A theoretical comparison of normalized gradient descent, Muon, and Adam-style updates on a tractable matrix optimization toy problem, showing finite-time convergence and why Muon's guarantees come out nicer than Adam's.
A rigorous derivation showing RoPE is almost optimally expressive under certain natural constraints, characterizing the allowable positional rotations with a free N-dimensional generalization and constructions for the rotation vectors.
Proof sketches and commentary for the IMO 2025 problems, written after doing the contest as a mock.
A practical overview of LLM inference quantization, from why memory bandwidth dominates local inference to GGUF, EXL, AWQ, GPTQ, KV-cache quants, and hardware tradeoffs.
A personal review of Math Academy from the perspective of a self-taught math-heavy user, focusing on its pedagogy, strengths, and annoyances.
A note on confidence calibration, why overconfidence and underconfidence both hurt decisions, and how to test and improve probabilistic judgement.
An intuition-first explanation of Simpson's paradox as a mismatch between local and global comparisons, followed by the algebra behind it.
A derivation-oriented guide to FFT implementations, moving from recursive Cooley-Tukey to iterative and in-place variants without explicit bit reversal.
A short practical note on why RSS feeds are useful and how to start using them to follow blogs, research feeds, and other updates.
A PSA about GCC 13 on Codeforces rejecting target pragmas, why the issue appears, and what changed in later GCC versions.