This paper proposes KAN/H, a variant of Kolmogorov-Arnold Network (KAN) that uses a Haar-variant basis system having both global and local bases instead of B-spline. The resulting algorithm is applied to function approximation problems and MNIST. We show that it does not require most of the problem-specific hyper-parameter tunings.

Theorem 1. Suppose that ˆ X In DB models, the commonly used p is either 1 or 2. When p = 2, DURA takes the form as the one in Equation (8) in the main text. If p = 1, we cannot expand the squared score function of the associated DB models as in Equation (4). Therefore, we choose p = 2 . 2 Table 2: Hyperparameters found by grid search. Suppose that k is the number of triplets known to be true in the knowledge graph, n is the embedding dimension of entities. That is to say, the computational complexity of weighted DURA is the same as the weighted squared Frobenius norm regularizer.

Lemma A.2. Assume W (0), β (0) and b have i.i.d. The proof for (A.5) is similar since V ar( To prove (A.6), since | y With a union bound argument, we can show (A.6). Finally, (A.7) followed from standard Gaussian tail bounds and union bound argument, yielding P(max Under the conditions of Theorem 3.2, we define matrices G(0),H (0) R Under the conditions of Theorem 3.2, if the error bound (3.1) holds for all t = 1, 2,...,t From the feedback alignment updates (A.3), we have for all t T | β Lemma A.5. Assume all the inequalities from Lemma A.2 hold. Under the conditions of Theorem 3.2, if the bound for the weights difference (3.2) holds for all t t We prove the inequality (3.1) by induction. Suppose (3.1) and (3.2) hold for all t = 1, 2,...,t Assume all the inequalities from Lemma A.2 hold.

By Prokhorov's theorem, there exists a

Table 4: The detailed sampling hyperparameters for Chameleon.

We begin by introducing some notations that will be used in this SM .

Theorem 1. Suppose that ˆ X In DB models, the commonly used p is either 1 or 2. When p = 2, DURA takes the form as the one in Equation (8) in the main text. If p = 1, we cannot expand the squared score function of the associated DB models as in Equation (4). Therefore, we choose p = 2 . 2 Table 2: Hyperparameters found by grid search. Suppose that k is the number of triplets known to be true in the knowledge graph, n is the embedding dimension of entities. That is to say, the computational complexity of weighted DURA is the same as the weighted squared Frobenius norm regularizer.

Table 4: The detailed sampling hyperparameters for Chameleon.

Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under which this technique is applicable, by considering not only dependencies between predicates but also their arguments and context. This allows splitting programs commonly used in practice to which previous results were not applicable.

We prove the first generalization bound for large-margin halfspaces that is asymptotically tight in the tradeoff between the margin, the fraction of training points with the given margin, the failure probability and the number of training points.