Overview
- Field: Machine Learning
- Authors: Jose Eduardo Escrig Molina, Daniel Probst
- Published: 2026-10-06
- arXiv: 2610.08750
- 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
- The enabling rule is the valence rule
- Atom mapping (no training): minimal firing vectors map 88.8% of the curated Golden set (RXNMapper: 85.6%) and 88.7% of enzymatic reactions in EnzymeMap (vs 77.9%)
- Forward prediction: on USPTO-480K, NPF predicts 87.7% of products (67.4% on a 1% training subset)
- EC number prediction: on ECREACT, NPF predicts 90.2% of reactions at the third EC level, outperforming the best published method by 5.6 percentage points
Summary
Petri nets have been used to describe chemical processes such as reactions. They map well to chemistry:
These semantics are not guaranteed by learned models of reactions or neural networks that use Petri nets merely as a scaffold for message passing. The authors ask: what architecture remains a Petri net for every value of its weights?
The answer lies in the theory: all semantics of a net share the firing form m' = m + Cσ, locality (enabling reads only the inputs of a transition), and the enabling rule. The paper proves that conservation forces the firing form, while non-negativity enforces the enabling rule on local rate laws. This leaves only the rate law — the propensity of each transition to fire — as a free choice.
Neural Petri Flows (NPF)
NPF learns this rate law (or a readout for classification), and hard-wires everything else as parameter-free layers. On valence nets, atom mapping, reaction classification, and forward prediction become three tasks on the same firing vector.
Results
*Auto-collected on 2026-10-08*