nor's blog
An elementary finite-time account of why wide networks trained on the same minibatches develop matching local loss fluctuations, and how width and batch size control initialization, data, and interaction noise, with implications on scaling.
A short note on Adam's update size, the coupling of beta1 and beta2, bias correction, epsilon, and how these relate to stability and warmup.
A refinement of Sawin's explicit unit-distance lower bound, mostly by GPT 5.5 Pro, for the Erdős problem recently solved by OpenAI's internal model.
A short note on why RMS-matching Muon to AdamW can break width transfer, causing either undertraining or instability depending on scale.
A research note on what breaks in long-context attention, deriving a logit scaling, with QK-norm, hybrid/local attention, gating, and small-scale experiments.
An intuition-building tour of dynamical systems, using canonical examples to connect feedback, thresholds, coupling, noise, reinforcement, spatial structure, and phase transitions.
A writeup of porting the modded nanoGPT speedrun to pure JAX on TPU v6e, including hardware bottlenecks, bugs, optimizations, and open performance questions.
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.
A near-optimal floating-point binary search template that searches representable values via bit-casts instead of hard-coded iteration counts.
A C++ template for recursive DP with automatic memoization, built from recursive lambdas, generalized hashing, and policy-based hash tables.
An elementary way to solve recurrences by changing variables until simpler structure appears, recovering characteristic-equation intuition without heavy machinery.
A practical introduction to the Akra-Bazzi theorem as a way to analyze divide-and-conquer recurrences with unequal splits, floors, and offsets.
A tutorial on lambdas, from lambda-calculus context and C++ closure mechanics to recursion, stateful patterns, STL use, and competitive-programming examples.
A note on a Euclidean GCD variant that greedily reduces the remainder, with benchmarks and an iteration-count improvement.
A discussion and generalization of post-increment through std::exchange, with examples in recurrences, GCD code, lazy updates, moves, locks, and iterators.
The Boost C++ library and examples of what it would give competitive programmers beyond the standard library.
A short PSA on increasing stack limits before MHC, with commands, compiler flags, and platform caveats.
A tour of Floyd-Warshall as an instance of aggregating over graph paths, leading to transitive closure, Kleene algebras, and the algebraic path problem.
A user-written editorial for Codeforces Round 513, which did not have an editorial before.
A beginner guide to inequalities involving floors and ceilings, with algebraic rules, examples, identities, and programming-language caveats.
On preserving Google Hash Code problems and infrastructure before the contest archive disappears.
A personal model of learning as building and querying a knowledge graph, with advice on theory, problem solving, creativity, feedback, and overfitting.
Suggestions for improving the Codeforces Catalog.
A collection of modern C++ tricks that make code succinct and clean, from negative indexing and ranges to lambdas and compact utilities.
A guide to permutations through orderings, cycles, and composition, with pointers to common competitive-programming applications.
Notes from testing and preparing programming contests.
A tutorial on greedoids as a framework for understanding when greedy-style reasoning works, with examples from matroids, antimatroids, and related structures.
An introduction to probability, conditional expectation, martingales, and stopping times, with math and competitive-programming examples.
A detailed competitive-programming setup guide for Vim, Make, and GDB, covering both onsite contest constraints and online practice.
A short meta post asking for underappreciated competitive-programming ideas and techniques worth writing about.
A discussion of using C on Codeforces.
A tutorial on Catalan numbers and uniform random balanced bracket generation, building bijections and generators from first principles.
The editorial and behind-the-scenes notes for InterviewForces Contest #1, including solution ideas, testing stories, and bonus problems.
The announcement for InterviewForces Contest #1, a Codeforces-style meme contest with nine problems.
An introduction to Mobius inversion through incidence algebras of posets, with inclusion-exclusion, subset transforms, number theory, and finite differences as examples.
A beginner-friendly guide to binary search as partition-point search, including invariants, variants, language APIs, and optimizations.
An explanation of GCC optimization and target pragmas, what common fake pragmas do not do, and when these flags help or hurt.
A bunch of DFS and BFS ways to traverse a complement graph efficiently, including linear-time BFS and a DSU-style trick for the DFS case.