Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet. Empirical and theoretical results clearly indicate th…
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48 results for “Heavy-Tailed Self-Regularization”
Random Matrix Theory (RMT) is applied to analyze weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet. Empirical and theoretical results clearly indicate that t…
AlphaPruning optimizes LLM pruning using HT-SR theory for better performance.
problem Improving pruning of large language models to reduce size without sacrificing performance.
method AlphaPruning uses HT-SR theory to allocate layerwise sparsity ratios more theoretically.
result AlphaPruning prunes LLaMA-7B to 80% sparsity with reasonable perplexity.
TempBalance boosts model performance with low data.
problem Low-data training and fine-tuning in model alignment.
method Inspired by HT-SR theory, TempBalance balances training quality across layers.
result TempBalance improves model performance as data decreases.
Introduces self-regularization for analyzing learning algorithms.
problem Analyzing and optimizing learning algorithms without explicit regularization.
method Develops a self-regularization framework for learning algorithms.
result Provides statistical analysis and minmax-optimal rates for self-regularized algorithms.
Study analyzes neural network models to understand generalization performance.
problem Understanding good generalization in neural networks.
method Analyzed a corpus of models from a public contest, breaking ALPHAHAT into scale and shape metrics.
result Identified a Simpson's paradox in metric performance across different model depths and regularization hyperparameters.
GRAC improves reinforcement learning by self-guiding and self-regularizing.
problem Learning divergence and slow updates in reinforcement learning algorithms.
method Self-regularized TD-learning and self-guided policy improvement.
result Achieved or outperformed state-of-the-art results on OpenAI gym tasks.
TempBalance improves neural network training by balancing learning rates across layers.
problem Improving neural network training performance.
method Layer-wise learning rate scheduling based on HT-SR Theory.
result TempBalance significantly outperforms ordinary SGD and state-of-the-art optimizers.
Given two or more Deep Neural Networks (DNNs) with the same or similar architectures, and trained on the same dataset, but trained with different solvers, parameters, hyper-parameters, regularization, etc., can we predict which DNN will have the best test accuracy, and can we do so without peeking at the test data? In …
NPMLE estimator automatically chooses the right model complexity for Gaussian mixtures.
problem Learning mixture models and empirical Bayes estimation with non-convex likelihoods.
method Nonparametric maximum likelihood estimator (NPMLE) using complex-analytic techniques.
result NPMLE solution has atoms with high probability, improving model complexity.
In many applications, one works with neural network models trained by someone else. For such pretrained models, one may not have access to training data or test data. Moreover, one may not know details about the model, e.g., the specifics of the training data, the loss function, the hyperparameter values, etc. Given on…
Unified theory for kernel regression generalizes well under realistic assumptions.
problem Analyzing kernel regression under realistic conditions.
method Unified theory providing rigorous bounds for various settings.
result Self-regularization phenomenon in kernel matrices enables good generalization.
Beyond Accuracy: A Unified Random Matrix Theory Diagnostic Framework for Crash Classification Modelscs.LG
Unified framework detects overfitting in crash classification models.
problem Evaluation metrics fail to detect overfitting in crash classification models.
method Random Matrix Theory and Heavy-Tailed Self-Regularization framework applied to various model types.
result Power-law exponent α reliably distinguishes well-regularized from overfit models.
CalNF models rare failures with limited data, improving safety in autonomous systems.
problem Challenges in modeling and debugging rare safety-critical failures due to limited data.
method CalNF, a self-regularized framework for posterior learning from limited data.
result Achieves state-of-the-art performance on data-limited failure modeling and inverse problems.
We propose , a novel self-regularized non-monotonic activation function which can be mathematically defined as: . As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks…
Why do Random Forests Work? Understanding Tree Ensembles as Self-Regularizing Adaptive Smoothersstat.ML
Paper explains how tree ensembles improve predictions by smoothing and regulating smoothness.
problem Understanding why tree ensembles perform well despite their complexity.
method Interpreting tree ensembles as adaptive and self-regularizing smoothers.
result Ensemble trees make more smooth predictions than individual trees and adjust smoothness based on input dissimilarity.
LEAK learns from mistakes to improve point cloud segmentation.
problem Improving point cloud semantic segmentation performance.
method Coarse-to-fine clustering, class-conditional prototypical feature alignment, fairness weighting.
result State-of-the-art performances on different architectures, datasets, and tasks.
Novel anti-grokking phase discovered in neural networks, revealed by HTSR layer quality metric.
problem Understanding and detecting overfitting in neural networks.
method 3-layer MLP, weight decay, HTSR layer quality metric , correlation traps, Kolmogorov–Smirnov tests.
result Anti-grokking phase detected late in training, revealed by and correlation traps.
Study improves ERM for heavy-tailed data with dependent inputs.
problem Empirical Risk Minimization with dependent and heavy-tailed data.
method Extending risk bounds for ERM with heavy-tailed, dependent data.
result Established risk bounds for ERM with dependent and heavy-tailed data.
Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliersstat.ML
Efficiently estimates sparse linear regression with heavy-tailed and outlier-contaminated data.
problem Estimating sparse linear regression coefficients with heavy-tailed and outlier-contaminated data.
method Efficient computation of estimators with sharp error bounds.
result Sharp error bounds for efficient estimators.
Is AdamW effective under heavy-tailed noise?
problem Stochastic gradient noise in LLM pretraining is typically heavy-tailed.
method Formulate as an open problem, prove a positive weighted-metric benchmark, and give a corridor lower-bound mechanism.
result No rigorous convergence theory for AdamW established in heavy-tailed regime.
Self-regulating annealing improves sampling from heavy-tailed datasets.
problem Sampling from heavy-tailed distributions using diffusion models.
method Proposed an SDE-based sampler with a state-dependent diffusion coefficient.
result State dependence induces a self-regulating annealing mechanism.
New diffusion models capture heavy-tailed distributions better.
problem Diffusion models struggle with rare or extreme events in heavy-tailed distributions.
method Repurposed diffusion framework using multivariate Student-t distributions, tailored perturbation kernel, and -divergence.
result Our models generate rare and extreme events more effectively than standard diffusion models.
New concentration inequalities for tensors with heavy-tailed coefficients.
problem Developing bounds for Euclidean functions of tensors with sub-Weibull distributions.
method Extending concentration inequalities to sub-Weibull random tensors, using new inequalities for heavy-tailed random variables and martingale analysis.
result Established a phase transition between sub-gaussian and heavy-tailed regimes for Euclidean functions of tensors.
New models explain heavy-tailed behavior in neural networks.
problem Heavy-tailed spectral densities in neural networks.
method High-temperature Marchenko-Pastur (HTMP) ensemble models.
result Heavy-tailed behavior arises from three factors: data structure, training temperature, and eigenvector entropy.
New PAC-Bayes bounds for heavy-tailed losses using supermartingales.
problem Extending PAC-Bayes bounds to heavy-tailed losses.
method Using supermartingales and bounded variance assumption.
result PAC-Bayes generalization bounds for heavy-tailed losses.
New bounds for heavy-tailed SDEs without info-theory terms.
problem Understanding generalization of heavy-tailed stochastic optimization.
method Fractional Fokker-Planck equation to estimate entropy flows.
result High-probability bounds with better dimension dependence.
Study on error probability for classification of heavy-tailed renewal processes.
problem Error probability in classification of heavy-tailed renewal processes.
method Asymptotic expressions for Bhattacharyya bound on misclassification error probabilities.
result Obtained asymptotic expressions for misclassification error probabilities.
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
Study tail behavior of sum of heavy-tailed risks with copulas.
problem Analyzing the tail behavior of sums of heavy-tailed risks with dependence modeled by copulas.
method Modeling dependence with copulas and analyzing tail asymptotics of sums of heavy-tailed risks.
result Obtained asymptotic expansions for Value-at-Risk of aggregate risk.
New sampling method for heavy-tailed distributions using Langevin Algorithm.
problem Sampling from heavy-tailed distributions efficiently.
method Transformed Unadjusted Langevin Algorithm on specific transformations.
result Polynomial-order oracle complexities for certain heavy-tailed densities.
Heavy-tailed distributions emerge in SGD's parameter evolution.
problem Understanding heavy-tailed distributions in SGD parameter evolution.
method Continuous diffusion approximation of SGD (homogenized SGD) analysis.
result Explicit upper and lower bounds on tail-index of homogenized SGD.
Paper tackles robust offline RL with heavy-tailed rewards.
problem Real-world applications often encounter heavy-tailed rewards, challenging offline RL.
method Proposes ROAM and ROOM algorithms using median-of-means method for robust off-policy evaluation and OPO.
result Demonstrates superior performance on heavy-tailed reward datasets compared to existing methods.
Privacy-preserving SGD with heavy-tailed noise achieves differential privacy guarantees.
problem Privacy preservation in noisy SGD with heavy-tailed noise.
method Differential privacy guarantees for SGD with heavy-tailed noise.
result SGD with heavy-tailed perturbations achieves -DP.
New bounds link SGD's generalization to heavy tails without topological assumptions.
problem Linking SGD's generalization error to heavy tails without additional assumptions.
method Developed Wasserstein stability bounds for heavy-tailed SDEs and their discretizations, converting to generalization bounds.
result Generalization bounds for a broader class of objective functions, including non-convex functions, without topological assumptions.
Work on SGDm under heavy-tailed noise, revealing its generalization properties.
problem Understanding generalization of SGDm under heavy-tailed noise.
method Analysis of continuous-time limit (SDE) and discrete-time SGDm, establishing generalization bounds.
result SGDm can have worse generalization in the presence of heavy-tailed noise for quadratic loss functions.
Optimized method tackles convex optimization with heavy-tailed noise.
problem Convex optimization problems with noisy gradients.
method Vanilla stochastic proximal subgradient method without gradient clipping or normalization.
result Achieves optimal complexity for various convex optimization types under heavy-tailed noise.
Efficiently estimates sparse linear regression with heavy-tailed data and outliers.
problem Sparse estimation of linear regression coefficients with heavy-tailed covariates and noises, including outliers.
method Efficient computation of robust estimator with nearly optimal error bound.
result Nearly optimal error bound for robust sparse estimation.
This work compresses heavy-tailed weight matrices for tighter generalization bounds.
problem Empirical evidence linking heavy-tailed weight matrices to test set accuracy but lack of formal relationship with generalization bounds.
method Utilized the compression framework to show that heavy-tailed matrices can be compressed, resulting in sparse weight matrices.
result Demonstrated a non-vacuous generalization bound for compressed networks with heavy-tailed weight matrices.
A simple log-transform fixes heavy-tailed data for generative models.
problem Standard generative models struggle with heavy-tailed data.
method Apply the soft-log transform to data before training and exponentiate samples after generation.
result Log-FM outperforms specialized baselines on multivariate benchmarks.
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
New RDP guarantees for heavy-tailed SDEs and SGD.
problem Characterizing differential privacy for heavy-tailed noise in learning algorithms.
method Rényi flow computations and fractional Poincaré inequalities.
result First RDP guarantees for heavy-tailed SDEs with weaker dependence on dimension.
New algorithm tackles multi-agent bandits with heavy-tailed data.
problem Maximizing system performance in multi-agent settings with heavy-tailed data.
method Algorithm exploits hub-like structures and synchronization among clients.
result Regret bound of for homogeneous settings, for heterogeneous.
Machine Learning Panel Data Regressions with Heavy-tailed Dependent Data: Theory and Applicationecon.EM
The paper improves machine learning for heavy-tailed panel data.
problem Improving estimates for financial and economic data with fat tails.
method Sparse-group LASSO regularization and Fuk-Nagaev concentration inequality.
result Oracle inequalities for panel data estimators.
Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations in sparsely populated regions. We show that heavy-tailed stochastic processes (…
HTFM improves mode coverage and tail-statistic recovery for heavy-tailed data.
problem Tackles heavy-tailed data in various domains with rare events.
method Proposes a framework using clock-conditioned Gaussian sources and truncated logsignature features.
result Improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and baselines.
Probability Weighting Meets Heavy Tails: An Econometric Framework for Behavioral Asset Pricingq-fin.MF
Econometric framework integrates heavy-tailed distributions with behavioral probability weighting for better asset pricing.
problem Underestimation of Value-at-Risk by traditional models in asset pricing.
method Developed an econometric framework combining heavy-tailed Student's distributions with behavioral probability weighting.
result Student's specifications outperform Gaussian models in 88.4% of cases, reducing underestimation of Value-at-Risk by 16.5 percentage points.
We propose a new heavy-tailed distribution --- Gaussian-Chain (GC) distribution, which is inspirited by the hierarchical structures prevailing in social organizations. We determine the mean, variance and kurtosis of the Gaussian-Chain distribution to show its heavy-tailed property, and compute the tail distribution tab…