相关论文: NOETHER: A Constructive Framework for Metamorphic …

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

Positron Emission Tomography (PET) is an important molecular imaging tool widely used in medicine. Traditional PET systems rely on complete detector rings for full angular coverage and reliable data collection. However, incomplete-ring PET…

Large language models have demonstrated remarkable capabilities across many tasks, yet face significant challenges when dealing with recursive reasoning problems, those requiring the resolution of nested hierarchical structures. While prior…

The extraction of geoelectric structural information from airborne transient electromagnetic(ATEM)data primarily involves data processing and inversion. Conventional methods rely on empirical parameter selection, making it difficult to…

Contemporary AI systems achieve extraordinary performance yet remain opaque and non-verifiable, creating a crisis of trust for safety-critical deployment. We introduce MathLedger, a substrate for verifiable machine cognition that integrates…

We introduce Mercator, a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The method assumes that the structure of networks is well described by the Popularity$\times$Similarity…

For a countably decomposable finite von Neumann algebra $\mathscr{R}$, we show that any choice of a faithful normal tracial state on $\mathscr{R}$ engenders the same measure topology on $\mathscr{R}$ in the sense of Nelson (J. Func. Anal.,…

Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial…

Transformers are a widespread and successful model architecture, particularly in Natural Language Processing (NLP) and Computer Vision (CV). The essential innovation of this architecture is the Attention Mechanism, which solves the problem…

In this paper, we present a complete Noether Symmetry analysis in the framework of scalar-tensor cosmology. Specifically, we consider a non-minimally coupled scalar field action embedded in the FLRW spacetime and provide a full set of…

Dimensionality reduction is essential in simulation-based shape design, where high-dimensional parameterizations hinder optimization, surrogate modeling, and systematic design-space exploration. Parametric Model Embedding (PME) addresses…

Transformer has been successfully used in practical applications, such as ChatGPT, due to its powerful advantages. However, users' input is leaked to the model provider during the service. With people's attention to privacy,…

Metamorphic testing (MT) is a general approach for the testing of a specific kind of software systems -- so-called ``non-testable'', where the ``classical'' testing approaches are difficult to apply. MT is an effective approach for…

Matrices often represent important information in scientific applications and are involved in performing complex calculations. But systematically testing these applications is hard due to the oracle problem. Metamorphic testing is an…

A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank…

Operating LLMs as coordinated multi-agent research systems over multi-hour runs surfaces failure modes that single-shot evaluation cannot: upstream providers throttle without warning, sub-agents drift the task to fit accessible tools,…

Recent years have witnessed a substantial increase in the use of deep learning to solve various natural language processing (NLP) problems. Early deep learning models were constrained by their sequential or unidirectional nature, such that…

Internet-scale distributed systems often replicate data at multiple geographic locations to provide low latency and high availability. The Conflict-free Replicated Data Type (CRDT) is a framework that provides a principled approach to…

We propose a new neural network framework, termed Neural Network Machine Regression (NNMR), which integrates trainable input gating and adaptive depth regularization to jointly perform feature selection and function estimation in an…

Fault tree analysis is a well-known technique in reliability engineering and risk assessment, which supports decision-making processes and the management of complex systems. Traditionally, fault tree (FT) models are built manually together…