The main result is presented in Theorem 2. According to the definition of the Fiedler vector, we have ( L + L)( f + f) = ( λ + λ)( f + f). We outline the proof below for interested readers. The main result is presented in Theorem 2. We first present Stewart's theorem in Lemma 1 to assist Actual times may differ depending on hardware and environment. We also show the number of model parameters required for each method in Table S3. Hyper-parameters were selected based on a coarse search on the validation set.

Determinantal point processes (DPPs) are well-suited to recommender systems where the goal is to generate collections of diverse, high-quality items.

Then,itsamplesafixednumber of nodes by the calculated probability,and recursively conducts such procedure per layer toconstruct the whole computation graph.

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observedsamples isanNP-hard combinatorial problem. In this paper, we first show that for a set of important graph families it is possible toconvertthestructural constraints ofstructure intoeigenvalueconstraints ofthe graph Laplacianmatrix.

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Orthogonally, algorithm unrolling[14] implements iterations of a model-based algorithm as a sequence of neural layers to build afeed-forward network, whose parameters can be learned endto-end via back-propagation from data. A classic example is the unrolling of theiterative soft-1While works existtoanalyze existing transformer architectures [5,6,7,8,9],only [10,11]characterized the performance ofasingle self-attention layer and ashallowtransformer,respectively.