Dmitry Vaintrob
researcher · Principles of Intelligence
I work on the mathematical foundations of deep learning, with a focus on AI safety and interpretability: how neural networks represent and compute, and what statistical physics and Bayesian learning theory say about generalization.
I'm a researcher at Principles of Intelligence; before that, a pure mathematician (more here).
Selected research
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Width-robust learnability in mean-field Bayesian neural networks
A family of Boolean-cube targets is learnable at infinite width iff it is learnable at polynomial width, iff its reduced entropy is polynomially bounded.
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Toward a mathematical framework for computation in superposition
How networks compute, not merely store, many more sparse features than they have neurons.
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A tale of three theories: sparsity, frustration, and statistical field theory
Feature sparsity and frustration in neural networks, via statistical field theory.
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The subset parity learning problem and the memorization–generalization spectrum
Learning coefficients, tempering, and singular learning theory in realistic networks.
Mean field theory
An introductory series on mean field theory for neural networks, with Lauren Greenspan — plus related resources and interactive tools hosted here.
Other writing
Mathematics
- Formality of little disks and algebraic geometry — an algebro-geometric proof of formality of the (framed) little disks operad.
- Moduli of framed formal curves.
- Categorical logarithmic Hodge theory.
- A bound on the Hodge filtration of the de Rham cohomology of supervarieties (with Alexander Polishchuk).
- Localization for CS manifolds and volume of homogeneous superspaces (with Vera Serganova).
- The Deligne–Mumford operad as a trivialization of the circle action (with Alexandru Oancea).
- The Gauss–Manin connection on periodic cyclic homology (Selecta Mathematica; with Alexander Petrov and Vadim Vologodsky).
- Coherent-constructible correspondences and log-perfectoid mirror symmetry. See also an older draft with some arguments in simpler form.
- Mirror symmetry on the Bruhat–Tits building and the K-theory of a p-adic group — Ph.D. thesis.
- On the surjectivity of Galois representations associated to elliptic curves over number fields (Bull. LMS; with Eric Larson).
- Determinants of subquotients of Galois representations associated to abelian varieties (J. Inst. Math. Jussieu; with Eric Larson).
- The string topology BV algebra, Hochschild cohomology and the Goldman bracket on surfaces.
- Introduction to representation theory (AMS; with Pavel Etingof et al.).