  This paper revisits two prominent adaptive filtering algorithms, namely
recursive least squares (RLS) and equivariant adaptive source separation
(EASI), through the lens of algorithm unrolling. Building upon the unrolling
methodology, we introduce novel task-based deep learning frameworks, denoted as
Deep RLS and Deep EASI. These architectures transform the iterations of the
original algorithms into layers of a deep neural network, enabling efficient
source signal estimation by leveraging a training process. To further enhance
performance, we propose training these deep unrolled networks utilizing a
surrogate loss function grounded on Stein's unbiased risk estimator (SURE). Our
empirical evaluations demonstrate that the Deep RLS and Deep EASI networks
outperform their underlying algorithms. Moreover, the efficacy of SURE-based
training in comparison to conventional mean squared error loss is highlighted
by numerical experiments. The unleashed potential of SURE-based training in
this paper sets a benchmark for future employment of SURE either for training
purposes or as an evaluation metric for generalization performance of neural
networks.
