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Mathematical modeling is a powerful tool for describing, predicting, and understanding complex phenomena exhibited by real-world systems. However, identifying the equations that govern a system's dynamics from experimental data remains a…
We give a simple algorithm to solve the subgroup membership problem for virtually free groups. For a fixed virtually free group with a fixed generating set $X$, the subgroup membership problem is uniformly solvable in time $O(n\log^*(n))$…
Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint…
Given an initial family of sets, we may take unions, intersections and complements of the sets contained in this family in order to form a new collection of sets; our construction process is done recursively until we obtain the last family.…
Retrieval-augmented generation (RAG) has emerged to address the knowledge-intensive visual question answering (VQA) task. Current methods mainly employ separate retrieval and generation modules to acquire external knowledge and generate…
We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…
Understanding how social networks form, whether through reciprocity, shared attributes, or triadic closure, is central to computational social science. Exponential Random Graph Models (ERGMs) offer a principled framework for testing such…
We extend our techniques developed in our earlier paper appeared in Computational Complexity, 2017 (preprint: arXiv:1508.00690) to obtain a deterministic polynomial time algorithm for computing the non-commutative rank together with…
Many algorithms have been proposed in the last ten years for the discovery of dynamic communities. However, these methods are seldom compared between themselves. In this article, we propose a generator of dynamic graphs with planted…
We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum…
In the recent research of data mining, frequent structures in a sequence of graphs have been studied intensively, and one of the main concern is changing structures along a sequence of graphs that can capture dynamic properties of data. On…
The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of generators. For a finite solvable group $G$ of order $N = p_{1}p_{2}\dots p_{n}$, where $p_{i}$'s are…
We present a simple but powerful architecture of convolutional neural network, which has a VGG-like inference-time body composed of nothing but a stack of 3x3 convolution and ReLU, while the training-time model has a multi-branch topology.…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
Retrieval-augmented generation (RAG) is a prevalent approach for building LLM-based question-answering systems that can take advantage of external knowledge databases. Due to the complexity of real-world RAG systems, there are many…
This paper is about solving polynomial systems. It first recalls how to do that efficiently with a very high probability of correctness by reconstructing a rational univariate representation (rur) using Groebner revlex computation,…
Fisher information and natural gradient provided deep insights and powerful tools to artificial neural networks. However related analysis becomes more and more difficult as the learner's structure turns large and complex. This paper makes a…
In a series of papers it has been shown that for many linear algebra operations it is possible to generate families of algorithms by following a systematic procedure. Although powerful, such a methodology involves complex algebraic…
A physically-motivated genetic algorithm (GA) and full enumeration for a tile-based model of self-assembly (JaTAM) is implemented using a graphics processing unit (GPU). We observe performance gains with respect to state-of-the-art…