Related papers: Laplace Transform Integration of a Baroclinic Mode…

We introduce the Lattice Deduction Transformer (LDT), a recurrent transformer that approximates logically sound deduction by projecting its latent state through a lattice between forward passes. We train on-policy in a process that mirrors…

In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…

Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function…

We present LTLS, a technique for multiclass and multilabel prediction that can perform training and inference in logarithmic time and space. LTLS embeds large classification problems into simple structured prediction problems and relies on…

Spatio-temporal forecasting plays a crucial role in various sectors such as transportation systems, logistics, and supply chain management. However, existing methods are limited by their ability to handle large, complex datasets. To…

We propose an innovative, learnable two-sided short-time Laplace transform (STLT) mechanism to supplant the traditional self attention in transformer-based LLMs. Our STLT introduces trainable parameters for each Laplace node, enabling…

Large language models (LLMs) have demonstrated their effectiveness in multivariate time series classification (MTSC). Effective adaptation of LLMs for MTSC necessitates informative data representations. Existing LLM-based methods directly…

Large-scale cosmological simulations are an indispensable tool for modern cosmology. To enable model-space exploration, fast and accurate predictions are critical. In this paper, we show that the performance of such simulations can be…

Time series forecasting is important for applications spanning energy markets, climate analysis, and traffic management. However, existing methods struggle to effectively integrate exogenous texts and align them with the probabilistic…

Recent studies have attempted to refine the Transformer architecture to demonstrate its effectiveness in Long-Term Time Series Forecasting (LTSF) tasks. Despite surpassing many linear forecasting models with ever-improving performance, we…

This paper is concerned with the application of time domain boundary integral methods(TDBIMs) to a non-stationary boundary value problem for the thermo-elasto-dynamic equations, based on the Lubich approach via the Laplace transform.…

Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent…

The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…

In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong…

The time integration of semilinear parabolic problems by exponential methods of different kinds is considered. A new algorithm for the implementation of these methods is proposed. The algorithm evaluates the operators required by the…

The development of efficient sampling algorithms catering to non-Euclidean geometries has been a challenging endeavor, as discretization techniques which succeed in the Euclidean setting do not readily carry over to more general settings.…

Large Language Models (LLMs) are powerful but often too slow and costly for real-world use during inference. Looped transformers save on parameters by reusing the same weights for multiple computational steps, or "loops." However, this…

Training state-of-the-art vision models has become prohibitively expensive for researchers and practitioners. For the sake of accessibility and resource reuse, it is important to focus on adapting these models to a variety of downstream…

This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…