Perturbative analysis of the breathing circle billiard map combined with a quantitative Mather converse-KAM criterion excludes invariant Lipschitz graphs and establishes positive topological entropy for sufficiently small angular momentum.
Some methods for classification and analysis of multivariate observations
9 Pith papers cite this work. Polarity classification is still indexing.
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Inflating the min-norm interpolator by a factor >1 reduces generalization error in linear regression with anisotropic covariances when d/n diverges to infinity.
Qlustering extracts cluster assignments for unlabeled data directly from steady-state transport currents in quantum networks using the GKSL master equation, enabling tomography-free unsupervised learning.
Kernel Affine Hull Machines map lexical features to semantic embeddings via RKHS and least-mean-squares, outperforming adapters in reconstruction and retrieval metrics while reducing latency 8.5-fold on a legal benchmark.
Mixup barcodes and summary statistics (total mixup, total percentage mixup) are defined to capture geometric-topological interactions between point sets and applied to assess class disentanglement in embeddings.
AVVA is a new framework adapting verbal analysis for classroom discourse with triangulation across ten steps and a four-criterion validation scheme for temporal stability, applied to 23 hours of recordings.
The effectiveness of dimensionality reduction before clustering depends on matching the specific technique and target dimension count to the data geometry and the clustering algorithm used.
A survey that taxonomizes data mixing strategies for LLM pretraining into static rule-based, learning-based, and dynamic adaptive families while highlighting transferability challenges and evaluation gaps.
Derives semiclassical propagators for Boltzmann-Gibbs, S± and Tsallis statistics via integrated Quantropy, yielding modified wave functions consistent with q-Schrödinger equation for free particle and corrections for harmonic oscillator.
citing papers explorer
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Breaking of invariant curves: from the Fermi-Ulam map to the breathing circle billiard
Perturbative analysis of the breathing circle billiard map combined with a quantitative Mather converse-KAM criterion excludes invariant Lipschitz graphs and establishes positive topological entropy for sufficiently small angular momentum.
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Shrinkage to Infinity: Reducing Test Error by Inflating the Minimum Norm Interpolator in Linear Models
Inflating the min-norm interpolator by a factor >1 reduces generalization error in linear regression with anisotropic covariances when d/n diverges to infinity.
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Qlustering for Data Clustering via Network-Based Quantum Transport
Qlustering extracts cluster assignments for unlabeled data directly from steady-state transport currents in quantum networks using the GKSL master equation, enabling tomography-free unsupervised learning.
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Kernel Affine Hull Machines for Compute-Efficient Query-Side Semantic Encoding
Kernel Affine Hull Machines map lexical features to semantic embeddings via RKHS and least-mean-squares, outperforming adapters in reconstruction and retrieval metrics while reducing latency 8.5-fold on a legal benchmark.
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Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds
Mixup barcodes and summary statistics (total mixup, total percentage mixup) are defined to capture geometric-topological interactions between point sets and applied to assess class disentanglement in embeddings.
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Audio Video Verbal Analysis (AVVA) for Capturing Classroom Dialogues
AVVA is a new framework adapting verbal analysis for classroom discourse with triangulation across ten steps and a four-criterion validation scheme for temporal stability, applied to 23 hours of recordings.
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Assessing the impact of dimensionality reduction on clustering performance -- a systematic study
The effectiveness of dimensionality reduction before clustering depends on matching the specific technique and target dimension count to the data geometry and the clustering algorithm used.
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Data Mixing for Large Language Models Pretraining: A Survey and Outlook
A survey that taxonomizes data mixing strategies for LLM pretraining into static rule-based, learning-based, and dynamic adaptive families while highlighting transferability challenges and evaluation gaps.
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Quantum implications of non-extensive statistics
Derives semiclassical propagators for Boltzmann-Gibbs, S± and Tsallis statistics via integrated Quantropy, yielding modified wave functions consistent with q-Schrödinger equation for free particle and corrections for harmonic oscillator.