Chemical Reaction Networks Learn Better than Spiking Neural Networks

Sophie Jaffard; Ivo F. Sbalzarini

cs.LGMar 12, 2026

Chemical Reaction Networks Learn Better than Spiking Neural Networks

Authors: Sophie Jaffard, Ivo F. Sbalzarini

Organizations: Max Planck Institute of Molecular Cell Biology and Genetics Center for Systems Biology Dresden Dresden, Germany · Dresden University of Technology, Faculty of Computer Science Max Planck Institute of Molecular Cell Biology and Genetics Center for Systems Biology Dresden Dresden, Germany

Abstract

We mathematically prove that chemical reaction networks without hidden layers can solve tasks for which spiking neural networks require hidden layers. Our proof uses the deterministic mass-action kinetics formulation of chemical reaction networks. Specifically, we prove that a certain reaction network without hidden layers can learn a classification task previously proved to be achievable by a spiking neural network with hidden layers. We provide analytical regret bounds for the global behavior of the network and analyze its asymptotic behavior and Vapnik-Chervonenkis dimension. In a numerical experiment, we confirm the learning capacity of the proposed chemical reaction network for classifying handwritten digits in pixel images, and we show that it solves the task more accurately and efficiently than a spiking neural network with hidden layers. This provides a motivation for machine learning in chemical computers and a mathematical explanation for how biological cells might exhibit more efficient learning behavior within biochemical reaction networks than neuronal networks.

Figures & tables

Figure 1: Schematic representation of the time evolution of the chemical reaction network during the selection and learning phases.

Figure 2: Analogy between the structure of the SNN proposed by Jaffard et al. (2026) (left) and the present CRN (right).

Figure 3: Example images from the handwritten digits data set. Each image shows a digit (ground-truth labels above the images) in 8 $\times$ 8 grayscale pixels.

Figure 4: Numerical results on the handwritten digits data set. We plot the CRN’s classification accuracy on the test set as a function of network complexity, quantified by the number of selected input sets

\lvert\bar{J}_{n}\rvert

during the selection phase. We show results for network depths

n=1

(no hidden layer, left panel) and

n=2

(one hidden layer, right panel). The shaded bands are the 10% confidence intervals over 100 independent repetitions of each configuration. All rate constants are equal to 1, except

c_{k}

and

d_{k}

for

k\in K

, which are equal to

\frac{10}{9}\eta

and

10\eta

, respectively. The initial species concentrations are

A=1

and

S=3

, and the noise variance is set to

\sigma^{2}=0.00001

. For network depth

n=1

, we chose

\eta=0.0005

and for network depth

n=2

, we chose

\eta=0.0001

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Neural Petri flows for chemical reactions

Jose Eduardo Escrig Molina, Daniel Probst

Bioinformatics Group Bioprocess Engineering Group Wageningen Unversity Wageningen, the Netherlands

AI-Assisted Scientific Research

Open paper AskPDF arXiv

Petri nets have been used to describe chemical processes such as reactions.They map well to chemistry: Places are the bonds between atoms and the free valence of each atom, a token is a unit of bond order, a transition forms or breaks a bond, the conserved quantities are the valence budgets of the atoms, and the enabling rule is the valence rule. These semantics are not guaranteed by learned models of reactions or neural networks that are built on Petri nets that use the net as a scaffold for message passing. Here, we ask what architecture remains a Petri net for every value of its weights. We find the answer in the theory, where all semantics of a net share the firing form

m^\prime=m+Cσ

, locality, as enabling reads only the inputs of a transition, and the enabling rule, and we prove that conservation forces the firing form and that non-negativity forces the enabling rule on local rate laws. This leaves free the rate law, which is the propensity of each transition to fire. We introduce Neural Petri Flow, which learns this rate law, or a readout for classification, and hard-wires the rest as parameter-free layers. On what we denote a valence net, atom mapping, reaction classification, and forward prediction become three tasks on one firing vector. Without training, the minimum firing vector maps 88.8% of the curated Golden set against 85.6% for RXNMapper, and 88.7 against 77.9% of the enzymatic reactions of EnzymeMap. On USPTO-480K, NPF trained on these firing vectors predicts 87.7% of the products and 67.4% when trained on a 1% subset of the training reactions. EC numbers of ECREACT are predicted at the third level for 90.2% of reactions, 5.6 points ahead of the best published method. With electrons as tokens, the same token game predicts 90.5% of the elementary steps of FlowER first, ahead of the published baseline, and every top-1 prediction is a valid molecule without a filter.

Abstract

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