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One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical…
Attention has been proved to be an efficient mechanism to capture long-range dependencies. However, so far it has not been deployed in invertible networks. This is due to the fact that in order to make a network invertible, every component…
This paper proposes a variant of the method of Gu\'edon and Verhynin for estimating the cluster matrix in the Mixture of Gaussians framework via Semi-Definite Programming. A clustering oriented embedding is deduced from this estimate. The…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
Motivated by the ever-increasing demands for limited communication bandwidth and low-power consumption, we propose a new methodology, named joint Variational Autoencoders with Bernoulli mixture models (VAB), for performing clustering in the…
While Large Language Models (LLMs) become ever more dominant, classic pre-trained word embeddings sustain their relevance through computational efficiency and nuanced linguistic interpretation. Drawing from recent studies demonstrating that…
Invertible logic can operate in one of two modes: 1) a forward mode, in which inputs are presented and a single, correct output is produced, and 2) a reverse mode, in which the output is fixed and the inputs take on values consistent with…
This paper introduces Least Volume (LV)--a simple yet effective regularization method inspired by geometric intuition--that reduces the number of latent dimensions required by an autoencoder without prior knowledge of the dataset's…
Adaptive lattice Boltzmann methods (LBMs) are based on velocity discretizations that self-adjust to local macroscopic conditions such as velocity and temperature. While this feature improves the accuracy and the stability of LBMs for large…
Algorithms are developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
We consider the probabilistic applicative bisimilarity (PAB), a coinductive relation comparing the applicative behaviour of probabilistic untyped lambda terms according to a specific operational semantics. This notion has been studied with…
Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretization error. However, the method requires the evaluation of…
There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…
Large-scale embedding-based retrieval (EBR) is the cornerstone of search-related industrial applications. Given a user query, the system of EBR aims to identify relevant information from a large corpus of documents that may be tens or…
One of the main methods for computational interpretation of a text is mapping it into a vector in some embedding space. Such vectors can then be used for a variety of textual processing tasks. Recently, most embedding spaces are a product…
Various reversible deep neural networks (DNN) models have been proposed to reduce memory consumption in the training process. However, almost all existing reversible DNNs either require special non-standard architectures or are constructed…
We present randUBV, a randomized algorithm for matrix sketching based on the block Lanzcos bidiagonalization process. Given a matrix $\bf{A}$, it produces a low-rank approximation of the form ${\bf UBV}^T$, where $\bf{U}$ and $\bf{V}$ have…
Traditional plane-based clustering methods measure the cost of within-cluster and between-cluster by quadratic, linear or some other unbounded functions, which may amplify the impact of cost. This letter introduces a ramp cost function into…