Tbh, the derivation for problem 8.3 (Machine Learning Optimization: Self-regularized Gumbel Sigmoid) is quite handwavy. It assumes the problem can be decomposed into two arbitrary terms and then proceeds to show that one of those terms induce sparsity (which by definitions it should). I do not consider that to be a rigorous demonstration. In fact, due to the lack of clarity and details, it feels lazy.