Study shows overparameterization helps in generalizing from smooth interpolants.
problem Understanding generalization in overparameterized linear models.
method Analysis of random Fourier series model with weighted trigonometric interpolation.
result Weighted trigonometric interpolation leads to lower generalization error in overparameterized scenarios.
Sharp global guarantees for noisy overparameterized low-rank recovery.
problem Understanding practical success of overparameterization in noisy conditions.
method Unified proof technique combining escape directions and counterexample inexistence.
result Near-second-order points achieve minimax-optimal recovery bounds.
Overparameterized ensembles don't offer generalization benefits over single large models.
problem Theoretical limitations of ensembles in overparameterized settings.
method Using ensembles of random feature (RF) regressors, the paper clarifies how modern ensembles differ from underparameterized counterparts.
result Infinite ensembles of overparameterized RF regressors become pointwise equivalent to single infinite-width RF regressors, and finite width ensembles converge to single models with the same parameter budget.
Classification and regression tasks in overparameterized models show different generalization properties.
problem Comparing classification and regression in overparameterized models.
method Comparison of least-squares minimum-norm interpolation and hard-margin SVM using different loss functions.
result Interpolating solutions generalize well with 0-1 loss but not with square loss.
New method improves generalization in deep learning models.
problem Improving generalization in overparameterized deep neural networks.
method Stochastic Gauss-Newton method with Levenberg-Marquardt damping and mini-batch sampling.
result Established finite-time convergence and non-asymptotic generalization bounds.
The paper examines VI for overparameterized BNNs, revealing a trade-off between likelihood and KL terms.
problem Critical issue in mean-field VI training for overparameterized BNNs.
method Theoretical and empirical study of overparameterized two-layer BNNs using VI.
result A trade-off between likelihood and KL terms in overparameterized regime, with KL scaling crucial.
CPCR mitigates bias in PCR for overparameterized models.
problem Bias in Principal Component Regression (PCR) for overparameterized models.
method Calibrated Principal Component Regression (CPCR) learns a low-variance prior in the PC subspace and calibrates the model in the original feature space.
result CPCR outperforms standard PCR in overparameterized settings, improving prediction across multiple problems.
This research shows loss weighting remains effective in last layer retraining despite model overparameterization.
problem Overcoming biases in machine learning models at scale.
method Theoretical and practical exploration of last layer retraining in an overparameterized setting.
result Loss weighting is still effective in last layer retraining, but weights must account for model overparameterization.
Overparameterization aids in model pruning, leading to improved test accuracy.
problem Improving lightweight model performance through pruning.
method Theoretical analysis and high-dimensional asymptotics of model pruning in overparameterized neural networks.
result Even with known informative features, training a large model and then pruning leads to better test accuracy.
Overparameterized models improve performance in sequential learning tasks.
problem Catastrophic forgetting in overparameterized neural networks.
method Two-task linear regression problem with random orthogonal transformations.
result Overparameterization mitigates catastrophic forgetting in sequential learning tasks.
Overparameterized models are more vulnerable to membership inference attacks.
problem Vulnerability of overparameterized models to membership inference attacks.
method Theoretical and empirical analysis of overparameterized linear and ridge-regularized linear regression models in the Gaussian data setting.
result Increased number of parameters and model complexity increase vulnerability to membership inference attacks.
Transfer learning improves image classifier performance in data-starved regimes.
problem Deploying image classifiers in domains with limited labeled data.
method Transfer learning with deep neural networks, focusing on feature reuse and overparameterization.
result Transfer learning enhances CNN performance in data-starved regimes.
A new criterion selects models in overparameterized settings.
problem Model selection for overparameterized models with more parameters than data.
method Establishes Bayesian duality and introduces the Interpolating Information Criterion.
result The Interpolating Information Criterion selects models in overparameterized settings.
Overparameterized models can worsen minority group errors even when overall test error improves.
problem Overparameterization exacerbates spurious correlations, harming minority groups.
method Simulations and experiments on image datasets, theoretical analysis of linear models.
result Subsampling the majority group can achieve low minority error in overparameterized models.
Study resolves conjecture on overparameterized linear models' generalization.
problem Asymptotic generalization of multiclass classification with overparameterized models.
method Gaussian covariates bi-level model, Hanson-Wright inequality variant.
result Min-norm interpolating classifier can be suboptimal compared to noninterpolating classifiers.
We analyze optimal weighted ridge regression in overparameterized linear models.
problem Optimal regularization in overparameterized linear regression models.
method Generalized ridge regression with weighted regularization.
result The optimal regularization parameter can be negative in overparameterized settings.
Bad models can teach well by replicating noise.
problem Overparameterized models can replicate noise in training data.
method Knowledge distillation from noisy samplers.
result Distillation from samplers approximates Bayes optimal classifier.
The paper shows how data and algorithm interactions affect overparameterized linear regression generalization.
problem Understanding generalization in overparameterized linear regression.
method Introducing data-algorithm compatibility and performing data-dependent trajectory analysis with gradient descent.
result Early stopping iterates lead to better generalization than last-iterate analysis, with weaker restrictions.
In this expository note we describe a surprising phenomenon in overparameterized linear regression, where the dimension exceeds the number of samples: there is a regime where the test risk of the estimator found by gradient descent increases with additional samples. In other words, more data actually hurts the estimato…
Quantum models show improved performance in overparameterized regimes.
problem Overfitting in quantum machine learning models.
method Analytical demonstration and numerical experiments on quantum kernel methods.
result Quantum models can operate in the modern, overparameterized regime without overfitting.
Sharp analysis of out-of-distribution error in overparameterized models with importance weights.
problem Understanding and quantifying the degradation of performance in overparameterized models when faced with underrepresented data.
method Sharp analysis of an overparameterized Gaussian mixture model with spurious features and cost-sensitive interpolating solutions incorporating importance weights.
result Characterization of a novel tradeoff between worst-case robustness and average accuracy as a function of importance weight magnitude.
This work analyzes how bottleneck layers and skip connections affect linear denoising autoencoders' generalization.
problem Understanding the generalization of linear denoising autoencoders in overparameterized regimes.
method Analyzes two-layer linear denoising autoencoders with a bottleneck layer and skip connection, deriving test risk formulas.
result Bottleneck layers introduce an additional complexity measure, while skip connections can mitigate variance.
New approach shows why overparameterized neural nets generalize well.
problem Understanding why overparameterized neural nets generalize well in practice.
method An alternative notion of capacity for attention-based models based on the effective rank of attention matrices.
result Generalization bound matches empirical scaling laws observed in large language models.
The paper explores how gradient descent trains associative memories, revealing oscillations and convergence issues.
problem Training dynamics of associative memories in overparameterized and underparameterized settings.
method Reduction to particle system dynamics, theory, and experiments.
result Oscillatory transitory regimes and benign loss spikes in overparameterized settings, suboptimal memorization in underparameterized settings.
Overparameterized models generalize well despite fitting noisy data.
problem Understanding why overparameterized models generalize well despite fitting noisy data.
method Statistical signal processing perspective.
result Overparameterized models often outperform underparameterized models in test performance.
Averaged SGD achieves optimal convergence rate for neural networks in the NTK regime.
problem Convergence analysis of averaged stochastic gradient descent for neural networks.
method Analyzed convergence of averaged stochastic gradient descent for overparameterized two-layer neural networks.
result Achieved minimax optimal convergence rate with global convergence guarantee.
Uniform bounds for neural networks' generalization error in overparameterized settings.
problem Generalization error in overparameterized neural networks.
method Neural Tangent kernel theory and Mercer decomposition of the NT kernel in spherical harmonics.
result Uniform generalization bounds for overparameterized neural networks in RKHS.
This work shows neural networks can solve non-convex constraints problems.
problem Training neural networks under non-convex constraints.
method Project stochastic gradient descent with no-regret analysis of online learning.
result Overparameterized neural networks achieve near-optimal and near-feasible solutions.
Analyzes bias-variance in overparameterized linear models using random features.
problem Understanding bias-variance trade-off in overparameterized models.
method Zero-temperature cavity method and random matrix theory.
result Three phase transitions in the linear random features model.
Ensembles of random-feature models can't outperform a single large model.
problem Finding the optimal balance between model size and ensemble size.
method Deterministic equivalent risk estimates and scaling laws analysis.
result Ensembles of random-feature models achieve near-optimal performance only under specific conditions.
Lower bounds show OLS outperforms basis pursuit in overparameterized linear regression.
problem Excess risk of sparse interpolating procedures in overparameterized linear regression.
method Proved lower bounds on excess risk for OLS and basis pursuit.
result Excess risk of basis pursuit can converge at an exponentially slower rate than OLS.
Neural networks generalize well despite overfitting due to high capacity.
problem Understanding why deep neural networks generalize well in overparameterized settings.
method High-dimensional asymptotic analysis of generalization under kernel regression with Neural Tangent Kernel.
result Test error exhibits non-monotonic behavior and can have additional peaks and descents in the overparameterized regime.
Study shows label noise impacts neural representations' information content, revealing double descent behavior.
problem Impact of label noise on neural network hidden representations.
method Information Imbalance proxy of conditional mutual information to compare hidden representations.
result Representations learned with noisy labels are more informative than those with clean labels in the underparameterized regime, and equally informative in the overparameterized regime.
Deep neural networks perform well on local tasks but struggle with global tasks.
problem Understanding the limitations of overparameterized deep neural networks in learning global functions.
method Introduced k-local and k-global functions to study the interplay between depth and function locality. result Depth is beneficial for learning local functions but detrimental to learning global functions.
Model shows loss curve with two distinct exponents due to sparse activations.
problem Sparse activations impact neural network scaling laws.
method Introduced a model for neural scaling laws under sparse activations, derived asymptotic population loss, and analyzed gradient-descent dynamics.
result Loss curve exhibits double-descent peak near interpolation threshold with two distinct scaling exponents.
The paper analyzes the maximum margin algorithm's performance on noisy data.
problem Analyzing the performance of maximum margin algorithm on noisy data.
method Finite-sample analysis of maximum margin algorithm applied to noisy data.
result The maximum margin algorithm can achieve nearly optimal population risk with sufficient over-parameterization.
Early stopping improves generalization in overparameterized diffusion models.
problem Understanding and optimizing generalization in overparameterized diffusion models.
method Revisiting diffusion models, showing generalization occurs before memorization, and developing a phase diagram.
result Generalization time scales with dataset size, supporting early-stopping criteria.
Deeper networks are better for local labels, but shallower for global labels.
problem Understanding the effect of depth in overparameterized neural networks.
method Introduced local and global labels to investigate the advantage of depth.
result Deeper networks are better for local labels, shallower for global labels.
This work challenges the Neural Tangent Kernel's role in overparameterized neural networks, especially with large width and depth.
problem The Neural Tangent Kernel's behavior in overparameterized neural networks with large width and depth is unclear.
method Experimental and theoretical analysis of ReLU networks with large width and depth.
result The aggregate norm of hidden neuron deviations does not vanish in infinitely-wide ReLU networks, indicating non-trivial behavior.
Privacy can be achieved without cost in overparameterized models.
problem Understanding the performance cost of differentially private gradient descent in overparameterized settings.
method Random features model with quadratic loss.
result Privacy can be obtained for free in the overparameterized regime, not dependent on privacy parameter ε.
The ability of deep neural networks to generalize well in the overparameterized regime has become a subject of significant research interest. We show that overparameterized autoencoders exhibit memorization, a form of inductive bias that constrains the functions learned through the optimization process to concentrate a…
Early stopping improves logistic regression's calibration and consistency in high dimensions.
problem Improving the statistical performance of gradient descent in overparameterized logistic regression.
method Investigates the effects of early stopping on gradient descent in logistic regression.
result Early-stopped gradient descent is well-calibrated and statistically consistent, while asymptotic gradient descent is not.
The paper explores how model complexity affects OOD detection performance.
problem Ensuring reliability and safety of machine learning systems through OOD detection.
method Investigates the relationship between model capacity and OOD detection performance using empirical and theoretical analysis.
result The Double Descent phenomenon is observed in post-hoc OOD detection, indicating that overparameterization can enhance OOD detection.
Study on neural network dynamics in high dimensions with quadratic activation.
problem Understanding training dynamics in overparameterized neural networks.
method Derivation of gradient flow equations and analysis under l2-regularization.
result Characterization of estimator performance and spectral properties in the high-dimensional limit.
Many modern neural network architectures are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Sufficiently overparameterized neural network architectures in principle have the capacity to fit any set of labels including random noise. However, given the hi…
Paper analyzes Gibbs and Langevin Monte Carlo for interpolation regime, showing generalization from low errors.
problem Analyzing Gibbs and Langevin Monte Carlo in overparameterized interpolation regime.
method Data-dependent bounds and stability under approximation with Langevin Monte Carlo.
result Generalization is signaled by small training errors in noisy regime, with bounds stable under approximation.
Paper proposes a new framework to improve stability-based bounds in deep learning.
problem Explaining generalization in overparameterized neural networks.
method Decomposes excess risk dynamics into signal and noise components, applying stability-based bounds only to the noise.
result The decomposition framework improves stability-based bounds and explains generalization in neural networks.
Overparameterized linear model shows strong classification but weak regression, susceptible to adversarial perturbations.
problem Adversarial vulnerability of overparameterized linear models.
method Lifted Fourier feature map, analyzing overparameterized linear ensemble.
result Spatial localization leads to adversarial vulnerability in an intermediate classification regime.