https://www.zhumengyao.com/scidraft/tags/lemma/Recent content in Lemma on SciDraft | A Hugo ThemeHugoenMon, 21 Sep 2026 12:02:00 +0900https://www.zhumengyao.com/scidraft/notes/demo-note-lemma-logsumexp/Mon, 21 Sep 2026 12:02:00 +0900https://www.zhumengyao.com/scidraft/notes/demo-note-lemma-logsumexp/<p><strong>Demo note.</strong> This note demonstrates what the <strong>SciDraft</strong> 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.</p> <p>The log-partition function appears wherever a normalising constant is needed, and it is trapped between two elementary bounds that are enough for most arguments: the largest term below, the largest term plus the log of the number of terms above.</p>https://www.zhumengyao.com/scidraft/notes/demo-note-lemma-softmax-shift/Mon, 21 Sep 2026 10:52:00 +0900https://www.zhumengyao.com/scidraft/notes/demo-note-lemma-softmax-shift/<p><strong>Demo note.</strong> This note demonstrates what the <strong>SciDraft</strong> 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.</p> <p>A lemma is a small result proved on the way to something larger, and this one is proved in two lines yet carries most of the numerical stability of a softmax: adding the same constant to every score changes nothing.</p>