Related papers: Scalar Levin-Type Sequence Transformations

Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…

Inspired by two basic mechanisms in animal visual systems, we introduce a feature transform technique that imposes invariance properties in the training of deep neural networks. The resulting algorithm requires less parameter tuning, trains…

We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…

Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of…

Determining whether a program terminates is a core challenge in program analysis with direct implications for correctness, verification, and security. We investigate whether transformer architectures can recognise termination patterns…

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…

We establish several closed pricing formula for various path-independent payoffs, under an exponential L\'evy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools…

Support vector machine (SVM) training is an active research area since the dawn of the method. In recent years there has been increasing interest in specialized solvers for the important case of linear models. The algorithm presented by…

Shapelets are phase independent subsequences designed for time series classification. We propose three adaptations to the Shapelet Transform (ST) to capture multivariate features in multivariate time series classification. We create a…

Linear systems of equations can be found in various mathematical domains, as well as in the field of machine learning. By employing noisy intermediate-scale quantum devices, variational solvers promise to accelerate finding solutions for…

We propose an approach for improving sequence modeling based on autoregressive normalizing flows. Each autoregressive transform, acting across time, serves as a moving frame of reference, removing temporal correlations, and simplifying the…

The correlation between a random sequence and its transformed sequences is studied. In the case of a permutation operation or, in other word, the shuffling operation, it is shown that the correlation can be so small that the sequences can…

We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…

Irregularly sampled time series are increasingly prevalent, particularly in medical domains. While various specialized methods have been developed to handle these irregularities, effectively modeling their complex dynamics and pronounced…

Learning image transformations is essential to the idea of mental simulation as a method of cognitive inference. We take a connectionist modeling approach, using planar neural networks to learn fundamental imagery transformations, like…

Scaling sequence length has become a critical demand in the era of large language models. However, existing methods struggle with either computational complexity or model expressivity, rendering the maximum sequence length restricted. To…

We introduce a family of sequence transformations, defined via partial Bell polynomials, that may be used for a systematic study of a wide variety of problems in enumerative combinatorics. This family includes some of the transformations…

The dominant approach to sequence generation is to produce a sequence in some predefined order, e.g. left to right. In contrast, we propose a more general model that can generate the output sequence by inserting tokens in any arbitrary…

Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by…

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…