Weibull weight-scale parameter λ evolves during AdamW training, with alignment, injection, and decay forces driving its growth and relaxation.
problem Understanding the evolution of the Weibull weight-scale parameter λ during AdamW training. method Deriving a leading-order three-force decomposition of the squared weight norm from AdamW updates.
result The alignment force dominates the rise phase, contributing 88-94% of the absolute force budget across four random seeds.
New regularizer improves neural network robustness and generalization.
problem Ineffective weight decay for networks with homogeneous activation functions.
method Proposes an invariant regularizer to penalize intrinsic weight norms.
result Improves generalization and adversarial robustness on various datasets.
Using the monotonicity formulas of Colding and Minicozzi, we prove that on any complete, non-parabolic Riemannian manifold (M3,g) with non-negative Ricci curvature, the asymptotic weighted scaling invariant integral of scalar curvature has an explicit bound in form of asymptotic volume ratio.
A new robust scaling approach improves downstream metabolomics analysis.
problem Challenges in choosing scaling techniques for metabolomics data.
method Introduces a weighted scaling approach robust to outliers.
result The proposed method outperforms traditional scaling techniques in both outlier-free and outlier-present datasets.
WISCA generates consensus explanations from conflicting model-agnostic interpretability methods.
problem Conflicting explanations from diverse interpretability algorithms.
method WISCA integrates class probability and normalized attributions to generate consistent explanations.
result WISCA consistently aligns with the most reliable individual method, improving explanation reliability.
Wavelet Kolmogorov-Arnold Networks improve federated learning performance.
problem Improving performance in federated learning with heterogeneous data.
method Implemented Wav-KAN with CWT and DWT for multiresolution capability, integrating wavelet-based activation functions.
result Significant improvements in computational efficiency, robustness, and accuracy in federated learning.
The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we …
Transfer learning from natural image datasets, particularly ImageNet, using standard large models and corresponding pretrained weights has become a de-facto method for deep learning applications to medical imaging. However, there are fundamental differences in data sizes, features and task specifications between natura…
A neuron is a basic physiological and computational unit of the brain. While much is known about the physiological properties of a neuron, its computational role is poorly understood. Here we propose to view a neuron as a signal processing device that represents the incoming streaming data matrix as a sparse vector of …
A new factor analysis method using ICA reduces portfolio concentration and diversifies excess kurtosis.
problem Standard factor analysis suffers from issues with pairwise correlations of asset returns.
method Identifies factors based on non-Gaussianity instead of variance, using ICA.
result Fat-tailed portfolios significantly reduce portfolio concentration and winner-takes-all problem.
Neural networks learn patterns in random data, improving downstream performance.
problem Understanding what deep networks learn with random labels.
method Analytical and empirical study of convolutional and fully connected networks pre-trained on random labels.
result Pre-trained networks on random labels transfer faster to real datasets, despite specialization effects.
The study examines numerical aspects of Karhunen-Loève expansions for stochastic processes.
problem Constructing Karhunen-Loève expansions for second-order stochastic processes.
method Spectral decomposition of covariance operator via Fredholm integral equation, discretization, singular value decomposition of weight-scaled sample matrix.
result Consistent solutions for model-based and data-driven KLE construction, characterized by convergence of SVD-based eigenvalue estimates and KL coefficients distributions.
We reparametrize ReLU NNs as splines to understand their learning dynamics.
problem Understanding the learning dynamics and inductive bias of neural networks.
method Reparametrize ReLU NNs as continuous piecewise linear splines to study learning dynamics.
result Standard weight initializations yield very flat functions, leading to strength and type of implicit regularization.
The study analyzes how covariance estimation errors affect the global minimum-variance portfolio under heavy-tailed distributions.
problem The impact of covariance estimation errors on the global minimum-variance portfolio under heavy-tailed distributions.
method Characterization of covariance-estimation error's effect on GMVP suboptimality, derivation of regret identity and bound, application to heavy-tailed returns.
result The decision geometry of GMVP regret is invariant to a (p-1)-dimensional projection of the error matrix, with invariance to the covariance-scale direction as an exact special case.
Graph Neural Networks (graph NNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up many layers and add non-lineality. To tackle this problem, we investigate the expressive power of g…
This paper explains how batch normalization auto-tunes the regularization parameter based on data statistics.
problem Batch normalization accelerates deep learning training but the exact relationship to regularization is unclear.
method Theoretical analysis and empirical validation of batch normalization's role in auto-tuning the regularization parameter.
result Batch normalization auto-tunes the regularization parameter based on data statistics.
A new metric framework for weighted projective spaces improves clustering and analysis.
problem Proximity measurement in weighted projective spaces with intrinsic scaling and topology.
method Hierarchical clustering framework based on Finsler geometry, quotienting weighted scaling action.
result The constructed metric dF satisfies the triangle inequality, making it a genuine metric.