Correction to: Nature Machine Intelligence https://doi.org/10.1038/s42256-022-00556-7, published online 15 November 2022.

In the version of this article initially published, Lemma 1 appeared at the end of the article rather than within the “Analytical LTC approximation for general inputs” subsection. In that subsection, the text now reading, in part, “Inspired by equations (7) and (8),” mention of equation (8) was missing in the original version. Also, equation (9) in Lemma 1 was incorrectly labeled as “(10)” and has been renumbered. Further, the Acknowledgements section was an incorrect version. All changes have been made to HTML and PDF versions of the article.