While this could be done using thesynthesis formulation, we demonstrate that this leads to slower performances. The main difficulty inapplying suchmethods intheanalysisformulation liesinproposing a way to compute the derivatives through the proximal operator.

Community detection is an essential tool for unsupervised data exploration and revealing theorganisational structure ofnetworkedsystems. Withalong history innetwork science, community detection typically relies on objectivefunctions, optimised with custom-tailored search algorithms, but often without leveraging recentadvancesindeeplearning.

Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. Most studies focus on the linear latent variable model or impose strict constraints on latent structures, which fail to address cases in discrete data involving non-linear relationships or complex latent structures.

Previous works attempting to close this gap have failed to fully investigate the exponentially growing number of feature combinations which deep networks consider automatically during training. In this work, we develop a tractable selection algorithm to efficiently identify the necessary feature combinations byleveraging techniques infeature interaction detection. Our proposed Sparse Interaction AdditiveNetworks (SIAN) construct abridge from thesesimple andinterpretable models tofullyconnected neuralnetworks.