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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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134268401535 · Jun 202019922001200920172026
48 results for multiple scales

This work extends the scaling law to multiple and kernel regression, challenging traditional machine learning principles.

problem Challenging traditional machine learning wisdom with scaling law in large practical models.
method Demonstrates the scaling law in multiple and kernel regression settings.
result The scaling law extends to multiple and kernel regression, providing deeper insights into LLMs.

Paper presents an efficient algorithm for learning minimax risk classifiers with large-scale data.

problem Efficient learning of minimax risk classifiers for large-scale data with multiple classes.
method Combination of constraint and column generation for efficient learning.
result 10x speedup for general large-scale data and 100x speedup with many classes.

This paper improves traditional Markowitz optimization by considering variance at multiple time scales.

problem Traditional Markowitz optimization limits to a single time scale, ignoring variance across different frequencies.
method Introduces multifrequency optimization allowing specification of target Hurst exponents across multiple time scales.
result Effective risk management strategy that aligns with investor preferences at various time scales.

HSSE framework embeds single-cell RNA-seq data at multiple scales.

problem Capturing heterogeneous local structure in single-cell RNA-seq data.
method Hierarchical sheaf spectral embedding (HSSE) framework.
result HSSE achieves competitive or improved performance in single-cell RNA-seq data representation learning.

Proposes a new hyperprior and predictive criterion for weakly informative hyperprior in relevance vector machine.

problem Capturing non-homogeneous data structure with limited kernel functions.
method Uses inverse gamma hyperprior with a shape parameter close to zero and a scale parameter not close to zero. Applies multiple kernel method with different widths. Proposes extended predictive information criterion for scale parameter selection.
result Obtains a multiple kernel relevance vector regression model with good predictive accuracy.

The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of areas of complex geometric analysis. Relations with other parts of mathematics are …

2006-10-24abs ↗pdf ↗

Bayesian optimization speeds up bioprocess development across scales.

problem Costly and complex bioprocess development across scales and biocatalyst selection.
method Multi-fidelity batch Bayesian optimization framework integrating Gaussian Processes and mixed-variable optimization.
result Reduction in experimental costs and increased yield in bioprocess optimization.

Framework learns surrogates for molecular dynamics across multiple time-scales.

problem Stable molecular dynamics simulations require small time-steps, but long-time-scale moments need repeated simulations.
method Implicit Transfer Operator Learning with denoising diffusion probabilistic models and SE(3) equivariant architecture.
result Models can generate self-consistent stochastic dynamics across multiple time-scales.

Flexible empirical Bayes for large-scale multiple linear regression.

problem Large-scale multiple linear regression with flexible priors and efficient computation.
method Adaptive shrinkage priors combined with variational approximations for hyperparameter estimation.
result The posterior mean from the empirical Bayes method solves a penalized regression problem.

This work studies scaling laws for low-precision training in high-dimensional linear regression.

problem Optimizing trade-off between model quality and training costs in high-dimensional linear regression.
method Theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework, analyzing multiplicative and additive quantization.
result Multiplicative quantization maintains full-precision model size, while additive quantization reduces effective model size.

Fast and accurate MRI image reconstruction from undersampled data is crucial in clinical practice. Deep learning based reconstruction methods have shown promising advances in recent years. However, recovering fine details from undersampled data is still challenging. In this paper, we introduce a novel deep learning bas…

2019-12-02abs ↗pdf ↗

New asymptotic e-values improve inference by eliminating data-dependent scaling inefficiency.

problem Data-dependent scaling inefficiency in existing asymptotic e-values.
method Drawing on Bentkus's near-optimal concentration inequalities, introduce Bentkus-type asymptotic e-values.
result Bentkus-type asymptotic e-values consistently deliver sharper inference than existing alternatives.

The paper analyzes learning curves for kernel ridge regression with dot-product kernels.

problem Understanding the learning curves for different scaling regimes of data and model.
method Precise formulas for mean test error, bias, and variance in the mom o\infty with m/drm/d^r constant regime.
result A peak in the learning curve at mdr/r!m \approx d^r/r! for any integer rr.

Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales, which do not comply with the nature of dynamical temporal patterns among sequences…

2019-02-15abs ↗pdf ↗

This dissertation advances scalable Gaussian processes using iterative methods and pathwise conditioning.

problem The classical Gaussian process formulation is not scalable for large datasets and modern hardware.
method Combining iterative methods and pathwise conditioning to improve scalability.
result Significantly reduced memory requirements and facilitated application to larger datasets.

Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting findings, such as the inverse cubic law in the tails of stock price fluctuation di…

2018-03-22abs ↗pdf ↗

Corrupting the input and hidden layers of deep neural networks (DNNs) with multiplicative noise, often drawn from the Bernoulli distribution (or 'dropout'), provides regularization that has significantly contributed to deep learning's success. However, understanding how multiplicative corruptions prevent overfitting ha…

2015-06-10abs ↗pdf ↗

We analyze the eigenvalue distribution of a neural network's kernel under specific scaling.

problem Analyzing the eigenvalue distribution of the Neural Tangent Kernel (NTK) of a neural network.
method Asymptotic analysis of the NTK matrix under given scaling conditions.
result The eigenvalue distribution is described as a free multiplicative convolution of the Marchenko-Pastur distribution and a deterministic distribution.

SHAKE-GNN scales GNNs for large graphs with multi-scale representations.

problem Scaling Graph Neural Networks (GNNs) to large graphs.
method SHAKE-GNN uses a hierarchy of Kirchhoff Forests for stochastic multi-resolution graph decompositions.
result SHAKE-GNN achieves competitive performance on large-scale graph classification benchmarks.

Study learning from multiple thinkers providing step-by-step solutions to problems.

problem Learning from multiple, possibly different, thinkers providing step-by-step solutions to problems.
method Active learning algorithm that uses CoT data from multiple thinkers and end-result data.
result Learning can be hard from CoT supervision provided by two or a few different thinkers, but a generic algorithm can learn efficiently.

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower …

2019-05-16abs ↗pdf ↗

Unintended effects from scaling neural network outputs with adaptive learning rates.

problem Adaptive learning rate optimization's behavior is altered by output scaling, leading to misinterpretation.
method Presented a modified optimization algorithm to mitigate unintended effects.
result Adaptive learning rate's effectiveness is significantly impacted by output scaling, especially for small scaling factors.

Detects singularities in complex data to improve machine learning models.

problem Real-world data often contains non-manifold structures (singularities) that can mislead machine learning models.
method Develops a topological framework to quantify local intrinsic dimension and Euclidicity score for multiple scales.
result Identifies singularities and captures local geometric complexity in image data.

The modern scale of data has brought new challenges to Bayesian inference. In particular, conventional MCMC algorithms are computationally very expensive for large data sets. A promising approach to solve this problem is embarrassingly parallel MCMC (EP-MCMC), which first partitions the data into multiple subsets and r…

2015-06-10abs ↗pdf ↗

In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of addition/multiplications and even avoiding multiplications altogether. We base our work on facto…

2018-12-09abs ↗pdf ↗