  Embedding computation in biochemical environments incompatible with
traditional electronics is expected to have wide-ranging impact in synthetic
biology, medicine, nanofabrication and other fields. Natural biochemical
systems are typically modeled by chemical reaction networks (CRNs), and CRNs
can be used as a specification language for synthetic chemical computation. In
this paper, we identify a class of CRNs called non-competitive (NC) whose
equilibria are absolutely robust to reaction rates and kinetic rate law,
because their behavior is captured solely by their stoichiometric structure.
Unlike prior work on rate-independent CRNs, checking non-competition and using
it as a design criterion is easy and promises robust output. 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 (IRIS and MNIST), as well as tasks better
aligned with potential biological applications including virus detection and
spatial pattern formation.
