l,j and wdec

The learnable parameters of the ACAE are the afﬁne
combination weights wenc
j,l , which can also be un-
derstood as (potentially negative) generalized barycentric
coordinates [29] for the latents w.r.t. the full joint set and
vice versa. Allowing negative coordinates is necessary, as
this allows the latents to spread outwards from the body,
similar to a cage used in graphics [62]. Restricting the en-
coder and decoder to convex combinations would severely
limit its expressiveness. To achieve sparsity in the weights
(i.e., spatially localized inﬂuence), we use (cid:96)1 regularization,
and this also reduces the amount of negative weights, pre-
ferring nearly convex combinations. We further adopt the
(cid:96)1 reconstruction loss, as it is robust to outliers which may
be present due to noise in the pseudo-GT.
Problem Statement. We can now formally state our pro-
posed ACAE problem in matrix notation for the weights.
Learning 3D Human Pose Estimation from Dozens of Datasets using a Geometry-Aware Autoencoder to Bridge Between Skeleton Formats