  A major task in particle physics is the measurement of rare signal processes.
These measurements are highly dependent on the classification accuracy of these
events in relation to the huge background of other Standard Model processes.
Reducing the background by a few tens of percent with the same signal
efficiency can already increase the sensitivity considerably. This work
demonstrates the importance of incorporating physical information into deep
learning-based event selection. The paper includes this information into
different methods for classifying events, in particular Boosted Decision Trees,
Transformer Architectures (Particle Transformer) and Graph Neural Networks
(Particle Net). In addition to the physical information previously proposed for
jet tagging, we add particle measures for energy-dependent particle-particle
interaction strengths as predicted by the leading order interactions of the
Standard Model (SM). We find that the integration of physical information into
the attention matrix (transformers) or edges (graphs) notably improves
background rejection by $10\%$ to $40\%$ over baseline models (a graph
network), with about $10\%$ of this improvement directly attributable to what
we call the SM interaction matrix. In a simplified statistical analysis, we
find that such architectures can improve the significance of signals by a
significant factor compared to a graph network (our base model).
