https://hackerpaper.kaipfister.de/p/1911.06491/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=29911027urn:hackerpapers:mention:1911.06491:29911027Wed, 12 Jan 2022 18:36:45 GMT<p>&gt; For example, the gradient of some function wrt to elements of a symmetric matrix is and should be different depending on whether the matrix is structurally symmetric Ugh. Yes and no, but mostly no. A gradient is a collection of partial derivatives. The normal meaning of partial derivative with respect to symmetric matrix elements does not actually exist, because you can&#x27;t vary them independently. This is actually a generic problem for any overparameterized constrained system. People still want to be able to use the standard tools of calculus though. You can reasonably do things like use…</p><p><a href="https://hackerpaper.kaipfister.de/p/1911.06491/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.NA