Technical explainers built the long way round: start at the smallest case you can hold in your head, count it upward with a pencil, and only then go and check whether the machine agrees. Every number here is measured, and every figure is one you can poke at.
Reinforcement learning on Qwen3.5-9B as a Cypher agent over a 650,000-node graph, rewarded only by executing its own queries. It gains on question shapes it never saw, gains on human questions only in answer form, and — measured by removing the hints — learns to get about half as much from a hint as before. Three pre-registered predictions; two failed.
The same recipe on Qwen3.8-27B through Fireworks' serverless training API: a 6.2-point gain on human-written questions against a same-route untrained control, all of it on questions the model could already sometimes answer.
Single tokens flipped GPT-3.5’s answers in 2024. Do they still flip a 2026 model’s? On a question Qwen is confident about, nothing moves. On a question it is torn about, six alternate tokens move the final answer — and being torn at the very first token turns out to predict it.
Why attention runs out of memory before it runs out of maths. Online softmax derived by hand from a 3×2 matrix, then the tiled kernel that never writes the N×N matrix down — ending in a measured benchmark, including the receipt I did not get.
A gentle on-ramp to the PyTorch “free normalization” work — derived from counting a 2×2 matrix upward, arriving at the roofline and the memory hierarchy that every article since has borrowed its vocabulary from.