  Feature selection is a crucial task in settings where data is
high-dimensional or acquiring the full set of features is costly. Recent
developments in neural network-based embedded feature selection show promising
results across a wide range of applications. Concrete Autoencoders (CAEs),
considered state-of-the-art in embedded feature selection, may struggle to
achieve stable joint optimization, hurting their training time and
generalization. In this work, we identify that this instability is correlated
with the CAE learning duplicate selections. To remedy this, we propose a simple
and effective improvement: Indirectly Parameterized CAEs (IP-CAEs). IP-CAEs
learn an embedding and a mapping from it to the Gumbel-Softmax distributions'
parameters. Despite being simple to implement, IP-CAE exhibits significant and
consistent improvements over CAE in both generalization and training time
across several datasets for reconstruction and classification. Unlike CAE,
IP-CAE effectively leverages non-linear relationships and does not require
retraining the jointly optimized decoder. Furthermore, our approach is, in
principle, generalizable to Gumbel-Softmax distributions beyond feature
selection.
