Related papers: A Heuristic Approach to Two Level Boolean Minimiza…
Two-view triangulation is a problem of minimizing a quadratic polynomial under an equality constraint. We derive a polynomial that encodes the local minimizers of this problem using the theory of Lagrange multipliers. This offers a simpler…
Consensus-based optimization (CBO) is a versatile multi-particle optimization method for performing nonconvex and nonsmooth global optimizations in high dimensions. Proofs of global convergence in probability have been achieved for a broad…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
The article proposes a heuristic approximation approach to the bin packing problem under multiple objectives. In addition to the traditional objective of minimizing the number of bins, the heterogeneousness of the elements in each bin is…
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the…
Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually over-weighted by document word counts; and 2) existing variational inference methods make…
Weight binarization has emerged as a promising strategy to reduce the complexity of large language models (LLMs). Existing approaches fall into post-training binarization, which is simple but causes severe performance loss, and…
Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC)…
In this paper, the decades-old clustering method k-means is revisited. The original distortion minimization model of k-means is addressed by a pure stochastic minimization procedure. In each step of the iteration, one sample is tentatively…
Cluster analysis plays an important role in decision making process for many knowledge-based systems. There exist a wide variety of different approaches for clustering applications including the heuristic techniques, probabilistic models,…
Boolean reaction networks are an important tool in biochemistry for studying mechanisms in the biological cell. However, the stochastic formulation of such networks requires the solution of a master equation which inherently suffers from…
We propose a generic variance-reduced algorithm, which we call MUltiple RANdomized Algorithm (MURANA), for minimizing a sum of several smooth functions plus a regularizer, in a sequential or distributed manner. Our method is formulated with…
We present general, analytic methods for Cosmological likelihood analysis and solve the "many-parameters" problem in Cosmology. Maxima are found by Newton's Method, while marginalization over nuisance parameters, and parameter errors and…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
This research investigates a multi-product capacitated lot-sizing and scheduling problem incorporating a novel learning effect, namely the period-based learning effect. This is inspired by a real case in a core analysis laboratory under a…
In this paper we discuss several heuristic strategies which allow one to solve the Whitehead's minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice…
We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed.…
Large language models (LLMs) have shown promise in formal theorem proving, but their token-level processing often fails to capture the inherent hierarchical nature of mathematical proofs. We introduce \textbf{Hierarchical Attention}, a…