  Active inference is a state-of-the-art framework for modelling the brain that
explains a wide range of mechanisms such as habit formation, dopaminergic
discharge and curiosity. Recently, two versions of branching time active
inference (BTAI) based on Monte-Carlo tree search have been developed to handle
the exponential (space and time) complexity class that occurs when computing
the prior over all possible policies up to the time horizon. However, those two
versions of BTAI still suffer from an exponential complexity class w.r.t the
number of observed and latent variables being modelled. In the present paper,
we resolve this limitation by first allowing the modelling of several
observations, each of them having its own likelihood mapping. Similarly, we
allow each latent state to have its own transition mapping. The inference
algorithm then exploits the factorisation of the likelihood and transition
mappings to accelerate the computation of the posterior. Those two
optimisations were tested on the dSprites environment in which the metadata of
the dSprites dataset was used as input to the model instead of the dSprites
images. On this task, $BTAI_{VMP}$ (Champion et al., 2022b,a) was able to solve
96.9\% of the task in 5.1 seconds, and $BTAI_{BF}$ (Champion et al., 2021a) was
able to solve 98.6\% of the task in 17.5 seconds. Our new approach
($BTAI_{3MF}$) outperformed both of its predecessors by solving the task
completly (100\%) in only 2.559 seconds. Finally, $BTAI_{3MF}$ has been
implemented in a flexible and easy to use (python) package, and we developed a
graphical user interface to enable the inspection of the model's beliefs,
planning process and behaviour.
