Framing RNN as a kernel method: A neural ODE approach Supplementary material A Mathematical details

This definition is valid when f is represented by a matrix. Let us first briefly recall some elements on tensor spaces. Proposition 7. Let X BV B.3 Proof of Proposition 3 According to Lyons (2014, Lemma 5.1), one has null X We first recall the fundamental theorem of calculus for line integrals (also known as gradient theorem). We start with the proof of the linear case before moving on to the general case. In the general case, the proof is two-fold.