Related papers: Limited memory predictors based on polynomial appr…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
Following the idea of the fractional space-time Fourier transform, a linear canonical space-time transform for 16-dimensional space-time $C\ell_{3,1}$-valued signals is investigated in this paper. First, the definition of the proposed…
The effectiveness of neural processes (NPs) in modelling posterior prediction maps -- the mapping from data to posterior predictive distributions -- has significantly improved since their inception. This improvement can be attributed to two…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
Recurrent Neural Networks were, until recently, one of the best ways to capture the timely dependencies in sequences. However, with the introduction of the Transformer, it has been proven that an architecture with only attention-mechanisms…
Contemporary wisdom based on empirical studies suggests that standard recurrent neural networks (RNNs) do not perform well on tasks requiring long-term memory. However, precise reasoning for this behavior is still unknown. This paper…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…
The ongoing development of quantum processors is driving breakthroughs in scientific discovery. Despite this progress, the formidable cost of fabricating large-scale quantum processors means they will remain rare for the foreseeable future,…
To effectively perform the task of next-word prediction, long short-term memory networks (LSTMs) must keep track of many types of information. Some information is directly related to the next word's identity, but some is more secondary…
We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range…
A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical…
Long-term memory is essential for persistent LLM agents, yet prevailing architectures store historical interactions as unstructured, flat text. This unconstrained storage induces provenance-role collapse, a critical failure mode where…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
Spatio-temporal data is intrinsically high dimensional, so unsupervised modeling is only feasible if we can exploit structure in the process. When the dynamics are local in both space and time, this structure can be exploited by splitting…
Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…
We propose a functional linear model to predict a response using multiple functional and longitudinal predictors and to estimate the effect lags of predictors. The coefficient functions are written as the expansion of a basis system (e.g.…
Recently, learned image compression methods have outperformed traditional hand-crafted ones including BPG. One of the keys to this success is learned entropy models that estimate the probability distribution of the quantized latent…
We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with $\sqrt{n}$-rate on the assumption that the smoothness of the functionals is larger than the…
This paper gives an overview on how to develop a dense and deep neural network for making a time series prediction. First, the history and cornerstones in Artificial Intelligence and Machine Learning will be presented. After a short…
A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular, it is shown that…