Related papers: Smoothing the gap between NP and ER
In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of…
A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved…
Mathematical reasoning is central to artificial intelligence, with applications in education, code generation, and research-level mathematical discovery. Mathematical competitions highlight two problem types: theorem proving, requiring…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…
Entity Resolution (ER) is the problem of determining when two entities refer to the same underlying entity. The problem has been studied for over 50 years, and most recently, has taken on new importance in an era of large, heterogeneous…
We investigate the complexity of counting Eulerian tours ({\sc #ET}) and its variations from two perspectives---the complexity of exact counting and the complexity w.r.t. approximation-preserving reductions (AP-reductions \cite{MR2044886}).…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
Learning-to-rank (LTR) is a class of supervised learning techniques that apply to ranking problems dealing with a large number of features. The popularity and widespread application of LTR models in prioritizing information in a variety of…
This paper investigates $\exists\mathbb{R}(r^{\mathbb{Z}})$, that is the extension of the existential theory of the reals by an additional unary predicate $r^{\mathbb{Z}}$ for the integer powers of a fixed computable real number $r > 0$. If…
The well-known empirical risk minimization (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is…
Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to…
Transformers and linear state space models can be evaluated in parallel on modern hardware, but evaluating nonlinear RNNs appears to be an inherently sequential problem. Recently, however, Lim et al. '24 developed an approach called DEER,…
Valuing intangible assets under uncertainty remains a critical challenge in the strategic management of technological innovation due to the information asymmetry inherent in high-dimensional technical specifications. Traditional…
The Evidential Regression Network (ERN) represents a novel approach that integrates deep learning with Dempster-Shafer's theory to predict a target and quantify the associated uncertainty. Guided by the underlying theory, specific…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
In the Exact Matching Problem (EM), we are given a graph equipped with a fixed coloring of its edges with two colors (red and blue), as well as a positive integer $k$. The task is then to decide whether the given graph contains a perfect…
Entity matching (EM) is the most critical step for entity resolution (ER). While current deep learningbased methods achieve very impressive performance on standard EM benchmarks, their realworld application performance is much frustrating.…
Empirical neural tangent kernels (eNTKs) can provide a good understanding of a given network's representation: they are often far less expensive to compute and applicable more broadly than infinite width NTKs. For networks with O output…
Many recent works on Entity Resolution (ER) leverage Deep Learning techniques involving language models to improve effectiveness. This is applied to both main steps of ER, i.e., blocking and matching. Several pre-trained embeddings have…