AI Safety and Alignment, Foundational Machine Learning Research · Almaty, Kazakhstan
My primary research focus is mechanistic interpretability of neural networks, with an emphasis on understanding how internal representations evolve during training. In particular, I study the emergence and breakdown of monosemantic features, and the transition toward polysemantic representations in large-scale models.
I aim to develop rigorous analytical tools for dissecting these transitions, drawing on spectral methods and operator-theoretic techniques from noncommutative harmonic analysis. The goal is to move beyond empirical interpretability and toward a mathematically grounded theory of representation structure.
As part of this, I use log-signature representations of sequences as a structured probe for studying how transformers compress and organise contextual information. Unlike standard embeddings, path signatures provide a graded algebraic basis, allowing us to isolate contributions from different interaction orders. This makes it possible to analyse how neural representations transition from high-order, entangled (polysemantic) regimes toward lower-order, structured (monosemantic) features under architectural or training constraints.
This perspective connects sequence modelling with tools from noncommutative harmonic analysis, where operator structure and spectral behaviour govern how information is distributed and transformed.
At HighSky, I work on transformer architectures for tabular data and synthetic pre-training via Bayesian priors and structural causal models. This serves as a controlled setting for probing representation learning dynamics and testing hypotheses about generalisation and feature structure in heterogeneous data regimes.
More broadly, I am interested in closing the gap between what we can train and what we can understand, treating interpretability as a scientific problem where mathematical structure — rather than heuristics — plays a central role.
Note: Log-signatures as structured compression and probes of representation geometry (March 2026)
12 peer-reviewed articles, 2 preprints; 220+ citations; h-index 7 (Google Scholar, 2026). This list follows my Global Talent visa CV; for live metrics see Google Scholar.
| 1. |
Hörmander–Mikhlin type theorem on non-commutative spaces
arXiv preprint arXiv:2503.01240
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| 2. |
Norms of certain functions of a distinguished Laplacian on the ax+b groups
Mathematische Zeitschrift, 302(4):2327–2352
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| 3. |
Contractions of group representations via geometric quantization
Letters in Mathematical Physics, 110(1):43–59
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| 4. |
Lp–Lq multipliers on locally compact groups
Journal of Functional Analysis, 278(3):108324
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| 5. |
Re-expansions on compact Lie groups
Analysis and Mathematical Physics, 10(3):33
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| 6. |
Hardy–Littlewood, Hausdorff–Young–Paley inequalities, and Lp–Lq Fourier multipliers on compact homogeneous manifolds
Journal of Mathematical Analysis and Applications, 479(2):1519–1548
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| 7. |
Smooth dense subalgebras and Fourier multipliers on compact quantum groups
Communications in Mathematical Physics, 362(3):761–799
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| 8. |
Net spaces on lattices, Hardy–Littlewood type inequalities, and their converses
Eurasian Mathematical Journal, 8(3):10–27
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| 9. |
Hausdorff–Young–Paley inequalities and Lp–Lq Fourier multipliers on locally compact groups
arXiv preprint arXiv:1510.06321
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| 10. |
Fourier multipliers and group von Neumann algebras
Comptes Rendus Mathématique, 354(8):766–770
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| 11. |
Hardy–Littlewood–Paley-type inequalities on compact Lie groups
Matematicheskie Zametki, 100(2):287–290
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| 12. |
Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2)
Studia Mathematica, 234(1):1–29
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| 13. |
Well-posed solvability of functional-differential equations with unbounded operator coefficients
Differential Equations, 50(9):1161–1172
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| 14. |
On an inequality for the non-increasing rearrangement of a function
Eurasian Mathematical Journal, no. 3, 34–36
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Prof. Michael Ruzhansky (Imperial / Ghent); Prof. Shahn Majid (QMUL); Prof. Yulia Kuznetsova (Franche-Comté); Prof. Terry Lyons FRS (Oxford); Dr Alexis Arnaudon (Imperial); Prof. Fedor Sukochev (UNSW, planned).