Related papers: Difference of Constrained Patterns in Logically Co…
We consider Conditional Random Fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) $x_1...x_n$ is the sum of terms over intervals $[i,j]$ where each term is non-zero only if the…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…
Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…
A datatype defining rewrite system (DDRS) is an algebraic (equational) specification intended to specify a datatype. When interpreting the equations from left-to-right, a DDRS defines a term rewriting system that must be ground-complete.…
Latent tree learning models represent sentences by composing their words according to an induced parse tree, all based on a downstream task. These models often outperform baselines which use (externally provided) syntax trees to drive the…
In computer science, divide and conquer (D&C) is an algorithm design paradigm based on multi-branched recursion. A D&C algorithm works by recursively and monotonically breaking down a problem into sub problems of the same (or a related)…
A nearly linear recurrence sequence (nlrs) is a complex sequence $(a_n)$ with the property that there exist complex numbers $A_0$,$\ldots$, $A_{d-1}$ such that the sequence $\big(a_{n+d}+A_{d-1}a_{n+d-1}+\cdots +A_0a_n\big)_{n=0}^{\infty}$…
In this paper, we examine how large language models (LLMs) solve multi-step problems under a language agent framework with three components: a generator, a discriminator, and a planning method. We investigate the practical utility of two…
Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and…
A simple and general definition of quasi cyclic low density parity check (QC LDPC) codes which are constructed based on circulant permutation matrices (CPM) is proposed. As an special case of this definition, we first represent one type of…
Designing component-based constraint solvers is a complex problem. Some components are required, some are optional and there are interdependencies between the components. Because of this, previous approaches to solver design and…
Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is…
Despite significant progress in transformer interpretability, an understanding of the computational mechanisms of large language models (LLMs) remains a fundamental challenge. Many approaches interpret a network's hidden representations but…
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…
Network Lasso (NL for short) is a methodology for estimating models by simultaneously clustering data samples and fitting the models to the samples. It often succeeds in forming clusters thanks to the geometry of the $\ell_1$-regularizer…
Biclustering is an unsupervised machine learning technique that simultaneously clusters rows and columns in a data matrix. Biclustering has emerged as an important approach and plays an essential role in various applications such as…
Learning distributed representations for relation instances is a central technique in downstream NLP applications. In order to address semantic modeling of relational patterns, this paper constructs a new dataset that provides multiple…
Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…
The Kleene star operator is an important pattern construct for representing a pattern that repeats multiple times. Due to its simplicity and usefulness, it is imported into various pattern-matching systems other than regular expressions.…