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Embedding computation in biochemical environments incompatible with traditional electronics is expected to have a wide-ranging impact in synthetic biology, medicine, nanofabrication, and other fields. Natural biochemical systems are typically modeled by chemical reaction networks (CRNs) which can also be used as a specification language for synthetic chemical computation. In this paper, we identify a syntactically checkable class of CRNs called noncompetitive (NC) whose equilibria are absolutely robust to reaction rates and kinetic rate law, because their behavior is captured solely by their stoichiometric structure. In spite of the inherently parallel nature of chemistry, the robustness property allows for programming as if each reaction applies sequentially. We also present a technique to program NC-CRNs using well-founded deep learning methods, showing a translation procedure from rectified linear unit (ReLU) neural networks to NC-CRNs. In the case of binary weight ReLU networks, our translation procedure is surprisingly tight in the sense that a single bimolecular reaction corresponds to a single ReLU node and vice versa. This compactness argues that neural networks may be a fitting paradigm for programming rate-independent chemical computation. As proof of principle, we demonstrate our scheme with numerical simulations of CRNs translated from neural networks trained on traditional machine learning datasets, as well as tasks better aligned with potential biological applications including virus detection and spatial pattern formation.