Study heavy-tailed weights' impact on neural network's spectral distribution.
problem Analyzing spectral distribution of conjugate kernel matrices with heavy-tailed weights.
method Computed limiting eigenvalue distribution through moments, considering heavy-tailed distributions and nonlinear activation functions.
result Heavy-tailed weights induce strong correlations, leading to fundamentally different spectral behavior.
Study uses spectral risk for learning with heavy-tailed data.
problem Learning with heavy-tailed loss distributions.
method Spectral risk with Lipschitz-continuous density, derivative-free learning.
result Excess risk guarantees and improved performance over traditional methods.
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.
Study on estimating rank-one tensors in noisy data with heavy tails.
problem Estimating rank-one spiked tensors in the presence of heavy tailed errors.
method Analysis of spectral norm of random tensors with iid entries.
result Signal strength requirements for optimal estimation are similar for heavy tailed and Gaussian noise, but vanish for noise with finite fourth moment.
Investigates spectral properties of neural networks, showing invariance under certain conditions.
problem Understanding the spectral evolution and invariance in linear-width neural networks.
method Empirical and theoretical analysis of spectra of weight matrices in high-dimensional settings.
result Spectra of weight matrices are invariant under certain training conditions, with implications for feature learning.
Heavy-tailed regularization improves deep neural network performance.
problem Improving generalization of deep neural networks.
method Introducing Heavy-Tailed Regularization, using differentiable penalty terms and Bayesian statistics.
result Heavy-tailed regularization outperforms conventional regularization techniques.
New insights into why neural networks generalize well.
problem Understanding why neural networks generalize well despite heavy-tailed weight distributions.
method Developed a simple model to analyze the emergence of heavy-tailed empirical spectral densities (ESDs) in two-layer neural networks without gradient noise.
result Learning rates play a crucial role in shaping the ESDs of two-layer neural networks, leading to better generalization.
Efficiently estimates sparse mean from heavy-tailed data.
problem Robustly estimating sparse mean from heavy-tailed distributions.
method Stability-based approach adapted for heavy-tailed data.
result Optimal sample complexity with logarithmic dependence on dimension.
Study uses detrended cross-correlation to analyze cryptocurrency market, revealing robust collective modes and distinguishing interdependencies.
problem Nonstationarity, long-range memory, and heavy-tailed fluctuations obscure traditional correlations in complex systems.
method Constructs detrended correlation matrices using multifractal detrended cross-correlation coefficient ρr to emphasize different fluctuations. result Detrending and fluctuation analysis reveal distinct spectral properties from random case, identifying market and sectoral components.
Muon optimizes Transformer training with heavy-tailed data, achieving optimal sample complexity.
problem Theoretical understanding of non-Euclidean optimisation methods for heavy-tailed data in training Transformers.
method Addressing the gap in theoretical understanding, we show Muon achieves optimal sample complexity under heavy-tailed noise.
result Muon finds an ε-stationary point in nuclear norm with optimal sample complexity, absorbing heavy-tailed noise without dimension dependence.
The difficulty of classification affects the weight matrices' heavy tail appearance in deep learning networks.
problem Understanding the spectral properties of weight matrices in deep learning networks.
method Spectral analysis of weight matrices in different modules of DNNs, classification difficulty as a driving factor for heavy tail appearance.
result Higher classification difficulty leads to more frequent appearance of heavy tails in weight matrices spectra.
Paper tackles robust matrix completion with heavy-tailed noise.
problem Estimating a low-rank matrix from noisy incomplete data.
method Adaptive Huber loss for robustness, nonconvex algorithm with spectral initialization.
result Achieves minimax-optimal statistical estimation error under bounded second moment condition.
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.
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.
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.
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.
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.
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.
The paper examines how heavy-tailed risks behave under Gaussian copula models.
problem Understanding tail risk probabilities with heavy-tailed marginal risks and Gaussian dependence.
method Modeling heavy-tailed risks using regular variation and analyzing tail probabilities under Gaussian copula.
result The rate of decay of tail set probabilities varies with the type of tail sets and Gaussian correlation matrix.
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.
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.
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 γ-divergence. result Our models generate rare and extreme events more effectively than standard diffusion models.
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.
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 algorithms handle heavy-tailed rewards in reinforcement learning.
problem Learning from heavy-tailed rewards in reinforcement learning.
method Robust mean estimation techniques for constructing algorithms.
result Near-optimal regret bounds achieved in heavy-tailed reward settings.
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.
PH-VAE models heavy-tailed data with flexible Phase-Type distributions.
problem Standard VAEs fail to capture heavy-tailed behavior in real-world data.
method PH-VAE uses Phase-Type distributions defined by continuous-time Markov chains to adaptively model tail behavior.
result PH-VAE significantly outperforms existing heavy-tail-aware VAEs in approximating diverse heavy-tailed distributions.
Studied how heavy-tailed behavior affects SGD's generalization in quadratic optimization.
problem Link between heavy-tailed behavior and generalization in SGD.
method Used heavy-tailed stochastic differential equation and proved stability bounds.
result Stability of SGD depends on the loss function's tail behavior.
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.
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 (0,O(1/n))-DP. 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.
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…
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.
Proposes a new distribution for robust time series modeling with heavy tails.
problem Robust modeling of time series with heavy-tailed noise.
method Spliced Binned-Pareto distribution for non-stationary time series.
result Accurately models extreme events and captures time dependencies in higher moments.
Markov chain decoders improve generative models' ability to produce heavy-tailed data.
problem Generative models struggle with heavy-tailed distributions.
method Replaced Gaussian decoder with Markov chain-based Phase-Type distributions.
result Significantly reduced tail Kolmogorov-Smirnov distance and extreme quantile error.
Paper tackles robust batched bandits for heavy-tailed rewards.
problem Clinical trials and other applications with heavy-tailed rewards.
method Proposes robust batched bandit algorithms for heavy-tailed rewards in finite-arm and Lipschitz-continuous settings.
result Heavier-tailed rewards require fewer batches for near-optimal regret in the instance-independent regime and Lipschitz setting.
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.
New framework controls generalization for heavy-tailed data in RLHF and SGLD.
problem Heavy-tailed data in modern learning pipelines.
method Tail-dependent information-theoretic framework for sub-Weibull data.
result Sharp generalization bounds for heavy-tailed data.
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 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.
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 O(M1−α1logT) for homogeneous settings, O(MlogT) for heterogeneous. 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.
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 t distributions with behavioral probability weighting. result Student's t specifications outperform Gaussian models in 88.4% of cases, reducing underestimation of Value-at-Risk by 16.5 percentage points. 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.
The paper investigates heavy-tailed behavior in offline SGD, showing it approximates power-law tails.
problem Understanding heavy-tailed behavior in offline (multi-pass) SGD with finite data.
method Proves nonasymptotic Wasserstein convergence bounds for offline SGD to online SGD.
result Offline SGD exhibits approximate power-law tails as the number of data points increases.
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.