Noise robustness of rate-independent CRNs with chemically implemented backpropagation

Determine the noise robustness of rate-independent chemical reaction networks when backpropagation, which requires non-linear computations, is implemented via chemical reactions; specifically, establish whether their rate-independence and robustness properties extend beyond semilinear feed-forward computations to the non-linear operations needed for training.

Background

Rate-independent CRNs are known to reliably compute semilinear functions for feed-forward neural network implementations without sensitivity to reaction rate variations. However, backpropagation involves non-linear operations, and its realization via chemical reactions may introduce sensitivity to noise.

The authors explicitly state that the noise robustness of rate-independent CRNs under chemically implemented backpropagation is unclear, highlighting a need to characterize conditions under which robustness might be preserved.