Equivalent tests for SGD batch size selection found.
problem Finding equivalent tests for adaptive batch size selection in SGD.
method Norm and inner product/orthogonality tests equivalence demonstration.
result Norm and inner product/orthogonality tests are equivalent under specific conditions.
We introduce a norm on the space of test configurations, which we call the minimum norm. We conjecture that uniform K-stability with respect to this norm is equivalent to the existence of a constant scalar curvature Kähler metric. This notion of uniform K-stability is analogous to coercivity of the Mabuchi functional. …
We introduce a new family of matrix norms, the "local max" norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the literature as regularizers for matrix reconstruction problems. We show that this…
New study shows how model complexity affects test risk, challenging classical theory.
problem Understanding how test risk scales with model complexity for large over-parametrized deep networks.
method Developed norm-based capacity measures for random features based estimators, providing precise characterization of estimator's norm concentration and test error.
result Predicted learning curve shows a phase transition from under- to over-parameterization, confirming classical U-shaped behavior with appropriate capacity measures.
A new metric predicts model performance on unseen data.
problem Predicting performance on out-of-distribution data without labels.
method Uses model predictions to pseudo-label data, trains a new model, and measures difference from in-distribution models.
result Empirically outperforms existing methods on image and text classification tasks.
Study confirms fractional norms and quasinorms do not help overcome curse of dimensionality.
problem Overcoming the curse of dimensionality in machine learning.
method Systematic testing of fractional norms and quasinorms (p<1) on classification problems.
result Distance concentration behavior is qualitatively the same for all norms and quasinorms as dimensionality increases.
New bounds for neural networks ensure robustness and accuracy.
problem Ensuring robustness of neural networks by computing Lipschitz constants.
method Analyzed and proposed new bounds for l1 and l∞ norms, using explicit and implicit methods for convnets. result One of the new bounds is optimal and more accurate than existing ones.
Paper analyzes singular subspace estimation in noisy matrix models.
problem Estimating low-rank signals in noisy matrix data.
method Asymptotic distributional theory, extreme value theory, saddle point approximation, random matrix theory.
result Plug-in test statistic based on two-to-infinity norm has higher power for detecting structured alternatives.
Paper proposes a robust test for high-dimensional models with large covariates and instruments.
problem Testing high-dimensional linear instrumental variable models with large covariates and instruments.
method Introduces a test based on the maximum norm of multiple parameters and a power-enhanced test.
result The proposed test is robust to heteroskedastic errors and has higher power than existing tests.
New model leads to optimal test loss in sparse linear regression.
problem Sparse linear regression with low test loss despite interpolating training data.
method Developed a new parametrization of the model that combines benefits of ℓ1 and ℓ2 norms.
result Training via gradient descent leads to an interpolator with near-optimal test loss.
Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the L2 distance between kernel-based distribution representatives to derive their test statistics. Here, we show that Lp distan…
We apply the integral formula of volumes to the family of graded linear series constructed from any test configuration. This solves the conjecture raised by Witt--Nyström so that the sequence of spectral measures for the induced C∗-action on the central fiber converges to the canonical Duistermatt--Heckman …
New tests for high-dimensional data improve on existing methods.
problem Testing mean vectors in high-dimensional data.
method Generalized multivariate sign transformation, using different norm functions.
result Tests using generalized signs have higher power than existing tests.
Power of network tests degrades when vertices are misaligned.
problem Power loss in network hypothesis testing due to vertex shuffling.
method Theoretical analysis and simulations of Frobenius norm differences in random dot product and stochastic block models.
result Shuffling vertices can significantly reduce the power of network tests.
The paper introduces a diagnostic method to detect grokking transitions in models before test accuracy improves.
problem Detecting the transition from training to generalization in machine learning models.
method Summarize task-dependent observables as empirical distributions, map them to Wasserstein/quantile coordinates, and analyze using Hankel dynamic mode decomposition.
result The diagnostic method achieves AUROC \(\approx\) 0.93 for grokking-vs-non-grokking discrimination at the run level.
Study shows gap between uniform convergence and test error in random feature models.
problem Understanding the gap between uniform convergence and test error in random feature models.
method Analytical expressions for uniform convergence over norm balls, interpolators, and minimum norm interpolator risk derived and proved.
result Uniform convergence over interpolators still gives a non-trivial bound of test error even when classical uniform convergence is vacuous.
Study improves image classifier robustness to random p-norm corruptions.
problem Improving robustness of image classifiers to real-world imperceptible corruptions.
method Training and testing with random p-norm corruptions, evaluating robustness against different p-norms.
result Training with a combination of p-norm corruptions significantly improves robustness.
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-ℓ2-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.
Deep ReLU networks generalize well with few parameters.
problem Generalization of overparametrized deep neural networks.
method Explicit bounds on test error independent of overparametrization and VC dimension.
result Generalization error is independent of network architecture and overparametrization.
New proof shows norms can't explain deep learning's implicit regularization.
problem Understanding the implicit regularization in deep learning.
method Mathematical proof on matrix factorization problems.
result Implicit regularization drives norms towards infinity, suggesting rank minimization is key.
The paper predicts survival functions using random survival trees and concordance maximization.
problem Predicting conditional survival functions in right-censored data.
method The approach combines regression strategies with random survival trees and maximizes concordance.
result The proposed weighted predictor outperforms the usual survival cobra in terms of concordance.
This paper certifies cluster assignments from sum-of-norms clustering algorithms.
problem Certifying the correct cluster assignments from approximate solutions of sum-of-norms clustering.
method Presented a clustering test that identifies and certifies the correct cluster assignment from an approximate solution.
result The correct cluster assignment is guaranteed to be certified by a primal-dual path following algorithm after sufficient iterations.
A new measure scales MMD to assess distribution closeness.
problem Testing statistical significance of distribution closeness.
method Norm-adaptive MMD (NAMMD) for distributional discrepancy.
result NAMMD-based DCT has higher test power than MMD-based DCT.
Robust covariance testing requires significantly more samples in contaminated data.
problem Testing the covariance matrix of a high-dimensional Gaussian in the presence of contamination.
method We study the problem in the Huber's contamination model, distinguishing between the identity matrix and matrices far from it in Frobenius norm.
result The sample complexity of covariance testing increases dramatically to Ω(d2) in the contaminated setting. Given a polarized complex manifold, projection of a torus-equivariant test configuration to holomorphic vector fields was introduced by G. Székelyhidi, as the limit of the associated C∗-actions. We show that there actually holds the moment convergence of the weight distributions. Our analytic approach at th…
Robust testing of sparse signals in corrupted data.
problem Testing the norm of high-dimensional sparse signals in the presence of arbitrary corruption.
method Two observation models: i.i.d. samples from N(θ,Id) and sparse linear regression model. result The robust testing requires significantly more samples than non-robust testing.
We consider the closeness testing problem for discrete distributions. The goal is to distinguish whether two samples are drawn from the same unspecified distribution, or whether their respective distributions are separated in L1-norm. In this paper, we focus on adapting the rate to the shape of the underlying distri…
Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…
Paper studies signal detection in noisy environments with limited communication.
problem Signal detection in Gaussian noise with 1-bit communication constraints.
method Derives lower bounds and exhibits optimal testing strategies.
result Optimal distributed testing strategies attain the derived lower bound.
Study shows minimizing the norm of the ERM solution stabilizes kernel ridge-less regression.
problem Stability of kernel ridge-less regression.
method Minimizing the norm of the ERM solution to minimize CV stability.
result Interpolating solution with minimum norm minimizes CV stability.
Free adversarial training reduces the generalization gap compared to vanilla method.
problem Improving generalization in adversarial training.
method Analysis of algorithmic stability in free adversarial training.
result Free adversarial training shows a lower generalization gap.
New insights into optimization and generalization for linear models.
problem Understanding the implicit regularization of optimization methods for linear models.
method Investigating the norms minimized by interpolating solutions and using projections to move between solutions.
result Proving that for over-parameterized linear classification, projections onto the data-span enable the use of under-parameterized techniques.
We introduce a general non-parametric independence test between right-censored survival times and covariates, which may be multivariate. Our test statistic has a dual interpretation, first in terms of the supremum of a potentially infinite collection of weight-indexed log-rank tests, with weight functions belonging to …
The paper develops tests for comparing means in high dimensions with unknown covariance.
problem Testing if the mean of a high-dimensional distribution is close to zero or different from another.
method Develops nonasymptotic tests using concentration inequalities and operator norms.
result Obtains bounds on the minimal separation distance for controlling Type I and Type II errors.
The study of networks leads to a wide range of high dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in this high-dimensional regime, where the goal is to test between two populations…
We provide a pointwise confidence bound for non-linear least-squares with fixed design.
problem Confidence estimation in non-linear ℓ2-regularized least squares. method Pointwise confidence bound for local minimizers, using weighted norm involving inverse-Hessian.
result The proposed confidence bound scales with the test input's similarity to the training data.
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…
MANO normalizes logits to estimate test accuracy without labels.
problem Estimating test accuracy of OOD samples without labels.
method Applies Lp norm to normalized logits. result Achieves state-of-the-art performance across various architectures.
We investigate conditions under which test statistics exist that can reliably detect examples, which have been adversarially manipulated in a white-box attack. These statistics can be easily computed and calibrated by randomly corrupting inputs. They exploit certain anomalies that adversarial attacks introduce, in part…
New bounds show linear predictors rarely overfit with certain optimization methods.
problem Bounding test error for linear predictors with stochastic optimization methods.
method Coupling argument for fixed point methods like stochastic and batch mirror descent.
result Locally-adapted rates that depend on predictor properties, not global problem structure.
The paper explores robustness in linear regression models under adversarial attacks.
problem The impact of test-time adversarial attacks on linear regression models.
method Quantitative estimates and phase transitions analysis.
result Precise characterization of tradeoffs between adversarial robustness and accuracy.
We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the convergence rate of our posterior update rule to the true probability function in…
Characterizes inductive bias in multi-channel linear CNNs with bounded weight norm.
problem Understanding the inductive bias in multi-channel linear convolutional networks.
method Function space characterization and empirical testing of gradient descent.
result The inductive bias depends on the number of output channels for multi-channel inputs but not for single-channel inputs.
Proves uniform K-stability is open in Kähler cone.
problem Stability of Kähler metrics in complex geometry.
method Introduced new norm on test configurations and estimates for non-archimedean energy functionals.
result Uniform K-stability is an open condition in the Kähler cone.
Attention models can overfit without harming test performance.
problem Understanding benign overfitting in single-head attention models.
method Analyzing conditions for benign overfitting in a single-head softmax attention model.
result A single-head attention model can overfit without harming test performance under certain conditions.
We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic function using finite differences within a common random number framework. We emplo…
In this paper, we propose ℓp-norm regularized models to seek near-optimal sparse portfolios. These sparse solutions reduce the complexity of portfolio implementation and management. Theoretical results are established to guarantee the sparsity of the second-order KKT points of the ℓp-norm regularized models…
We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a considerable challenge to optimization algorithms due to the non-smoothness and non-s…