Wethenseparate theoptimization process into two steps, corresponding to weight update and structure parameter update. For the former step, we use the conventional chain rule, which can be sparse via exploiting the sparse structure.

Inrecentyears,quantitativestatistical and algorithmic treatments of these formulations have produced insights into modern computational methods-resulting innovelapproaches todifficult, open problems.

Formally, the CCA problem is defined as follows.

Among potential attacks against FR systems [Galbally et al., 2014, Biggio et al., 2015, Hadid et al., 2015, Mai et al., 2018, Marcel et al., 2023], the template inversion (TI) attack significantly jeopardizes the users' privacy. In a TI attack, the adversary gains access to templates stored in the FR system's database and aims