Related papers: Connecting Width and Structure in Knowledge Compil…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
Global SLS-resolution is a well-known procedural semantics for top-down computation of queries under the well-founded model. It inherits from SLDNF-resolution the {\em linearity} property of derivations, which makes it easy and efficient to…
We consider a family of deep neural networks consisting of two groups of convolutional layers, a downsampling operator, and a fully connected layer. The network structure depends on two structural parameters which determine the numbers of…
Query-focused summarization (QFS) aims to provide a summary of a document that satisfies information need of a given query and is useful in various IR applications, such as abstractive snippet generation. Current QFS approaches typically…
DNN structures are continuously developing and achieving high performances in classification problems. Also, it is observed that success rates obtained with DNNs are higher than those obtained with traditional neural networks. In addition,…
This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width…
We represent 3D shape by structured 2D representations of fixed length making it feasible to apply well investigated 2D convolutional neural networks (CNN) for both discriminative and geometric tasks on 3D shapes. We first provide a general…
Cardinality constraints or, more generally, weight constraints are well recognized as an important extension of answer-set programming. Clearly, all common algorithmic tasks related to programs with cardinality or weight constraints - like…
We give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are…
The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some…
In this article, we study the problem of enumerating the models of DNF formulas. The aim is to provide enumeration algorithms with a delay that depends polynomially on the size of each model and not on the size of the formula, which can be…
We show that any quantum circuit of treewidth $t$, built from $r$-qubit gates, requires at least $\Omega(\frac{n^{2}}{2^{O(r\cdot t)}\cdot \log^4 n})$ gates to compute the element distinctness function. Our result generalizes a…
Feature models are commonly used to specify the valid configurations of a product line. In industry, feature models are often complex due to a large number of features and constraints. Thus, a multitude of automated analyses have been…
Epistemic logics are a primary formalism for multi-agent systems but major reasoning tasks in such epistemic logics are intractable, which impedes applications of multi-agent epistemic logics in automatic planning. Knowledge compilation…
Ontology-based data access is an approach to organizing access to a database augmented with a logical theory. In this approach query answering proceeds through a reformulation of a given query into a new one which can be answered without…
With good explanatory power and controllability, rule-based methods play an important role in many tasks such as knowledge reasoning and decision support. However, existing studies primarily focused on learning chain-like rules, which limit…
The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free…
The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with $T$ gates whose underlying graph has treewidth $d$ can be simulated deterministically in…
In this paper, we investigate computational power of threshold circuits and other theoretical models of neural networks in terms of the following four complexity measures: size (the number of gates), depth, weight and energy. Here the…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…