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In the present article, we introduce a Kantorovich variant of the neural network interpolation operators activated by smooth ramp functions proposed by Qian and Yu (2022). We discuss the convergence of these operators in the spaces, C([c,d])$$ C\left(\left[c,d\right]\right) $$ and Lp([c,d]),1≤p<∞$$ {\mathtt{L}}&amp;#x0005E;{\mathtt{p}}\left(\left[c,d\right]\right),1\le \mathtt{p}&lt;\infty $$, and establish some direct approximation theorems. Further, we derive the converse results by means of Berens–Lorentz lemma and Peetre's K‐functional. We present a multivariate version of the aforementioned Kantorovich neural network interpolation operators and investigate the direct and converse results in the continuous and Lp,1≤p<∞$$ {\mathtt{L}}&amp;#x0005E;{\mathtt{p}},1\le \mathtt{p}&lt;\infty $$, spaces. [ABSTRACT FROM AUTHOR]