  Generating facial reactions in a human-human dyadic interaction is complex
and highly dependent on the context since more than one facial reactions can be
appropriate for the speaker's behaviour. This has challenged existing machine
learning (ML) methods, whose training strategies enforce models to reproduce a
specific (not multiple) facial reaction from each input speaker behaviour. This
paper proposes the first multiple appropriate facial reaction generation
framework that re-formulates the one-to-many mapping facial reaction generation
problem as a one-to-one mapping problem. This means that we approach this
problem by considering the generation of a distribution of the listener's
appropriate facial reactions instead of multiple different appropriate facial
reactions, i.e., 'many' appropriate facial reaction labels are summarised as
'one' distribution label during training. Our model consists of a perceptual
processor, a cognitive processor, and a motor processor. The motor processor is
implemented with a novel Reversible Multi-dimensional Edge Graph Neural Network
(REGNN). This allows us to obtain a distribution of appropriate real facial
reactions during the training process, enabling the cognitive processor to be
trained to predict the appropriate facial reaction distribution. At the
inference stage, the REGNN decodes an appropriate facial reaction by using this
distribution as input. Experimental results demonstrate that our approach
outperforms existing models in generating more appropriate, realistic, and
synchronized facial reactions. The improved performance is largely attributed
to the proposed appropriate facial reaction distribution learning strategy and
the use of a REGNN. The code is available at
https://github.com/TongXu-05/REGNN-Multiple-Appropriate-Facial-Reaction-Generation.
