Blog
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Data scaling works for equilibrium tasks like AlphaFold and hits a structural ceiling at per-trajectory prediction of chaotic systems.
Scientific ML Weather
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Dynamic batching switches kernels, the switch reorders floating-point summation, and the resulting drift turns RLVR training off-policy.
LLM Systems
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The adjoint of the Koopman operator on a stochastic Markov process, when it is normal, and why non-normality makes the SVD the natural object.
Operator theory Scientific ML
- Spectral theorem and the operator SVD 4 parts
A four-part construction of the spectral theorem, from finite dimensions to general bounded operators, and the operator SVD it delivers.
- Spectral Theorem I: adjoint, normality, and the finite-dimensional case
- Spectral Theorem II: compact operators via the variational principle
- Spectral Theorem III: general bounded operators via functional calculus
- Operator SVD: from spectral theorem to polar form to singular values
Operator theory
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The library default for solar radiation was a different physical quantity than GraphCast's training data. How I found that and rebuilt the right one.
Weather Systems
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Four design decisions in a single-node ETL for terabyte-scale weather data, and the alternatives I rejected.
Systems Weather