Hiring nowLearning theory and statistical machine learning

Learning Theory Researcher

Also called Computational Learning Theorist

A Learning Theory Researcher works out what learning algorithms can and cannot do, and proves it. For an AI company, that means firmer ground for decisions about data, model size and what a system can safely be expected to deliver.

What they do

The work starts with a question about an algorithm: when does it generalise, how much data does it need, where does it fail? The researcher turns that into a precise statement, picks assumptions, and tries to prove it. Often the proof fails, and the failure points to a counterexample or a weaker claim. They read recent papers, run small experiments in Python or PyTorch to test whether a bound matches behaviour, and write results up clearly. They also explain to engineers and researchers what a result does and does not mean in practice.

What a strong hire delivers

In the first months, a strong hire delivers a small set of clean, correct results tied to a question the company actually cares about. That might be a generalisation bound for a training setup, a counterexample that retires a shaky assumption, or a clear note on how much data a task needs. They also leave colleagues better able to judge which claims are worth trusting.

How you can tell they are good

Ask them to walk through a result they proved, including the assumptions and where those assumptions break. Strong people state the theorem simply, explain why each condition is needed, and volunteer a counterexample. Ask how they would test a bound empirically. Be wary of vague claims, proofs that hide behind notation, or assumptions chosen only to make the maths work.

Why it is hard to fill

The title varies. People call themselves learning theorists, statisticians, theoretical computer scientists or mathematicians, and few use the exact title you advertise. True depth in sample complexity and generalisation is rare, and most of those people are in academia and happy there. Many theorists also cannot run deep learning experiments, while many practitioners cannot prove anything. The mix is the scarce part.

Where to find them

Look in university groups in theoretical computer science, statistics and mathematics, especially postdoctoral researchers and recent PhD graduates working on statistical learning, online learning or optimisation. Some sit in the theory teams of frontier labs and large industrial research groups. Others come from quantitative research, or from statistics departments with a strong machine learning bent. Check their papers, not their job titles.

Indicative pay

Not enough published evidence yet to give a fair range for this role, which is common for work this new. We benchmark it for you as part of a search.

Interview questions for a Learning Theory Researcher

  1. Tell us about a generalisation result you proved. What were the assumptions and which one mattered most?

    A strong answer states the result plainly, names the assumptions and explains which were essential and why. They should say what happens when it fails. Worry if they cannot separate technical convenience from real constraints.

  2. How would you decide whether a sample complexity bound is useful for our training setup?

    Good answers compare assumptions with the real data and model, check tightness, and consider constants and scale. They might propose a small experiment. Worry if they treat any valid bound as useful, or dismiss theory entirely.

4 more questions, with what a strong answer covers, are in the Role Kit.

Job description you can post

We are looking for a Learning Theory Researcher to establish what our learning algorithms can and cannot do. You will turn open questions about generalisation and data needs into precise statements, prove them or disprove them, and help the team act on the results.

What you will do

  • Formulate research questions about learning and generalisation as precise theorem statements
  • Write proofs and construct counterexamples
  • Derive sample complexity and generalisation bounds for our methods
  • Run small experiments in Python and PyTorch to test whether theory matches behaviour
  • Review recent literature and judge which results apply to our work
  • Explain results and their limits clearly to researchers and engineers

What you will bring

  • Published or documented proofs in statistical learning theory or a closely related area
  • Strong command of probability and statistics
  • Solid linear algebra and optimisation
  • Clear writing that states assumptions explicitly
  • Working ability to implement experiments with Python, scikit-learn or PyTorch
  • Sound judgement about when assumptions are realistic

Nice to have

  • Experience with deep learning theory
  • Experience designing experiments to test theoretical claims
  • Background in online learning or optimisation theory

Free to use and adapt. If it saves you time, a link back to this page is appreciated.

Skills that matter

  • Probability and statisticsAdvancedQuantify variability and statistical evidence
  • Linear algebra and optimisationAdvancedReason about matrix operations and objective functions
  • Experimental designWorkingChoose comparisons that identify credible effects
  • Deep learningWorkingBuild and diagnose trainable neural models

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How we wrote this

Role definitions are our own editorial work, checked against occupational classifications, standards, research and employer pages. Titles vary by company, and this is a description of the work, not a job advert.

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