  In high-energy particle physics events, it can be advantageous to find the
jets associated with the decays of intermediate states, for example, the three
jets produced by the hadronic decay of the top quark. Typically, a
goodness-of-association measure, such as a $\chi^2$ related to the mass of the
associated jets, is constructed, and the best jet combination is found by
optimizing this measure. As this process suffers from a combinatorial explosion
with the number of jets, the number of permutations is limited by using only
the $n$ highest $p_T$ jets. The self-attention block is a neural network unit
used for the neural machine translation problem, which can highlight
relationships between any number of inputs in a single iteration without
permutations. In this paper, we introduce the Self-Attention for Jet Assignment
(SaJa) network. SaJa can take any number of jets for input and outputs
probabilities of jet-parton assignment for all jets in a single step. We apply
SaJa to find jet-parton assignments of fully-hadronic $t\bar{t}$ events to
evaluate the performance. We show that SaJa achieves better performance than a
likelihood-based approach.
