have stayed there ever since.

The Focus of My Research

My research centres on the mathematical foundations of machine learning algorithms. I study how modern optimisation methods work—those used to train neural networks and other models. These algorithms often exhibit random behaviour, and my goal is to understand how to predict their dynamics, assess errors, and make reliable forecasts. Essentially, I investigate the fundamental mathematical properties of these methods so they can be used more effectively in the future.

My First Scientific Assignment

At first, it was beyond my capabilities. I was finishing my second year of bachelor's studies and had not yet learned stochastic analysis. But I came to the laboratory and said that I wanted to do some programming. I was given an assignment based on a research paper about known diffusion models and score matching. I started reading the literature but quickly realised that I lacked the foundational knowledge in the field.

That summer, I attended a session at the Sirius Educational Centre, where we were expected to develop and present a project within a month. That was where I completed my first mini-research project. The assignment was to use well-known sampling methods to try to improve samples generated by a generative adversarial network (GAN). It was more of a programming task, and to handle it, I had to learn a great deal. Another girl and I worked on the project together, and we ended up winning the project competition at that session.

After that, I returned to the laboratory and said that I wanted to try working on more theoretical projects. I realised that I was more interested not just in implementing algorithms, but in understanding their fundamental properties. Programming doesn’t necessarily involve research tasks—your goal is mainly to run experiments and try different approaches. It’s a creative activity, too, but it didn’t quite feel like my path then. Now, however, I enjoy alternating between the two, because it’s difficult to focus on just one type of work all the time.

What My Term Papers Were About

In my bachelor’s thesis, I established Rosenthal- and Bernstein-type inequalities for Markov chains with the correct variance in the leading term. It was a substantial piece of theoretical work that required precise estimates and detailed mathematical analysis.

While in my master's programme, I began working on stochastic approximation. My colleagues had published a paper on a method that improves the convergence rate of stochastic gradient descent, and we proposed an algorithm that achieves the same order of convergence but with a much simpler approach. The resulting paper, which I co-authored with Alexey Naumov, Sergey Samsonov, and several others at the laboratory, was accepted to the ICLR 2025 conference.

My Dream

To leave a mark on science—not simply by publishing many papers, but by contributing something genuinely useful to future generations of researchers, helping them move their fields forward. I may never know whether this dream comes true, because sometimes results only become relevant decades later.

This is how I hope to realise myself and what I aspire to achieve. And on a more everyday level, I would simply like to continue enjoying this work as much as I do now.

My Other Interests

In addition to theoretical research, I work on projects focused on recommendation systems and lead several student groups. I don’t write much code myself anymore, but I help students understand the underlying methods and concepts.

When you visit Kinopoisk or Netflix, you see suggestions for other films or TV shows you might like—this is a recommendation system. There are many potential algorithms these systems can be based on. It is a popular and rapidly growing field.

For example, there are algorithms designed for multi-armed bandit problems. Unlike sequential recommendation algorithms, which employ a user’s entire history to make the next prediction, bandit algorithms assume that each event is independent and base their predictions solely on the user’s current context.

The context can vary depending on the situation. It might be something simple, like a person’s gender, age, or other basic characteristics, or something more complex. Our goal is to explore how, based on the data already collected, we can determine which of two contextual bandit–based algorithms performs better. This is not easy, because recommendation systems often have massive catalogues of items—books, films, products—which creates unique methodological challenges and makes the task a truly interesting problem to solve.

Whether I Have the Ambition to Solve a Millennium Problem

Devoting my life to trying to solve a problem, only to perhaps fail, would not bring me satisfaction. I enjoy thinking deeply about problems, but if no one has solved a particular problem in a thousand years, its solution is likely far from trivial. I prefer to achieve tangible results—writing something, having it published, and knowing that it has been recognised as valuable.

If I Hadn't Become a Scientist

As a child, I studied dance, pop and jazz singing, and completed a violin programme at music school. I began learning singing at the age of five and continued until 11th grade, practicing and performing in concerts and competitions. I sang both in a group and as a soloist. At first, our band was called Thumbelinas, but as we grew older, we renamed it Adagio.

Until seventh grade, I even considered pursuing an acting career. Then I switched to a school with a focus on mathematics and developed an interest in math olympiads. I have kept creativity as a personal hobby.

Who I Would Like to Meet

I’ve always wanted to attend a Christina Aguilera concert because I admire her vocal skills. I loved the movie Burlesque and all its songs—they have a slightly jazzy style but also incredible drive. I even performed one of the songs in a competition and won the grand prize. Nowadays, this passion isn’t as strong, but even today, at karaoke, I always sing ‘Something's Got a Hold On Me,’ my favourite song performed by Aguilera.

A Typical Day for Me

I have a corgi named Jordan, so my day begins with taking him for a walk. This is a morning ritual for my husband and me: we go outside, breathe in the fresh air, and gradually wake up.

My husband teaches children olympiad mathematics. We named our dog after the French mathematician Camille Jordan, who developed the concept of the Jordan measure. At home, we also call our corgi Chowder, because he loves his food a little too much.

Since the end of last year, I have been working not only in the laboratory but also teaching and leading seminars on mathematical statistics and Markov chains.

I practice pole fitness twice a week as a way to relax and shift from mental to physical activity. In 2021, this sport was officially recognised in Russia. It is similar to gymnastics, as it demands strength, flexibility, agility, and coordination. Some elements require significant muscle strength to maintain proper positions.

Why I Chose Pole Sports

I don’t like doing the same thing for a long time. I tried going to the gym but quickly got bored, as workouts there consist of repetitive sets of the same exercises. In pole sports, however, there are countless elements, and the training programme is always different. You can practice the splits, or the flag—a trick where you hold onto the pole using only your hands.

Whether I Have Experienced Burnout

Yes. It seems to me that in today’s world, almost no one is completely immune to burnout. Life in Moscow moves at a frenzied pace, and in general, if you don’t pause and take care of yourself while striving to grow, your goals can eventually exceed your strength and energy. For me, this hasn’t led to severe depression—I simply recognise when I need to rest.

What I Enjoy Doing Besides Science and Pole Sports

I taught myself to play the guitar and sometimes enjoy performing classics of Russian rock from bands like Korol i Shut, Splean, and Kino. I also enjoy colouring by numbers. In general, I’m drawn to any kind of creative activity.

What I Have Read Recently

I’m a Harry Potter fan, but I belong to the generation that grew up with the film series. For a long time, I only knew the universe through the films, but I had a strong desire to read the original books. My husband gave me the complete set for my birthday, and I devoured it in just two or three months. Every evening, I would sit down to read and couldn’t tear myself away.

As it turned out, the films leave out so much! This year, during our laboratory's retreat, I organised a Harry Potter quiz for the staff. I created it while I still remembered all the tricky details from both the books and the films.

My Favourite Harry Potter Character

Sirius Black. I always felt sorry for Harry who was growing up in a family where he was unloved. Everything changed when Sirius appeared—suddenly, Harry had a close friend he could confide in. Even when Ron turned away, Sirius was there for Harry, offering support and companionship.

Advice for Aspiring Scientists

The life of an early-career scientist can be full of stressful moments, so it’s important to find activities that help you relax and recharge emotionally. Equally important is choosing tasks that genuinely interest you. Science is a long journey, driven primarily by sincere curiosity. If you are truly interested in your work and eager to understand things more deeply, you will grow as a researcher. Everything else—skills, experience, and recognition—will come with time.

My Favourite Place in Moscow

Timiryazevsky Park, which is close to my home. I enjoy strolling there alone or walking my dog—perhaps I simply enjoy being in this urban forest. I also love spending summers at our summer home in the Tver Region. While the property doesn’t have a vegetable garden, it is surrounded by pines and birches. Nature, with its calm and quiet, brings strength and inner peace. I especially enjoy picking blueberries in the forest; it’s a meditative activity that allows me to forget about my tasks and simply live in the moment.