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Large language models (LLMs) excel in many natural language tasks, yet they struggle with complex mathemat-ical problem-solving, particularly in symbolic reasoning and maintaining consistent output. This study evalu-ates 10 LLMs with 7 to 8…
Advances in large language models (LLMs) are accelerating discovery in molecular science. However, adapting molecular information to the serialized, token-based processing of LLMs remains a key challenge. Compared to other representations,…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
We study spherical charged black holes in the presence of a cosmological constant with corrections motivated by the theory of loop quantum gravity. The effective theory is constructed at the Hamiltonian level by introducing certain…
With the expanding application of Large Language Models (LLMs) in various domains, it becomes imperative to comprehensively investigate their unforeseen behaviors and consequent outcomes. In this study, we introduce and systematically…
Monocular depth estimation (MDE) has witnessed remarkable progress driven by Convolutional Neural Networks and transformer-based architectures. However, these approaches typically treat the problem as a generic image-to-image regression on…
The transformer architecture has become the foundation of modern Large Language Models (LLMs), yet its theoretical properties are still not well understood. As with classic neural networks, a common approach to improve these models is to…
Recent advancements in multimodal large language models (MLLMs) have demonstrated remarkable capabilities in processing diverse data types, yet significant disparities persist between human cognitive processes and computational approaches…
LLM pre-training efficacy increasingly depends on data composition rather than sheer volume. Yet, optimal mixing is hindered by categorization flaws: human taxonomies suffer from ontological misalignment, and Euclidean clustering fails to…
The problem of resolution of singularities in positive characteristic can be reformulated as follows: Fix a hypersurface $X$, embedded in a smooth scheme, with points of multiplicity at most $n$. Let an $n$-sequence of transformations of…
In this paper, we develop the blow-up analysis and establish the energy quantization for solutions to super-Liouville type equations on Riemann surfaces with conical singularities at the boundary. In other problems in geometric analysis,…
We consider the semilinear wave equation with power nonlinearity in one space dimension. Given a blow-up solution with a characteristic point, we refine the blow-up behavior first derived by Merle and Zaag. We also refine the geometry of…
Internal representations within deep neural architectures encode high-dimensional abstractions of linguistic structures, yet they often exhibit inefficiencies in feature distribution, limiting expressiveness and adaptability. Contextual…
Our concerns here are blow-up solutions for ODEs with exponential nonlinearity from the viewpoint of dynamical systems and their numerical validations. As an example, the finite difference discretization of $u_t = u_{xx} + e^{u^m}$ with the…
Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have…
In this paper, we study general Toda systems with homogeneous Neumann boundary conditions on Riemann surfaces. Assuming the surface satisfies the ``$k$-symmetric'' condition, we construct a family of bubbling solutions using singular…
The idea in the title is to blow up a finite structure, replacing each 'colour or atom' by infinitely many, using blurs to represent the resulting term algebra, but the blurs are not enough to blur the structure of the finite structure in…
Large language models (LLMs) have demonstrated strong reasoning capabilities in text-based mathematical problem solving; however, when adapted to visual reasoning tasks, particularly geometric problem solving, their performance…
Enabling large language models (LLMs) to effectively process and reason with graph-structured data remains a significant challenge despite their remarkable success in natural language tasks. Current approaches either convert graph…
Despite the evident necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of topological quantum logic gates had arguably remained shaky, both regarding their physical realization as well…