  With the impressive progress of deep learning, applications relying on
machine learning are increasingly being integrated into daily life. However,
most deep learning models have an opaque, oracle-like nature making it
difficult to interpret and understand their decisions. This problem led to the
development of the field known as eXplainable Artificial Intelligence (XAI).
One method in this field known as Projective Simulation (PS) models a
chain-of-thought as a random walk of a particle on a graph with vertices that
have concepts attached to them. While this description has various benefits,
including the possibility of quantization, it cannot be naturally used to model
thoughts that combine several concepts simultaneously. To overcome this
limitation, we introduce Multi-Excitation Projective Simulation (mePS), a
generalization that considers a chain-of-thought to be a random walk of several
particles on a hypergraph. A definition for a dynamic hypergraph is put forward
to describe the agent's training history along with applications to AI and
hypergraph visualization. An inductive bias inspired by the remarkably
successful few-body interaction models used in quantum many-body physics is
formalized for our classical mePS framework and employed to tackle the
exponential complexity associated with naive implementations of hypergraphs. We
prove that our inductive bias reduces the complexity from exponential to
polynomial, with the exponent representing the cutoff on how many particles can
interact. We numerically apply our method to two toy environments and a more
complex scenario modelling the diagnosis of a broken computer. These
environments demonstrate the resource savings provided by an appropriate choice
of inductive bias, as well as showcasing aspects of interpretability. A quantum
model for mePS is also briefly outlined and some future directions for it are
discussed.
