相关论文: A consistent formalism for the Thomas-Ehrman Level…
Autoformalization aims to convert informal mathematical proofs into machine-verifiable formats, bridging the gap between natural and formal languages. However, ensuring semantic alignment between the informal and formalized statements…
Despite their empirical success, the internal mechanism by which transformer models align tokens during language processing remains poorly understood. This paper provides a mechanistic and theoretical explanation of token alignment in LLMs.…
Which amount of parallel resources is needed for updating a query result after changing an input? In this work we study the amount of work required for dynamically answering membership and range queries for formal languages in parallel…
Topological loss based on persistent homology has shown promise in various applications. A topological loss enforces the model to achieve certain desired topological property. Despite its empirical success, less is known about the…
Many works make the eye-catching claim that Transformers are Turing-complete. However, the literature often conflates two distinct settings: (i) a fixed Transformer system setting, in which a fixed autoregressive Transformer is coupled with…
Neural networks are widely used, yet their analysis and verification remain challenging. In this work, we present a Lean 4 formalization of neural networks, covering both deterministic and stochastic models. We first formalize Hopfield…
In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration. We use a displacement-Herrmann pressure formulation for the…
Real world applications as in industry and robotics need modelling rich and diverse automated planning problems. Their resolution usually requires coordinated and concurrent action execution. In several cases, these problems are naturally…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of…
We carry further our work [DV2] on orthonormal integrators based on Householder and Givens transformations. We propose new algorithms and pay particular attention to appropriate implementation of these techniques. We also present a suite of…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
In a previous work one of the authors proposed a simple model for studying systems under pressure based on the Thomas-Fermi (TF) model of single atom. In this work we intend to extend the previous work to more general Thomas-Fermi models…
We examine the dynamic and geometric phases of the electron in quantum mechanics using Hestenes' spacetime algebra formalism. First the standard dynamic phase formula is translated into the spacetime algebra. We then define new formulas for…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
The use of lightweight formal methods (LFM) for the development of industrial applications has become a major trend. Although the term "lightweight formal methods" has been used for over ten years now, there seems to be no common agreement…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
The typical workflow for a professional translator to translate a document from its source language (SL) to a target language (TL) is not always focused on what many language models in natural language processing (NLP) do - predict the next…