Final states with several jets from the decays of heavy particles pose a combinatorial problem, since the jets must be assigned, at least implicitly, to their parent particles. We describe the Combinatorial Residual Network (CoReNet), a classifier that encodes the assumed decay chain of the final state in its architecture. CoReNet builds its event representation level by level along the decay hierarchy, evaluates every jet assignment hypothesis with weights shared across objects, and combines the hypotheses with learned weights using residual networks. The exchange symmetries of the decay are built into the construction, the size of the network does not depend on the number of hypotheses, and the network is trained with the classification loss alone, without generator-level jet assignments. The architecture was developed for the $b\bar{b}b\bar{b}$ final state and has been used in several CMS searches. On fast-simulation samples of Higgs boson pair production in the $b\bar{b}b\bar{b}$ final state against QCD multijet production, CoReNet with 1508 trainable parameters performs well above kinematic baselines and trains in minutes on a single GPU. Its hypothesis weights select the truth-matched jet pairing in most of the signal events in which it is defined, although no assignment target is used in training. Since only the encoded decay chain is specific to the final state, the construction carries over to other topologies, which we test with $HH \to b\bar{b}W^+W^-$ against semileptonic $t\bar{t}$. There, encoding the decay chain of the background as well as that of the signal further improves the classification, at a cost of about $10^3$ parameters. In both final states its performance is comparable to that of a state-of-the-art transformer-based network more than two orders of magnitude larger. The implementation is publicly available at https://github.com/cms-cmu/CoReNet.

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