GRAIN: Group Aggregation via Min-Norm Objective
problem Learning instability in large models
method Replacing mean aggregation with min-norm convex combination
result Improves performance and reduces variance
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12 results for “min-norm”
The paper analyzes the generalization error of min-norm interpolators in transfer learning with limited test samples.
problem Characterizing the generalization error of min-norm interpolators in transfer learning with limited test samples.
method Characterizes the bias and variance of pooled min--norm interpolation under covariate shift and model shift.
result Shows that adding data can hurt when SNR is low and is beneficial at higher SNR levels under certain conditions.
Interpolation hurts robust generalization even without noise.
problem The challenge of robust generalization in the absence of noise.
method Avoiding interpolation through ridge regularization.
result Ridge regularization improves robust generalization.
Precise Asymptotic Generalization for Multiclass Classification with Overparameterized Linear Modelscs.LG
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.
Our paper examines binary linear classification under Gaussian mixtures, revealing conditions for optimal performance.
problem Understanding the conditions for optimal performance of binary linear classifiers under Gaussian mixtures.
method We study max-margin SVM and min-norm interpolating classifiers, deriving bounds and conditions for optimal performance.
result Interpolating estimators achieve asymptotically optimal performance under certain conditions, emphasizing the role of SNR and covariance.
This study reveals fundamental trade-offs between memorization and robustness in neural networks.
problem Understanding the balance between memorization and robustness in neural networks.
method Analyzes two-layer neural networks in various high-dimensional linearized regimes, focusing on Sobolev-seminorm.
result Establishes fundamental trade-offs between memorization and robustness, with lower bounds on Sobolev-seminorm.
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization (QDSFM), which allows to model a number of learning tasks on graphs and hypergraphs. The problem exhibits close ties to decomposable submodular function minimization (DSFM), yet is much more challenging to sol…
New research shows SVM and related methods can overfit without harm in multiclass classification.
problem Understanding benign overfitting in multiclass classification.
method Analyzing three training algorithms: ERM with cross-entropy, least-squares, and one-vs-all SVM.
result All three algorithms can lead to classifiers that interpolate training data and have equal accuracy under high overparameterization.
Study interpolating estimators for causal learning from observational data.
problem Learning causal models from observational data in complex model classes.
method Investigate min-norm interpolators and ridge-regularized regressors in a linearly confounded model.
result Interpolators cannot be optimal for causal learning under the principle of independent causal mechanisms, requiring stronger regularization.
This work studies finite-sample properties of the risk of the minimum-norm interpolating predictor in high-dimensional regression models. If the effective rank of the covariance matrix of the regression features is much larger than the sample size , we show that the min-norm interpolating predictor is not de…
This paper explores adaptive methods in over-parameterized linear regression.
problem Understanding why neural networks generalize well in over-parameterized settings.
method Characterizes two sub-classes of adaptive methods and their generalization performance.
result Adaptive methods in over-parameterized linear regression converge to the minimum norm solution.
Overfitting can make models vulnerable to adversarial attacks even if they are robust to standard risks.
problem Adversarial robustness of models trained to fit noisy data.
method Theoretical analysis of overparameterized linear models and neural networks.
result Overfitting can lead to adversarial vulnerability, even if the model is robust to standard risks.