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This paper shows that ResNets, NeuralODEs, and CT-RNNs, are particular neuralregulatory networks (NRNs), a biophysical model for the nonspiking neuronsencountered in small species, such as the C.elegans nematode, and in the retinaof large species. Compared to ResNets, NeuralODEs and CT-RNNs, NRNs have anadditional multiplicative term in their synaptic computation, allowing them toadapt to each particular input. This additional flexibility makes NRNs $M$times more succinct than NeuralODEs and CT-RNNs, where $M$ is proportional tothe size of the training set. Moreover, as NeuralODEs and CT-RNNs are $N$ timesmore succinct than ResNets, where $N$ is the number of integration stepsrequired to compute the output $F(x)$ for a given input $x$, NRNs are in total$M\,{\cdot}\,N$ more succinct than ResNets. For a given approximation task,this considerable succinctness allows to learn a very small and thereforeunderstandable NRN, whose behavior can be explained in terms of wellestablished architectural motifs, that NRNs share with gene regulatorynetworks, such as, activation, inhibition, sequentialization, mutual exclusion,and synchronization. To the best of our knowledge, this paper unifies for thefirst time the mainstream work on deep neural networks with the one in biologyand neuroscience in a quantitative fashion.

ResNets, NeuralODEs and CT-RNNs are Particular Neural Regulatory Networks