Classically, sketching has been applied to design low-memory algorithms in the streaming setting, when the input is presented to the algorithm as a sequence of updates.

Classically, sketching has been applied to design low-memory algorithms in the streaming setting, when the input is presented to the algorithm as a sequence of updates.

ARXIV PREPRINT 1 Attention-Based V ariational Framework for Joint and Individual Components Learning with Applications in Brain Network Analysis Yifei Zhang, Meimei Liu, and Zhengwu Zhang Abstract Brain organization is increasingly characterized through multiple imaging modalities, most notably structural connectivity (SC) and functional connectivity (FC). Integrating these inherently distinct yet complementary data sources is essential for uncovering the cross-modal patterns that drive behavioral phenotypes. However, effective integration is hindered by the high dimensionality and non-linearity of connectome data, complex non-linear SC-FC coupling, and the challenge of disentangling shared information from modality-specific variations. To address these issues, we propose the Cross-Modal Joint-Individual Variational Network (CM-JIVNet), a unified probabilistic framework designed to learn factorized latent representations from paired SC-FC datasets. Our model utilizes a multi-head attention fusion module to capture non-linear cross-modal dependencies while isolating independent, modality-specific signals. V alidated on Human Connectome Project Y oung Adult (HCP-Y A) data, CM-JIVNet demonstrates superior performance in cross-modal reconstruction and behavioral trait prediction. By effectively disentangling joint and individual feature spaces, CM-JIVNet provides a robust, interpretable, and scalable solution for large-scale multimodal brain analysis.

One reason for this is the intractability of analyzing NNs, ODEs and hybrid systems.

This article looks at how reasoning works in current Large Language Models (LLMs) that function using the token-completion method. It examines their stochastic nature and their similarity to human abductive reasoning. The argument is that these LLMs create text based on learned patterns rather than performing actual abductive reasoning. When their output seems abductive, this is largely because they are trained on human-generated texts that include reasoning structures. Examples are used to show how LLMs can produce plausible ideas, mimic commonsense reasoning, and give explanatory answers without being grounded in truth, semantics, verification, or understanding, and without performing any real abductive reasoning. This dual nature, where the models have a stochastic base but appear abductive in use, has important consequences for how LLMs are evaluated and applied. They can assist with generating ideas and supporting human thinking, but their outputs must be critically assessed because they cannot identify truth or verify their explanations. The article concludes by addressing five objections to these points, noting some limitations in the analysis, and offering an overall evaluation.

Transcatheter Aortic Valve Replacement (TAVR) has emerged as a minimally invasive treatment option for patients with severe aortic stenosis, a life-threatening cardiovascular condition. Multiple transcatheter heart valves (THV) have been approved for use in TAVR, but current guidelines regarding valve type prescription remain an active topic of debate. We propose a data-driven clinical support tool to identify the optimal valve type with the objective of minimizing the risk of permanent pacemaker implantation (PPI), a predominant postoperative complication. We synthesize a novel dataset that combines U.S. and Greek patient populations and integrates three distinct data sources (patient demographics, computed tomography scans, echocardiograms) while harmonizing differences in each country's record system. We introduce a leaf-level analysis to leverage population heterogeneity and avoid benchmarking against uncertain counterfactual risk estimates. The final prescriptive model shows a reduction in PPI rates of 26% and 16% compared with the current standard of care in our internal U.S. population and external Greek validation cohort, respectively. To the best of our knowledge, this work represents the first unified, personalized prescription strategy for THV selection in TAVR.

This paper presents a formal, categorical framework for analysing how humans and large language models (LLMs) transform content into truth-evaluated propositions about a state space of possible worlds W , in order to argue that LLMs do not solve but circumvent the symbol grounding problem.