https://hackerpaper.kaipfister.de/p/2406.09699/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=45291554urn:hackerpapers:mention:2406.09699:45291554Thu, 18 Sep 2025 16:22:04 GMT<p>Interesting to see this here! This example is one of the ones mentioned in the appendix of https://arxiv.org/abs/2406.09699, specifically &quot;4.1.2.4 When AD is algorithmically correct but numerically wrong&quot;. If people want a tl;dr, the main idea is you can construct an ODE where the forward pass is trivial, i.e. the ODE solution going forwards is exact, but its derivative is &quot;hard&quot;. An easy way to do this is to make it so you have for example `x&#x27; = x - y, y&#x27; = y - x`, with initial conditions x(0)=y(0). If you start with things being the same value, then the solution to the ODE is constant since…</p><p><a href="https://hackerpaper.kaipfister.de/p/2406.09699/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.NA