Related papers: On the contraction method with degenerate limit eq…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for…
Sequential dependencies present a fundamental bottleneck in deploying large-scale autoregressive models, particularly for real-time applications. While traditional optimization approaches like pruning and quantization often compromise model…
In this article we establish new central limit theorems for Ruppert-Polyak averaged stochastic gradient descent schemes. Compared to previous work we do not assume that convergence occurs to an isolated attractor but instead allow…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
We propose Range and Roots which are two common patterns useful for specifying a wide range of counting and occurrence constraints. We design specialised propagation algorithms for these two patterns. Counting and occurrence constraints…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
We present and analyse a numerical framework for the approximation of nonlinear degenerate elliptic equations of the Stefan or porous medium types. This framework is based on piecewise constant approximations for the functions, which we…
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
Let $\{X, X_n, n\geq 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \sum^n_{i=1} X_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n\ge 1.$ A weak convergence theorem is established for the…
Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…
In this paper, we study a stochastic strongly convex optimization problem and propose three classes of variable sample-size stochastic first-order methods including the standard stochastic gradient descent method, its accelerated variant,…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
We present a conceptually clear and algorithmically useful framework for parameterizing the costs of tensor network contraction. Our framework is completely general, applying to tensor networks with arbitrary bond dimensions, open legs, and…
As a structured prediction task, scene graph generation aims to build a visually-grounded scene graph to explicitly model objects and their relationships in an input image. Currently, the mean field variational Bayesian framework is the de…
Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement…
The distributed Kaczmarz algorithm is an adaptation of the standard Kaczmarz algorithm to the situation in which data is distributed throughout a network represented by a tree. We isolate substructures of the network and study convergence…
We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…
The deconfounder was proposed as a method for estimating causal parameters in a context with multiple causes and unobserved confounding. It is based on recovery of a latent variable from the observed causes. We disentangle the causal…
This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging…