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Demo note. This note demonstrates what the SciDraft Hugo theme can do for academic and scientific publishing — for research institutions, researchers and students. Its content is demonstration material only: readers should ignore whether the demo content is correct. A conjecture is a statement believed on the weight of evidence but not proved, and the best-known one in this field concerns how loss falls as models grow. Fits are tight over the measured range, and the conjecture is that the same form continues past it. ...

Demo note. This note demonstrates what the SciDraft Hugo theme can do for academic and scientific publishing — for research institutions, researchers and students. Its content is demonstration material only: readers should ignore whether the demo content is correct. Multi-head attention reads better as shape bookkeeping than as prose: every symbol below is a tensor, and the shapes alone decide which products are legal, which is why papers about attention variants usually open with a notation table before showing a single result. ...

Demo note. This note demonstrates what the SciDraft Hugo theme can do for academic and scientific publishing — for research institutions, researchers and students. Its content is demonstration material only: readers should ignore whether the demo content is correct. Evaluating a system that uses tools needs its own body of sources: benchmarks for tool use, for long-context reasoning and for end-to-end knowledge work, together with the model reports those numbers are read against. This note keeps that literature in a bibliography of its own, separate from the prompting and fine-tuning lists used elsewhere on this site. ...

Demo note. This note demonstrates what the SciDraft Hugo theme can do for academic and scientific publishing — for research institutions, researchers and students. Its content is demonstration material only: readers should ignore whether the demo content is correct. Convexity is often described as the property that guarantees a unique optimum, and the statement is false as written: convex functions can have a whole interval of minimisers. The counterexample is a flat-bottomed function, convex everywhere and constant on a segment. ...

Demo note. This note demonstrates what the SciDraft Hugo theme can do for academic and scientific publishing — for research institutions, researchers and students. Its content is demonstration material only: readers should ignore whether the demo content is correct. A language model does not emit a token; it emits a probability for every token in the vocabulary, and something has to choose one. Choosing the single most probable token makes output repetitive, while sampling from the full distribution occasionally picks from its long tail of near-zero probabilities. Nucleus sampling keeps the smallest set of tokens whose combined probability reaches a threshold and samples only from those. ...