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Paper#Dynamical Systems, Koopman Operator, Spectral Analysis, Data-Driven Methods🔬 ResearchAnalyzed: Jan 3, 2026 06:39

Data-Driven Spectral Analysis with Pseudo-Resolvent Koopman Operator

Published:Dec 31, 2025 16:33
1 min read
ArXiv

Analysis

This paper introduces a data-driven method to analyze the spectrum of the Koopman operator, a crucial tool in dynamical systems analysis. The method addresses the problem of spectral pollution, a common issue in finite-dimensional approximations of the Koopman operator, by constructing a pseudo-resolvent operator. The paper's significance lies in its ability to provide accurate spectral analysis from time-series data, suppressing spectral pollution and resolving closely spaced spectral components, which is validated through numerical experiments on various dynamical systems.
Reference

“The method effectively suppresses spectral pollution and resolves closely spaced spectral components.”

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Research Paper#Quantum Physics, Entanglement, Quantum Criticality🔬 ResearchAnalyzed: Jan 3, 2026 18:56

Entanglement Growth in Quantum Critical Systems

Published:Dec 29, 2025 10:43
1 min read
ArXiv

Analysis

This paper investigates entanglement dynamics in fermionic systems using imaginary-time evolution. It proposes a new scaling law for corner entanglement entropy, linking it to the universality class of quantum critical points. The work's significance lies in its ability to extract universal information from non-equilibrium dynamics, potentially bypassing computational limitations in reaching full equilibrium. This approach could lead to a better understanding of entanglement in higher-dimensional quantum systems.
Reference

“The corner entanglement entropy grows linearly with the logarithm of imaginary time, dictated solely by the universality class of the quantum critical point.”

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Paper#LLM🔬 ResearchAnalyzed: Jan 3, 2026 19:07

Model Belief: A More Efficient Measure for LLM-Based Research

Published:Dec 29, 2025 03:50
1 min read
ArXiv

Analysis

This paper introduces "model belief" as a more statistically efficient measure derived from LLM token probabilities, improving upon the traditional use of LLM output ("model choice"). It addresses the inefficiency of treating LLM output as single data points by leveraging the probabilistic nature of LLMs. The paper's significance lies in its potential to extract more information from LLM-generated data, leading to faster convergence, lower variance, and reduced computational costs in research applications.
Reference

“Model belief explains and predicts ground-truth model choice better than model choice itself, and reduces the computation needed to reach sufficiently accurate estimates by roughly a factor of 20.”

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Research Paper#Quantum Computing, Machine Learning🔬 ResearchAnalyzed: Jan 3, 2026 23:55

Machine Learning for Quantum Entanglement Quantification

Published:Dec 26, 2025 06:46
1 min read
ArXiv

Analysis

This paper explores the application of supervised machine learning to quantify quantum entanglement, a crucial resource in quantum computing. The significance lies in its potential to estimate entanglement from measurement outcomes, bypassing the need for complete state information, which is a computationally expensive process. This approach could provide an efficient tool for characterizing entanglement in quantum systems.
Reference

“Our models predict entanglement without requiring the full state information.”

PermalinkArXiv
Research#llm🔬 ResearchAnalyzed: Dec 25, 2025 04:37

Bayesian Empirical Bayes: Simultaneous Inference from Probabilistic Symmetries

Published:Dec 24, 2025 05:00
1 min read
ArXiv Stats ML

Analysis

This paper introduces Bayesian Empirical Bayes (BEB), a novel approach to empirical Bayes methods that leverages probabilistic symmetries to improve simultaneous inference. It addresses the limitations of classical EB theory, which primarily focuses on i.i.d. latent variables, by extending EB to more complex structures like arrays, spatial processes, and covariates. The method's strength lies in its ability to derive EB methods from symmetry assumptions on the joint distribution of latent variables, leading to scalable algorithms based on variational inference and neural networks. The empirical results, demonstrating superior performance in denoising arrays and spatial data, along with real-world applications in gene expression and air quality analysis, highlight the practical significance of BEB.
Reference

“"Empirical Bayes (EB) improves the accuracy of simultaneous inference \"by learning from the experience of others\" (Efron, 2012)."”

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Research#computer vision📝 BlogAnalyzed: Dec 29, 2025 02:09

Introduction to Neural Radiance Fields (NeRF)

Published:Dec 4, 2025 04:35
1 min read
Zenn CV

Analysis

This article provides a concise introduction to Neural Radiance Fields (NeRF), a technology developed by Google Research in 2020. NeRF utilizes neural networks to learn and reconstruct 3D scenes as continuous functions, enabling the generation of novel views from arbitrary viewpoints given multiple 2D images and their corresponding camera poses. The article highlights the core concept of representing 3D scenes as continuous functions, a significant advancement in the field of computer vision and 3D reconstruction. The article's brevity suggests it's an introductory overview, suitable for those new to the topic.
Reference

“NeRF (Neural Radiance Fields) is a technique that learns and reconstructs radiance fields of 3D space using neural networks.”

PermalinkZenn CV
Research#llm📝 BlogAnalyzed: Jan 3, 2026 06:48

Running an Embedded Vector Database in 10 Lines of Code

Published:Jun 6, 2023 00:00
1 min read
Weaviate

Analysis

The article highlights the ease of use of Weaviate, emphasizing its ability to run locally from client code. This suggests a focus on accessibility and developer convenience. The brevity of the title implies a quick and simple process.
Reference

“The Weaviate server can be run locally directly from client code.”

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