We show the similarities between our method, Neural ODE, and differentiable physics in Figure 4. All the three approaches have a differentiable system governed by some kinds of differential equations. Our method parametrizes the dynamics using continuous basis functions; Neural ODE uses neural networks; and Differentiable physics describes the dynamics system using physics equations like Newton's Second Law, Navier-Stokes equations. Let Uv(t2,t1) be as defined in Theorem 3.2. Let Lbe defined as (4), and H(v,t) = P jfj(v,t)Hj.

Two types of expression of empirical interest have been studied: sentences in English and other'natural' languages, and programs written in some high-level procedural language like ALGOL. Expressions in these languages consist of sets of elements (words and characters) co-ordinated with one another according to the sensorily manifest relationship'alongside', more commonly termed'followed by'.

In Meltzer, Bernard and Donald Michie (Eds.), Machine Intelligence 4. Edinburgh University Press.